SIGNAL PROCESSING EQUIPMENT AND SIGNAL PROCESSING METHOD

Abstract

Signal processing device comprising: a signal acquisition unit (11) for acquiring an input signal; a signal extraction unit (12) for extracting a specific signal by multiplying the input signal by a window function; a frequency conversion unit (13) for performing a frequency conversion of the extracted signal;and a signal output unit (14) for outputting the frequency-converted signal, wherein the window function comprises a synthesis of one or a plurality of cosine function terms, and the window function is obtained by multiplying a negative coefficient with the cosine function term selected from one or the plurality of cosine function terms, such that a zero value is set in the middle of the window range and a peak power of a side lobe corresponding to the cosine function term in a frequency domain is reduced, a reduction of a frequency resolution is suppressed, or both of these to a greater extent than that of multiplying positive values ​​with all cosine function terms.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to a signal processing device and a signal processing method. BACKGROUND TO THE STATE OF THE ART

[0002] There is a well-known signal processing technology that extracts a specific signal component contained in a signal, performs frequency conversion on the extracted signal component, and performs frequency analysis on the frequency conversion data of the signal component. For example, there is the technology of using a window function to reduce side lobes of the frequency component of a radio signal. Examples of the window function include a raised cosine window described in Non-Patent Literature 1.

[0003] The raised cosine window is a window function that has a constant term and a term obtained by adding a cosine function (hereinafter referred to as the cosine function) multiplied by a positive coefficient for each constant period. In the raised cosine window, cosine function terms are linearly combined by multiplying the cosine function by an appropriate coefficient value, which can reduce side lobes of the frequency component of a signal extracted with the raised cosine window. REFERENCE LISTS NON-PATENT LITERATURE

[0004] Non-Patent Literature 1: FJ Harris, “On the Use of Windows for Harmonic Analysis With the Discrete Fourier Transform,” in proc. IEEE. vol. 66, No. 1, Jan. 1978. SUMMARY OF THE INVENTIONTECHNICAL PROBLEM

[0005] The state-of-the-art window functions, which are represented by the raised cosine window, have the problem that when the sidelobe component in the frequency domain is reduced, the frequency resolution is reduced accordingly.

[0006] The present disclosure solves the above problem and aims to obtain a signal processing device and a signal processing method capable of more preferentially balancing the frequency resolution and the sidelobe characteristics than the window functions in the related art. SOLUTION TO THE PROBLEM

[0007] A signal processing device according to the present disclosure includes: a signal acquisition unit that acquires an input signal; a signal extraction unit that extracts a specific signal by multiplying the input signal by a window function; a frequency conversion unit that performs frequency conversion of the extracted signal; and a signal output unit that outputs the frequency-converted signal, in which the window function includes one or a plurality of cos function terms in which at least one of the sign of a coefficient for multiplying a cos function or a degree of the cos function is set so that both a frequency resolution and a reduction amount of side lobes fall within allowable ranges. ADVANTAGEOUS EFFECTS OF THE INVENTION

[0008] By using the window function in which both the frequency resolution and the reduction amount of the side lobes fall within the allowable ranges, the signal processing device according to the present disclosure can more advantageously make a trade-off between the frequency resolution and the side lobe characteristics than is the case when using a window function of the related art represented by a raised cosine window. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a block diagram illustrating a configuration of a signal processing device according to a first embodiment. Fig. 2 is a flowchart illustrating a signal processing method according to the first embodiment. Fig. Figure 3 is a graph showing the response in the frequency domain of a cos function term (cos(2πkx)) and the response in the frequency domain of sinc functions. Fig. Figure 4 is a graph showing an overlaid representation of the frequency domain response of a cos function term (cos(2πkx)) and the frequency domain response of a sin function. Fig. Figure 5 is a graph showing an overlaid representation of the frequency domain response of a cos function term (cos(4πx)) and the frequency domain response of a sin function. Fig. Figure 6 is a graph showing an overlaid representation of the frequency domain response of a cos function term (cos(5πx)) and the frequency domain response of the sin function. Fig. 7 is a graph illustrating the shape of a window function in the first embodiment. Fig. Figure 8 is a graph showing an overlaid representation of the response in the frequency domain of the window function in Fig. 7 and the response in the frequency domain of a rectangular window function. Fig. 9A and Fig. 9B are block diagrams showing a hardware configuration for implementing the functions of the signal processing device according to the first embodiment. Fig. Figure 10 is a graph showing the superimposed representation of the responses in the frequency domain of the sinc function, cos(2πx), -cos(4πx) and cos(6πx). Fig. 11 is a graph showing a relationship between the frequency resolution and the peak level of the side lobes for the window function in a second embodiment and a generalized Hamming window. Fig. Figure 12 is a graph showing the response in the frequency domain of sinc functions shifted by ±1 / 2 and the response in the frequency domain of cos(πx) obtained by combining these sinc functions. Fig. 13 is a graph showing an overlaid representation of the frequency domain response of cos(πx) and the frequency domain response of cos(3πx), each included in the window function in a third embodiment. Fig. 14 is a graph illustrating the shapes of the window functions of a fourth embodiment. Fig. 15 is a diagram showing the frequency components of the window function in Fig. 14 shows. DESCRIPTION OF THE EMBODIMENTSFirst Embodiment

[0009] Fig. 1 is a block diagram illustrating a configuration of a signal processing device 1 according to a first embodiment. In Fig. 1, the signal processing device 1 acquires an input signal from an input signal storage unit 2, extracts a signal by multiplying the input signal by a window function, and outputs a signal obtained by performing frequency conversion on the extracted signal as an output signal to an output signal storage unit 3. The window function includes one or a plurality of cos function terms in which at least one of the sign of a coefficient for multiplying a cos function or the degree of the cos function is adjusted so that both the frequency resolution and the amount of reduction of side lobes fall within allowable ranges.

[0010] The permissible range is a range of frequency resolution and sidelobe reduction that cannot be achieved with state-of-the-art window functions. For state-of-the-art window functions represented by a raised cosine window, sidelobes can be reduced, for example, by adjusting the value of a positive coefficient multiplying the cosine function; however, the frequency resolution deteriorates depending on the amount of sidelobe reduction.

[0011] On the other hand, since signal processing devices according to the first to fourth embodiments extract a signal using the above window function or the like, both the range of frequency resolution in the frequency domain of the signal and the range of the reduction amount of side lobes can be maintained within the predetermined allowable range. Consequently, the signal processing devices according to the first to fourth embodiments can advantageously balance the deterioration of frequency resolution with the reduction of side lobes.

[0012] The signal processing device 1 is used, for example, in a radar system. In the radar system, the signal processing device 1 can prevent poor detection of a target due to side lobes by reducing the side lobes of a received signal of an incoming wave from the target using the window function.

[0013] The signal processing device 1 can also be used in a radar imaging system with a synthetic aperture radar. In this case, the signal processing device 1 can reduce noise due to sidelobes in a radar image by reducing the sidelobes of a received signal.

[0014] The input signal storage unit 2 is a storage device that stores the input signal. In a radar system, the input signal storage unit 2 is, for example, a storage device that temporarily stores a received signal from a radar device. Furthermore, a signal processing program that implements the function of the signal processing device 1 can be stored in the input signal storage unit 2. For example, a processor included in a computer executes the signal processing program read from the input signal storage unit 2, with the computer functioning as the signal processing device 1.

[0015] The output signal storage unit 3 is a storage device that stores an output signal output by the signal processing device 1. For example, a display device (in Fig. 1 not shown) display information related to the output signal stored in the output signal storage unit 3. Examples of the display information include a radar image using a synthetic aperture radar. Note that the input signal storage unit 2 and the output signal storage unit 3 may be a single signal processing device included in the signal processing device 1 or may be separate storage devices.

[0016] As in Fig. 1, the signal processing device 1 comprises a signal acquisition unit 11, a signal extraction unit 12, a frequency conversion unit 13 and a signal output unit 14. Fig. 2 is a flowchart showing a signal processing method according to the first embodiment, illustrating a signal processing method by the signal processing device 1.

[0017] Hereinafter, details of the functions of the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13 and the signal output unit 14 included in the signal processing device 1 will be described with reference to Fig. 1 and Fig. 2 described.

[0018] The signal acquisition unit 11 acquires an input signal that is a signal processing target (step ST1). The signal acquisition unit 11 acquires, for example, the input signal stored in the input signal storage unit 2. The dimension of the input signal is not limited; however, the frequency conversion is performed with respect to the dimension of t. In the following, it is assumed that the input signal is a one-dimensional signal and is denoted as s(t).

[0019] The signal extraction unit 12 extracts a specific signal by multiplying the input signal acquired by the signal acquisition unit 11 by a window function (step ST2). The window function used by the signal extraction unit 12 includes one or a plurality of cos function terms, in which at least one of the sign of a coefficient for multiplying a cos function or the degree of the cos function is set so that both the frequency resolution and the amount of reduction of side lobes fall within allowable ranges. Hereinafter, it is assumed that the width of the signal extracted using the window function is 1. In addition, the window function is denoted by w(x), and it is assumed that x is a real value in the description below; however, x may also be a discrete value.

[0020] Furthermore, the description assumes that the design range of the window function w(x) is -0.5 ≤ x ≤ 0.5. Note that this design range can be changed depending on the width of a signal extracted using the window function w(x). A signal s w (t), which is extracted by multiplying the input signal s(t) by the window function w(x), can be expressed by the following equations (1). In the following equations (1), t0 denotes the center of the width of the signal s to be extracted. w (t).

[0021] If -0.5 ≤ t - t0 ≤ 0.5, then s w (t) = w(t - t0)s(t). In cases other than -0.5≤t−t0≤0.5, then sw(t)=0

[0022] The frequency conversion unit 13 performs a frequency conversion of the signal s extracted by the signal extraction unit 12 w(t) by (step ST3). For example, the frequency conversion unit 13 obtains a frequency spectrum of the signal s w (t) by performing a Fourier transformation of the signal s w (t) is carried out.

[0023] When frequency conversion is performed on a signal extracted using a prior art window function, side lobes appear in the frequency component of the signal. On the other hand, when the window function of the first embodiment is used, side lobes of the frequency component of the extracted signal are reduced. At this point, a function that performs frequency conversion of the signal s w (t) into a frequency f, as F t [s w (t)](f), a frequency component S w (f) of the signal s w (t) is expressed by the following equation (2). Sw(f)=Ft[Sw(t)](f)

[0024] The signal output unit 14 outputs the signal calculated by the frequency conversion unit 13 (step ST4). The signal output unit 14 outputs, for example, the frequency component S w (f) to the output signal storage unit 3. As a result, a Fig. 2 is completed. By using the window function in the first embodiment, the side lobes of the frequency component S w (f) reduced.

[0025] The raised cosine window of the prior art is described as an aid to understanding the window function in the first embodiment. In a case where -0.5 ≤ x ≤ 0.5, the raised cosine window w c (x) is expressed by a function expressed by the following equation (3). As expressed in the following equation (3), w c(x) is represented by a linear combination of a constant term a0 and a cosine window function whose period is adjusted. Hereinafter, k denotes an order. Note that Σ[k = 1]a k- cos(2πkx) in the following equation (3) indicates that in a case where M =a k cos(2πkx), the value of M is added for each degree k successively starting from k = 1. wc(x)=a0+Σ[k=1]akcos(2πkx)ak≥0

[0026] In the raised cosine window w c (x) The side lobe generation positions (peak positions) in the frequency domain of the constant term a0 and the side lobe generation positions (peak positions) in the frequency domain of each cosine function are harmonized, and these positions are close to each other. Therefore, it is possible to effectively reduce the side lobes by linearly combining the constant term a0 and the cosine functions.

[0027] In a case where -0.5 ≤ x ≤ 0.5, the response in the frequency domain of the constant term a0 in w c (x) is given by a sinc function. In w c (x), since the cos functions are added according to the coefficients, side lobes in the frequency domain of the sinc function are subtracted.

[0028] Next, the response in the frequency domain of the cos function term is described, which is in the raised cosine window w c (x). The value in w c The term cos(2πkx) contained in (x) can be transformed as shown in the following equation (4). Since -0.5 ≤ x ≤ 0.5 in this example, by performing frequency conversion of cos(2πkx), the response of cos(2πkx) in the frequency domain is expressed by a function obtained by combining sinc functions in which shifts of ±k have occurred, as shown in the following equation (4). cos(2πkx)=(ej2πkx+e−j2πkx) / 2

[0029] Fig. Figure 3 is a graph showing the frequency domain response of cos(2πkx) and the frequency domain response of sinc functions. Fig. 3, k = 2. Furthermore, F x [cos(2πkx)](f), which is the response in the frequency domain of cos(2πkx), is indicated by a dot-dash line A, the response in the frequency domain of sinc(f - k) / 2 is indicated by a solid line B, and the response in the frequency domain of sinc(f + k) / 2 has a dashed line C as a feature. As in Fig. 3, the answer of F x [cos(2πkx)](f) is a function obtained by combining two sinc functions in which shifts of ±k have occurred.

[0030] Note that in the case where k is a natural number, the zero point of F x [cos(2πkx)](f) intersects with the zero points of the sinc functions.

[0031] Next, a generalized Hamming window, which is a typical window function of the raised cosine window, is described, and the principle of the raised cosine window is explained in detail. A generalized Hamming window w h (x) is expressed by the following equation (5). The symbol α represents a real number parameter. wh(x)=(1−α)+αcos(2πx)

[0032] Fig. Figure 4 is a graph showing a superimposed representation of the frequency domain response of cos(2πkx) and the frequency domain response of a sinc function. Fig. 4, sinc(f), which is the response in the frequency domain of the sinc function, is represented by a dashed line D. F x [cos(2πx)](f), which is the response of cos(2πx) in the frequency domain, is represented by a solid line E.

[0033] As if through a hollow point in Fig. 4, in the generalized Hamming window w h (x) the zero point of sinc(f), indicated by the dashed line D, and the zero point of F x [cos(2πx)](f), which is indicated by the solid line E, so that the generation positions of the side lobes of the two coincide. In addition, as shown in Fig. 4, the signs of the side lobes of sinc(f) and the side lobes of F x [cos(2πx)](f) is inverted. By superposing sinc(f) and F x [cos(2πx)](f) therefore reduces the side lobes.

[0034] In the generalized Hamming window w h (x), however, the main lobes of F x [cos(2πx)](f) added when sinc(f) and F x [cos(2πx)](f) are superimposed, resulting in a deterioration in frequency resolution. Furthermore, depending on the value of α, the first side lobes of sinc(f) are excessively reduced.

[0035] A raised cosine window w c (x) of higher order further reduces the side lobes by increasing the values ​​of the individual cos function terms that must be added for each order.

[0036] However, increasing the values ​​of the cos function terms also leads to a broadening of the main lobes of F x [cos(2πx)](f) and thus to a deterioration of the frequency resolution.

[0037] Meanwhile, the window function in the first embodiment serves to limit the deterioration of the frequency resolution to an allowable range and to reduce the side lobes of frequency components so that they fall within an allowable range. For example, the window function w p (x) in the first embodiment is expressed by the following equation (6). In the following equation (6), a ka coefficient for multiplying the cos function term for each degree k. Note that Σ[k = 1]a k cos(πkx) in the following equation (6) indicates that in a case where M =a k cos(πkx), the value of M is added for each degree k successively starting from k = 1. wp(x)=a0+Σ[k=1]akcos(πkx)

[0038] With the window function w p (x) can a k be a negative value. This means that the window function w p (x) includes a cos function term with a negative value among the cos function terms of the respective degrees k. This allows the cos function terms to be adjusted in the negative direction.

[0039] An example of the window function w p (x) in the first embodiment will be described in comparison with a rectangular window function.

[0040] The window function w p(x) can reduce the peak sidelobes of the frequency component while suppressing the degradation of frequency resolution compared to state-of-the-art rectangular window functions. For example, in the state-of-the-art window functions, the peak levels of the sidelobes vary in the frequency domain; by using the window function w p (x), however, the peak levels of the sidelobes are aligned in a part of the frequency domain and the peak levels of the sidelobes are reduced.

[0041] In a case where -0.5 ≤ x ≤ 0.5, the response in the frequency domain of the constant term a0 is given by a sinc function. In a case where a window function is formed by the constant term a0 and the term cos(2πx) similar to the generalized Hamming window, F x [cos(2πx)](f), which is the frequency component of cos(2πx), the frequency resolution of the sinc function.

[0042] The window function w p (x) in the first embodiment does not have cos(2πx), which is a low-order cos function term that causes a deterioration in frequency resolution. As a result, the window function w p (x) the frequency resolution can be improved compared to the state-of-the-art rectangular window functions.

[0043] Fig. Figure 5 is a graph showing a superimposed representation of the frequency domain response of cos(4πx) and the frequency domain response of a sinc function. Fig. 5, the response of the sinc function in the frequency domain is indicated by a dashed line F and a response F x [cos(4πx)](f) of cos(4πx) in the frequency domain is given by a solid line G. As can be seen from the dashed line F and the solid line G, the main lobes of F x[cos(4πx)](f) is superimposed on the first side lobes of the frequency component of the sinc function. Since the signs of the two are inverted, the first side lobes of the sinc function are reduced.

[0044] The main lobes of F x However, [cos(4πx)](f) are also superimposed on the second side lobes of the sinc function. Adding the cos(4πx) term therefore leads to an unfavorable increase in the second side lobes.

[0045] The window function w p (x) in the first embodiment reduces the side lobes to be reduced by superimposing the main lobes, which correspond to the cos function term in the frequency domain, on the side lobes to be reduced. The window function w p (x), for example, also contains a term of cos(5πx). Therefore, in the window function w p (x) the main lobes of F x [cos(5πx)](f) is used to subtract the side lobes of the sinc function.

[0046] Fig. Figure 6 is a graph showing a superimposed representation of the frequency-domain response of cos(5πx) and the frequency-domain response of a sinc function. Fig. 6, the response of the sinc function in the frequency domain is indicated by a dashed line F and a response F x [cos(5πx)](f) of cos(5πx) in the frequency domain is indicated by a solid line H. As indicated by a dashed vertical line in Fig. 6, the generation positions of the main lobes of F x [cos(5πx)](f) is related to the generation positions of the second side lobes of the sinc function. Therefore, by subtracting cos(5πx) from the constant term a0, the second side lobes of the sinc function can be reduced.

[0047] The window function w p(x) in the first embodiment may be a function expressed by the following equation (7). In the following equation (7), α denotes a constant term, β and γ denote coefficients, and α, β and γ > 0. The window function w p (x), expressed in the following equation (7), can reduce the peaks of the side lobes, almost without degrading the frequency resolution with respect to the sinc function. wp(x)=α+β(4πx)−ycos(5πx)

[0048] Fig. Fig. 7 is a graph illustrating the shape of the window function in the first embodiment and illustrates the window function w p (x), expressed by the above equation (7). As in Fig. 7, the characteristic form of the window function w p (x) highlights both end sections, and a central section is set back compared to the two end sections. By adjusting the window function wp (x) with the Fig. 7, the frequency resolution can be improved to fall within an allowable range, and furthermore, the peak levels of the side low side lobes can also be reduced to fall within an allowable range.

[0049] Fig. Figure 8 is a graph showing an overlaid representation of the response in the frequency domain of the window function w p (x) in Fig. 7 and the response in the frequency domain of a prior art window function with a rectangular characteristic shape. In Fig. 8 is the response in the frequency domain of the window function w p(x) is indicated by a solid line l and the response in the frequency domain of the rectangular window function is indicated by a dashed line J. As can be seen from the solid line l and the dashed line J, in the response in the frequency domain of the window function w indicated by the solid line l p (x) reduces the peak levels of the side lobes, while the frequency resolution is hardly degraded compared to the prior art window function indicated by the dashed line J, with respect to the sinc function. In addition, the response in the frequency domain of the window function w p (x) first, second and third low side lobes are equalized to approximately the same level and their peak levels are reduced.

[0050] The window function w p (x) in the first embodiment can be obtained by improving the Hann window.

[0051] A Hann window w han (x) is a prior art window function given by the following equation (8). As expressed in the following equation (8), in the Hann window w han (x) a constant term and a term of cos(2πx) with equal gain are added, so that the attenuation rate of side lobes in the frequency direction is high. The Hann window w han (x) shows an excellent effect of damping the side lobes in the frequency direction, but has the problem that first side lobes of a sinc function are relatively high. whan(x)={1+cos(2πx)} / 2

[0052] The window function w p(x) in the first embodiment reduces the peak power of the side lobes without deteriorating the attenuation rate of the side lobes in the frequency direction. This is expressed, for example, by the following equation (9). In the following equation (9), α and β are real numbers, and α and β > 0. wp(x)=(1−α+β){1+cos(2πx)} / 2+α{cos(4πx)+cos(6πx)} / 2−β{(6πx)+cos(8πx)} / 2

[0053] The window function w shown in equation (9) above p (x) reduces the first side lobes of the Hann window, expressed by {1 + cos(2πx)} / 2, by the main lobes of the term of (cos(4πx) + cos(6πx)) / 2 and reduces the second side lobes of the Hann window by the main lobes of the term of -{cos(6πx) + cos(8πx)} / 2. As a result, in the window function w p(x) expressed by the above equation (9), the levels of the side lobes that have varied are partially equalized without affecting the attenuation rate of the side lobes, and at the same time, the peak power of the side lobes can be reduced.

[0054] Since the window function w expressed in equation (9) above p (x) does not have the term {cos(2πx) + cos(4πx)} / 2, the peak power of the side lobes can be reduced without excessively degrading the frequency resolution compared to the Hann window.

[0055] It should be noted that the window function w expressed in equation (9) p (x) can be generalized as in the following equation (10) by setting the constant term a0 ≥ 0.

[0056] Σ[k = 0](-1) k a k [{cos(2kπx) + cos(2(k + 1)πx)} / 2] in the following equation (10) indicates that in a case where M = (-1) k a k[{cos(2kπx) + cos(2(k + 1)πx)} / 2]), the value of M is added for each degree k successively starting from k = 1. wp(x)=Σ[k=0](−1)kak[{cos(2kπx)+cos(2(k+1)πx)} / 2]

[0057] In addition, as a prior art window function that has excellent side lobe attenuation, there is a window function expressed by the following equation (11). wp(x)=0.75cos(πx)+0.25cos(3πx)

[0058] The window function w p (x) in the first embodiment can be obtained by improving the prior art window function expressed by the above equation (11). A window function w p (x), which is expressed by the following equation (12), is obtained, for example, by inserting a coefficient a k into the above equation (11).

[0059] It should be noted that the window function w p(x), which is expressed by the following equation (12), side lobes according to a similar principle to that of the window function w p (x), which is expressed by the above equation (9). In the following equation (12), Σ[k = 1](-1) k-1 a k that in a case where M1 = (-1) k-1 a k , the value of M1 is added successively for each degree k starting from k = 1. In addition, Σ[k = 1](-1) k-1 a k F k (x) indicates that in a case where M2 = (-1) k-1 a k F k (x), the value of M2 is added successively for each degree k starting from k = 1. wp(x)=(1−Σ[k=1](−1)k−1ak){0.75cos(πx)+0.25cos(3πx)}+Σ[k=1](−1)k−1akFk(x)

[0060] The function F k (x) in the above equation (12) is expressed by the following equation (13). Fk(x)=[0.125cos{(2k+1)πx}+0.375cos{(2k+3)πx}]+0.375cos[{(2k+5)πx}+0.125cos{(2k+7)πx}]

[0061] As described above, the window function w p(x) In the first embodiment, focusing on the correspondence relationship between the main lobes of the frequency component of the cos function term and the side lobes of the frequency component of the sin function, which is the constant term, reduces the side lobes while suppressing deterioration in frequency resolution. For example, by using the signal processing device 1 in a radar system, the signal processing device 1 can reduce lower-order side lobes superimposed on a reception signal from a target by multiplying the reception signal from the target by the window function, and thus it is possible to reduce the probability of the target being missed due to lower-order side lobes.By using the signal processing device 1 in a synthetic aperture radar, the signal processing device 1 can also reduce low-order sidelobes by multiplying a radar signal by the window function, so that the noise due to the low-order sidelobes in a radar image can be made less noticeable.

[0062] Next, a hardware configuration for implementing the functions of the signal processing device 1 is described.

[0063] The functions of the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13, and the signal output unit 14 included in the signal processing device 1 are implemented by a processing circuit. That is, the signal processing device 1 comprises a processing circuit for executing the Fig. 2. The processing circuit may be dedicated hardware or a central processing unit (CPU) for executing a program stored in a memory.

[0064] Fig. 9A is a block diagram showing a hardware configuration for implementing the functions of the signal processing device 1. Fig. 9B is a block diagram showing a hardware configuration for executing the software that implements the functions of the signal processing device 1. In Fig. 9A and Fig. 9B, an input interface 100 forwards an input signal acquired by the signal processing device 1 from the input signal storage unit 2. An output interface 101 forwards an output signal output by the signal processing device 1 to the output signal storage unit 3.

[0065] In a case where the processing circuit is a dedicated hardware processing circuit 102 shown in Fig. 9A, the processing circuit 102 may be, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination thereof. The functions of the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13, and the signal output unit 14 included in the signal processing device 1 may be implemented by separate processing circuits, or these functions may be implemented jointly by one processing circuit.

[0066] In a case where the processing circuitry is Fig. 9B, the functions of the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13, and the signal output unit 14 included in the signal processing device 1 are implemented by software, firmware, or a combination of software and firmware. Note that the software or firmware is described as a program and stored in the memory 104.

[0067] The processor 103 reads the program stored in the memory 104 and executes it to implement the functions of the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13 and the signal output unit 14 in the signal processing device 1. The signal processing device 1 has, for example, the memory 104 for storing programs whose execution by the processor 103 is used to execute the Fig. 2. These programs cause a computer to execute operations or methods performed by the processing performed by the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13, and the signal output unit 14. The memory 104 may be a computer-readable storage medium on which the programs that cause a computer to operate as the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13, and the signal output unit 14 are stored.

[0068] The memory 104 corresponds to a non-volatile or volatile semiconductor memory such as a random access memory (RAM), a read-only memory (ROM), a flash memory, an erasable programmable ROM (EPROM) or an electrical EPROM (EEPROM) (registered trademark), a magnetic disk, a floppy disk, an optical disk, a compact disk, a minidisk, a DVD, or the like.

[0069] Some of the functions of the signal acquisition unit 11, the signal extraction unit 12, the frequency conversion unit 13, and the signal output unit 14 included in the signal processing device 1 can be implemented by dedicated hardware, and other parts can be implemented by software or firmware. For example, the functions of the signal acquisition unit 11 and the signal output unit 14 are implemented by the processing circuit 102, which is dedicated hardware, and the functions of the signal extraction unit 12 and the frequency conversion unit 13 are implemented by the processor 103, which reads and executes a program stored in the memory 104. In this way, the processing circuit can implement the above-described functions by hardware, software, firmware, or a combination thereof.

[0070] As described above, the signal processing device 1 according to the first embodiment comprises the signal acquisition unit 11 which acquires the input signal s(t), the signal extraction unit 12 which extracts the specific signal s w (t) by multiplying the input signal s(t) with the window function w p (x) extracted, the frequency conversion unit 13, which performs a frequency conversion of the extracted signal s w (t), and the signal output unit 14, which outputs the frequency-converted signal s w (f). The window function w p(x) comprises one or a plurality of cosine function terms, in which at least one of the sign of the coefficient for multiplying the cosine function or the degree of the cosine function is adjusted so that both the frequency resolution and the amount of reduction of side lobes fall within allowable ranges. The signal processing device 1 can also adjust the cosine function terms in the negative direction by using the window function. As a result, the signal processing device 1 can more advantageously achieve a trade-off between frequency resolution and side lobe characteristics than is the case when using a prior art window function represented by the raised cosine window. It should be noted that similar effects also occur in the Fig. 2, which is carried out by the signal processing device 1.

[0071] In the signal processing device 1 according to the first embodiment, the window function w p (x) does not contain a low-order cos function term, which would degrade the frequency resolution. As a result, the window function w p (x) the degradation of frequency resolution is lower compared to that of the prior art rectangular window function, and the side lobes of the frequency component of the sinc function can be reduced.

[0072] In the signal processing device 1 according to the first embodiment, the window function w reduces p (x) the side lobes to be reduced by superimposing the main lobes, which correspond to the cos function term in the frequency domain, on the side lobes to be reduced. In this way, the window function w p (x) reduce the side lobes of the frequency component of the sinc function. Since the window function w p(x) has a term of cos(kπx), the side lobes are reduced by reducing the main lobes of F x [cos(kπx)](f) in the frequency domain are superimposed on the side lobes. Note that the window function w p (x) may have a term obtained by expanding a window function such as the Hann window.

[0073] In the signal processing device 1 according to the first embodiment, the window function w p (x) has a characteristic shape in which the central section is recessed compared to the two end sections. This allows the window function w p (x) improve the frequency resolution compared to that achieved by a state-of-the-art window function with a rectangular characteristic shape. Second embodiment

[0074] A window function in a second embodiment includes a cos(kπx) term in addition to the generalized Hamming window function, which can reduce side lobes of the frequency component while suppressing degradation of frequency resolution. For example, the window function in the second embodiment is obtained by adding a cos(4πx) term and a cos(6πx) term to the generalized Hamming window function.

[0075] Similar to the first embodiment, a signal processing device 1 according to the second embodiment comprises a signal acquisition unit 11 which acquires an input signal s(t), a signal extraction unit 12 which extracts a specific signal s w (t) by multiplying the input signal s(t) with a window function w p(x) extracted, a frequency conversion unit 13 which performs a frequency conversion of the extracted signal s w (t), and a signal output unit 14 which outputs the frequency-converted signal s w (f). As described above, the window function w p (x) a cos function term with a negative value.

[0076] Fig. Figure 10 is a graph showing the superimposed representation of the responses in the frequency domain of a sinc function, cos(2πx), -cos(4πx), and cos(6πx). In Fig. 10 is sinc(f), which is the response in the frequency domain of the sinc function, represented by a dashed line D and F x [cos(2πx)](f), which is the response in the frequency domain of cos(2πx), is represented by a solid line E. In addition, F x [cos(4πx)](f), which is the response in the frequency domain of -cos(4πx), indicated by a dot-dash line K and F x[cos(6πx)](f), which is the response in the frequency domain of cos(6πx), is given by a dot-dash line L.

[0077] As in Fig. As shown in Figure 10, the side lobes distant from the main lobes in each frequency-domain response of cos(2πx), -cos(4πx), and cos(6πx) are inverted in sign relative to the side lobes in the frequency-domain response of the sinc function. Unlike the generalized Hamming window, which only has the constant term and cos(2πx), the window function in the second embodiment includes the terms of -cos(4πx) and cos(6πx), which can further reduce the side lobes of the frequency component.

[0078] It should be noted that the main lobes of F x [-cos(4πx)](f) excessively increase the first side lobes of sinc(f) but excessively decrease the second side lobes.

[0079] In addition, the main lobes of F x[cos(6πx)](f) excessively increase the second side lobes of sinc(f) while excessively reducing the third side lobes.

[0080] In the generalized Hamming window, the main lobes of F x [cos(2πx)](f) depending on the value of α the first side lobes of sinc(f) are excessive.

[0081] In view of this, in the window function in the second embodiment, the value of the term -cos(4πx) is determined depending on the reduction amount of the first side lobes of sinc(f) generated by the main lobes of F x [cos(2πx)](f), and the second side lobes in sinc(f) are determined by the main lobes of F x [-cos(4πx)](f). In addition, the value of the term cos(6πx) is determined depending on the amount of reduction of the second side lobes of sinc(f) caused by the main lobes of F x [-cos(4πx)](f) can be reduced.

[0082] In the window function of the second embodiment, the values ​​of a coefficient multiplying the term of -cos(4πx) and a coefficient multiplying cos(6πx) are both small, so the deterioration in frequency resolution due to these terms is small. Furthermore, the window function in the second embodiment can equalize the levels of sidelobes in the frequency domain and reduce the overall level of sidelobes. Therefore, with the window function in the second embodiment, the deterioration in frequency resolution is smaller than with the generalized Hamming window, which can reduce the sidelobes in the frequency domain.

[0083] The window function w p (x) in the second embodiment is expressed, for example, by the following equation (14). In the following equation (14), α, β, and γ are real numbers, and α, β, and γ > 0.

[0084] The symbol α corresponds to α in the generalized Hamming window.

[0085] The symbol β is determined depending on the amount of reduction of the first side lobes by the main lobes of F x [cos(2πx)](f). The symbol γ is set as a function of the reduction amount of the second side lobes of sinc(f), reduced by the main lobes of F x [-cos(4πx)](f), set. wp(x)=(1−α)+αcos(2πx)−βcos(4πx)+ycos(6πx)

[0086] Fig. Figure 11 is a graph showing a relationship between the frequency resolution and the peak level of the side lobes for the window function in the second embodiment and a generalized Hamming window. The horizontal axis in Fig. Figure 11 represents an index of frequency resolution obtained by normalizing a 3 dB width of a power profile of the frequency component with a width of 3 dB in a rectangular window. The vertical axis in Fig. Figure 11 shows the normalized peak level of the side lobe. The relationship of the window function in the second embodiment is indicated by hollow dots, and the relationship of the generalized Hamming window is indicated by hollow squares. As shown in Fig. As shown in Figure 11, in the window function according to the second embodiment, the sidelobe peak levels are reduced compared to those of the generalized Hamming window.

[0087] In a radar system which uses the signal processing device 1 using the window function w p(x) of the second embodiment, the signal processing device 1 can, for example, reduce low-order sidelobes superimposed on a reception signal from a target by multiplying the reception signal from the target by the window function, and thus it is possible to reduce the probability that the target is not detected due to low-order sidelobes. Furthermore, by applying the signal processing device 1 to a synthetic aperture radar, the signal processing device 1 can reduce low-order sidelobes by multiplying a radar signal by the window function, so that the noise due to the low-order sidelobes in a radar image can be made less noticeable.

[0088] It should be noted that the window function w expressed in equation (14) p(x) can be generalized as in the following equation (15) by setting the constant term a0 ≥ 0. A term Σ[k = 0](-1) k -1 a k cos(2kπx) in the following equation (15) indicates that in a case where M = (-1) k-1 a k cos(2kπx), the value of M is added for each degree k successively starting from k = 1. wp(x)=a0+Σ[k=1](−1)k−1akcos(2kπx)

[0089] As described above, the signal processing device 1 according to the second embodiment comprises the signal acquisition unit 11 which acquires the input signal s(t), the signal extraction unit 12 which extracts the specific signal s w (t) by multiplying the input signal s(t) with the window function w p (x) extracted, the frequency conversion unit 13, which performs a frequency conversion of the extracted signal s w(t), and the signal output unit 14, which outputs the frequency-converted signal s w (f). The window function w p (x) includes a cosine function term in which the sign of a coefficient for multiplying the cosine function is adjusted so that both the frequency resolution and the amount of sidelobe reduction fall within allowable ranges. The signal processing device 1 can also adjust the cosine function terms in the negative direction by using the window function. As a result, the signal processing device 1 can achieve a more favorable trade-off between frequency resolution and sidelobe characteristics than is the case when using a prior art window function represented by the raised cosine window.

[0090] In the signal processing device 1 according to the second embodiment, the window function w p(x) cos(2πx), -cos(4πx), and cos(6πx), which are cos function terms of the respective degrees k, depending on the reduction amount of the side lobes in the frequency domain. Consequently, the window function w p (x) Reduce side lobes of the frequency component of the generalized Hamming window with almost no degradation of the frequency resolution. Third embodiment

[0091] A window function in a third embodiment contains a cos function term instead of a constant term and can reduce sidelobes in the frequency domain. In particular, the performance of the window function in the third embodiment is midway between that of the generalized Hamming window and the prior-art Blackman window, enabling a trade-off between frequency resolution and sidelobe characteristics that is better than those window functions.

[0092] Similar to the first embodiment, a signal processing device 1 according to the third embodiment comprises a signal acquisition unit 11 that acquires an input signal s(t), a signal extraction unit 12 that extracts a specific signal s w (t) by multiplying the input signal s(t) with a window function w p (x) extracted, a frequency conversion unit 13 which performs a frequency conversion of the extracted signal s w (t), and a signal output unit 14 which outputs the frequency-converted signal s w (f) issues.

[0093] First, the prior art Blackman window is described to facilitate understanding of the window function in the third embodiment. The generalized Hamming window described above has the advantage that the characteristics can be specified by a single parameter α. Although the Blackman window has lower frequency resolution than the generalized Hamming window, the features can be designed with a single parameter similar to the generalized Hamming window. The Blackman window is expressed by the following equation (16). For example, a Blackman window with α = 0.08 is well-known. This Blackman window has lower frequency resolution than the generalized Hamming window, but can reduce sidelobes. wb(x)=(0.5−α)+0.5cos(2πx)+αcos(4πx)

[0094] The window function in the third embodiment can shape the characteristics by a single parameter α using a half-cycle sine window, and its performance is midway between that of the generalized Hamming window and the Blackman window. In a case where -0.5 ≤ x ≤ 0.5, the half-cycle sine window can be expressed by the following equation (17). ws(x)=cos(πx)

[0095] The frequency characteristic of the window function given by cos(πx) is obtained by adding the two frequency-shifted sinc functions, and the side lobes in the frequency domain are reduced.

[0096] Fig. Figure 12 is a graph showing the response in the frequency domain of sinc functions shifted by ±1 / 2 and the response in the frequency domain of cos(πx) obtained by combining these sinc functions. Fig. 12 becomes F x[cos(πx)](f), which is the response of cos(πx) in the frequency domain, is indicated by a solid line M. Furthermore, sinc(f - 0.5) / 2, which is the response in the frequency domain of the sinc function shifted by -1 / 2, is indicated by a dashed line N, and sinc(f + 0.5) / 2, which is the response in the frequency domain of the sinc function shifted by +1 / 2, is indicated by an alternating long and short dashed line O.

[0097] As can be seen from the solid line M, the dashed line N and the alternating long and short dashed line O, F x [cos(πx)](f) is equal to a combination of sinc(f - 0.5) / 2 and sinc(f + 0.5) / 2. As indicated by the hollow points in Fig. 12, the zero points of sinc(f - 0.5) / 2 and sinc(f + 0.5) / 2 coincide, and the signs of the overlapping side lobes are inverted. Therefore, the side lobes in F x[cos(πx)](f), which is obtained by combining sinc(f - 0.5) / 2 and sinc(f + 0.5) / 2. Since the half-cycle sine window, as described above, corresponds to a combination of the two frequency-shifted sinc functions, it is possible to preferentially reduce sidelobes despite low frequency resolution.

[0098] By using cos(πx), the window function in the third embodiment can balance frequency resolution and sidelobe characteristics in a range where neither the generalized Hamming window nor the Blackman window can achieve the same. In a case where l is a natural number, the zero points of cos{(2l + 1)πx} coincide with the zero points of F x [cos(π\x)](f), which is the response in the frequency domain of cos(πx).

[0099] The window function in the third embodiment includes a term of cos(3πx) expressed by cos{(2l + 1) πx} and the term of cos(πx) which is the half-cycle sine window.

[0100] By setting a parameter α to α > 0, the window function in the third embodiment can be expressed by the following equation (18). wp(x)=(1−α)cos(πx)+αcos(3πx)

[0101] Fig. Figure 13 is a graph showing a superimposed representation of the response in the frequency domain of cos(πx) and the response in the frequency domain of cos(3πx), each included in the window function in the third embodiment. Fig. 13 is F x [cos(πx)](f), which is the response in the frequency domain of cos(πx), indicated by a solid line M and F x[cos(3πx)](f), which is the response in the frequency domain of cos(3πx), is indicated by a dashed line P. As can be seen from the solid line M and the dashed line P, the generation positions of the side lobes of F x [cos(πx)](f) and the generation positions of the side lobes of F x [cos(3πx)](f) is harmonized, and the signs of the two are inverted. Since the cos(πx) and cos(3πx) terms are added to the window function in the third embodiment, the side lobes of the frequency component are reduced.

[0102] That is, in the window function according to the third embodiment, in addition to cos(πx), the half-cycle sine window from which favorable sidelobe characteristics can be obtained, other favorable sidelobe characteristics can be obtained by using the term cos(3πx). The window function in the third embodiment can be designed with a single parameter, similar to the generalized Hamming window and the Blackman window.

[0103] In addition, the window function w p (x) In the third embodiment, improve the performance as in the following equation (19) by adopting the design concept of the window function described in the second embodiment, setting the coefficients for multiplying the cos function terms to α, β and γ, and setting α, β and γ > 0. The window function w given by the following equation (19) p(x) is similar to equation (14) described above in the second embodiment. wp(x)=(1−α)cos(πx)+αcos(3πx)−βcos(5πx)+γcos(7πx)

[0104] It should be noted that the window function w expressed in equation (19) p (x) can be generalized as in the following equation (20) by setting the constant term a0 ≥ 0. Σ[k = 0](-1) k-1 a k- cos{(2k + 1) πx} in the following equation (20) indicates that in a case where M = (-1) k-1 a k cos{(2k + 1)πx}, the value of M is added for each degree k successively starting from k = 1. wp(x)=a0cos(πx)+∑[k=1](−1)k−1akcos{(2k+1)πx}

[0105] In the signal processing device 1 according to the third embodiment, the window function w p(x) does not have the constant term a0, but is formed by cos function terms. The signal processing device 1 according to the third embodiment can preferably achieve a balance between the frequency resolution and the sidelobe characteristics by using the window function w p (x). With the window function w p (x), which in addition to cos(πx), which is the half-cycle sine window, also has cos(3πx), it is possible, for example, to have its performance midway between those of the generalized Hamming window and the Blackman window and preferably to achieve a trade-off between the frequency resolution and sidelobe characteristics compared to the state-of-the-art window functions. Fourth embodiment

[0106] A window function in the fourth embodiment has a characteristic shape in which a central portion is recessed compared to the two end portions. In the window function in the fourth embodiment, the discontinuity at the two end portions that form the boundaries between the inside and outside of the window is emphasized, and, for example, the depth of the recess in the central portion can be adjusted depending on the value of the coefficient α. Since the depth of the recess in the central portion of the window function affects the width of the main lobes in the frequency domain, the frequency resolution can be improved by adjusting the value of the coefficient α accordingly.

[0107] Similar to the first embodiment, a signal processing device 1 according to the fourth embodiment comprises a signal acquisition unit 11 that acquires an input signal s(t), a signal extraction unit 12 that extracts a specific signal s w (t) by multiplying the input signal s(t) with a window function w p (x) extracted, a frequency conversion unit 13 which performs a frequency conversion of the extracted signal s w (t), and a signal output unit 14 which outputs the frequency-converted signal s w (f). As described above, the window function w p (x) a cos function term with a negative value.

[0108] A state-of-the-art window function is generally designed to reduce sidelobes in the frequency domain by emphasizing the continuity at the two end portions that form the boundaries between the interior and exterior of the window.

[0109] Meanwhile, the window function in the fourth embodiment has a characteristic shape in which the central portion is recessed compared to the two end portions, and a discontinuity at both end portions is emphasized. With this shape, deterioration of frequency resolution can be suppressed. The window function w p (x) in the third embodiment can be expressed by the following equation (21) by setting the coefficient α > 0. wp(x)=1−αcos(πx)

[0110] Fig. 14 is a graph illustrating the form of the window function w p(x) in the fourth embodiment and shows the window functions w p (x) corresponding to the respective coefficients α1, α2, α3, α4 and α5. In Fig. 14 are α1 = 0.2, α2 = 0.4, α3 = 0.6, α4 = 0.8 and α5 = 0.95. In the form of the window function w p (x) When the value of the coefficient α is increased from α1 to α5, the depression in the central section is deeper, and since the depression in the central section is deeper, the level of the protrusion of the two end sections is also steeper, and the discontinuity is emphasized.

[0111] Fig. 15 is a diagram illustrating the frequency component of the window function w p (x) of Fig. 14 and shows the window functions w p (x) corresponding to the respective coefficients α0, α1, α2, α3, α4 and α5. In Fig. 15 are α0 = 0, α1 = 0.2, α2 = 0.4, α3 = 0.6, α4 = 0.8 and α5 = 0.95. In the frequency component of the window function w p(x) The side lobes increase with increasing value of the coefficient α, while the width of the main lobes decreases, thus improving frequency resolution. For example, by appropriately adjusting the value of the coefficient α depending on the application of the window function, the signal processing device 1 according to the third embodiment can improve frequency resolution more than a window function of the related art can.

[0112] It should be noted that the window function w p (x) in the fourth embodiment only needs to have a characteristic shape in which the central portion is recessed compared to the two end portions, and that the components of the function implementing this shape are not limited to those described above. Furthermore, in the window function w p(x) In the fourth embodiment, it is also possible to design the parameters so that the frequency resolution and the amount of reduction of the side lobes fall within permissible ranges.

[0113] In addition, the window function w p (x) in the fourth embodiment can also be expressed as the following equation (22) by setting the coefficients for multiplying the cos function terms to α, β, and γ and setting α, β, and γ > 0 by adopting the design concept of the window function described in the first embodiment. As described in the first embodiment, the window function w reduces p (x) of the following equation (22) the side lobes around the main lobes of the frequency component of cos(kπx). wp(x)=1−αcos(πx)+βcos(3πx)−γcos(5πx)

[0114] It should be noted that the window function w expressed in equation (22) p(x) can be generalized as in the following equation (23) by setting the constant term a0 ≥ 0. Σ[k = 0](-1) k a k cos{(2k - 1)πx} in the following equation (23) indicates that in a case where M = (-1) k a k cos{(2k - 1)πx}, the value of M is added for each degree k successively starting from k = 1. wp(x)=a0+∑[k=1](−1)kakcos{(2k−1)πx}

[0115] Application examples for the window functions described in the first to fourth embodiments are described below.

[0116] The following Reference 1 describes an example of a synthetic aperture radar image (hereinafter referred to as a SAR image) using multi-apodization. Multi-apodization is a method for reducing sidelobes without degrading frequency resolution by extracting a signal with the lowest intensity from signals processed without using a window function or from signals processed using multiple window functions.

[0117] The signal extraction unit 12 multiplies, for example, the window function w p(x) and extracts a signal from the input signal. The frequency conversion unit 13 performs frequency conversion of the signal extracted by the signal extraction unit 12. The signal output unit 14 extracts a signal with the minimum intensity from the signal frequency-converted by the frequency conversion unit 13 and outputs the signal.

[0118] In addition to the processing result that the window function w p (x), an output signal can be extracted from a processing result that does not meet the window function w p (x). For example, the signal output unit 14 can generate a signal obtained by frequency conversion of a signal from the window function w p (x) multiplied input signal and a signal obtained by frequency converting the input signal, extract a signal with the minimum strength.

[0119] As described above, by using the window function w p (x) in the fourth embodiment, as a window function in multi-apodization, it is possible to reduce side lobes and at the same time improve the frequency resolution.

[0120] (Reference 1) HC Stankwitz, RJ Dallaire, and JR Fienup, "Nonlinear apodization for sidelobe control in SAR imagery," IEEE Trans. Aerosp. Electron. Syst., Vol. 31, No. 1, pp. 267–279, January 1995.

[0121] Furthermore, in the signal processing device 1, a finite impulse response filter (hereinafter referred to as FIR filter) can replace the window function processing. For example, the frequency conversion unit 13 performs frequency conversion of the input signal s(t) to generate a signal S(f). The signal output unit 14 extracts a frequency-converted specific signal S w(f) from the frequency-converted input signal S(f) using the FIR filter adjusted so that both the frequency resolution and the amount of sidelobe reduction are within the allowable ranges. FIR filtering is expressed by the following equation (24) as S(f) = Ft[s(t)](f). In the following equation (24), FIR filtering gives a weight w to each of the signals shifted by ±Δf. A symbol Δf denotes a frequency bin when performing Nyquist sampling to digitally process a signal. In a case where the signal shifted by Δf corresponds to one sample, the signals shifted by ±1 sample are assigned the weight w. Sw(f)=S(f)+wS(f+Δf)+wS(f+Δf)

[0122] Reference 1 shows an FIR filtering where a weight w, which is a real number, is 0 < w ≤ 0.5 only for the purpose of reducing side lobes.

[0123] Meanwhile, the signal processing device 1 according to the first embodiment can improve the frequency resolution similarly to the multiplication of the input signal by the window function described in the embodiment by performing the FIR filtering expressed by the above equation (24) in the range of -0.5 < w < 0.

[0124] Furthermore, a sidelobe reduction technology called super-spatially variable apodization is described in Reference 1. By applying this technology to the FIR filtering described above, it is also possible to reduce sidelobes while simultaneously improving frequency resolution.

[0125] Specifically, if a weighting w u(m), image data is g(m), and the image data g(m) obtained by FIR filtering is g'(m), FIR filtering is performed on them set in the relationship of the following equations (25) to (27). If wu(m)<α, then g'(m)=g(m)+α[g(m−1)+g(m+1)] If α≤wu(m)≤1 / 2, g'(m)=g(m)+wu(m)[g(m−1)+g(m+1)] If 1 / 2≤wu(m), then g'(m)=g(m)+(1 / 2)[g(m−1)+g(m+1)]

[0126] Note that α in the above equations (25) and (26) is a real number, which is set within -0.5 ≤ α ≤ 0 and is adjusted depending on the desired power. The FIR filtering described above can not only reduce sidelobes but also improve frequency resolution.

[0127] As described above, the window function w p(x) in the signal processing device 1 according to the fourth embodiment has a characteristic shape in which the central portion is recessed compared to the two end portions. As a result, the window function w p (x) improve the frequency resolution compared to that provided by a rectangular window function.

[0128] In the signal processing device 1 according to the fourth embodiment, the signal output unit 14 can extract and output a signal with the minimum intensity from a signal obtained by frequency converting the signal extracted from the input signal multiplied by the window function. This enables a reduction in side lobes while simultaneously improving frequency resolution.

[0129] In the signal processing device 1 according to the fourth embodiment, the signal output unit extracts and outputs a signal with the minimum intensity from a signal obtained by frequency converting the input signal extracted from the input signal multiplied by the window function and a signal obtained by frequency converting the input signal. This enables side lobes to be reduced while simultaneously improving frequency resolution.

[0130] In the signal processing device 1 according to the fourth embodiment, the frequency conversion unit 13 performs frequency conversion of the input signal, and the signal output unit 14 extracts a frequency-converted specific signal from the frequency-converted input signal using a finite impulse response filter adjusted so that both the frequency resolution and the amount of sidelobe reduction fall within the allowable ranges. It is possible to perform FIR filtering, which can extract a signal that reduces sidelobes while improving frequency resolution.

[0131] It should be noted that it is possible to incorporate a combination of the embodiments or a modification of any component of each of the embodiments or to omit any component in each of the embodiments. INDUSTRIAL APPLICABILITY

[0132] The signal processing device according to the present disclosure can be used, for example, for a radar system. LIST OF REFERENCE SYMBOLS

[0133] 1: Signal processing unit, 2: Input signal storage unit, 3: Output signal storage unit, 11: Signal acquisition unit, 12: Signal extraction unit, 13: Frequency conversion unit, 14: Signal output unit QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited non-patent literature

[0000] F. J. Harris, „On the Use of Windows for Harmonic Analysis With the Discrete Fourier Transform“, in proc. IEEE. vol. 66, Nr. 1, Jan. 1978

[0004] H. C. Stankwitz, R. J. Dallaire und J. R. Fienup, „Nonlinear apodization for sidelobe control in SAR imagery“, IEEE Trans. Aerosp. Elektronen. Syst., Bd. 31, Nr. 1, S. 267-279, Jan. 1995

[0120]

Claims

[1] Signal processing device comprising: a signal acquisition unit for obtaining an input signal; a signal extraction unit for extracting a specific signal by multiplying the input signal by a window function; a frequency conversion unit for performing frequency conversion of the extracted signal; and a signal output unit for outputting the frequency-converted signal, wherein the window function comprises one or a plurality of cosine function terms in which at least one of a sign of a coefficient for multiplying a cosine function or a degree of the cosine function is set so that both the frequency resolution and a reduction amount of a side lobe fall within allowable ranges. [2] A signal processing device according to claim 1, wherein the window function does not have a low-order cosine function term that contributes to the deterioration of the frequency resolution. [3] A signal processing device according to claim 1 or 2, wherein the window function reduces a side lobe to be reduced by superimposing a main lobe corresponding to a cosine function term in a frequency domain on the side lobe to be reduced. [4] A signal processing device according to claim 1 or 2, wherein the window function is obtained by determining a cosine function term of each degree depending on a reduction amount in the side lobe in the frequency domain. [5] A signal processing device according to claim 4, wherein the window function does not comprise a constant term but comprises a cosine function term. [6] A signal processing device according to any one of claims 1 to 5, wherein the window function has a characteristic shape in which a central part is recessed compared to the two end parts. [7] Signal processing device comprising: a signal acquisition unit for obtaining an input signal; a signal extraction unit for extracting a specific signal by multiplying the input signal by a window function; a frequency conversion unit for performing frequency conversion of the extracted signal; and a signal output unit for outputting the frequency-converted signal, where the window function has a characteristic shape in which a central part is recessed compared to the two end parts. [8] A signal processing device according to any one of claims 1 to 7, wherein the signal output unit extracts and outputs a minimum intensity signal from a signal obtained by performing frequency conversion on the signal extracted from the input signal by multiplying the window function. [9] A signal processing device according to any one of claims 1 to 7, wherein the signal output unit extracts and outputs a signal having a minimum intensity from a signal obtained by performing frequency conversion on the signal extracted from the input signal by multiplying the window function and a signal obtained by frequency converting the input signal. [10] Signal processing device according to claim 1, wherein the frequency conversion unit performs frequency conversion of the input signal, and the signal output unit extracts a frequency-converted specific signal from the frequency-converted input signal using a finite impulse response filter adjusted so that both the frequency resolution and the side lobe reduction amount are within the allowable ranges, and outputs the specific signal. [11] A signal processing method of a signal processing device, the signal processing method comprising: a step of acquiring an input signal by a signal acquiring unit; a step of extracting a specific signal by a signal extraction unit by multiplying the input signal by a window function; a step of performing frequency conversion of the extracted signal by a frequency conversion unit; and a step of outputting the frequency-converted signal by a signal output unit, wherein the window function comprises one or a plurality of cosine function terms in which at least one of a sign of a coefficient for multiplying a cosine function or a degree of the cosine function is set so that both the frequency resolution and a reduction amount of a side lobe fall within allowable ranges. [12] A signal processing method according to claim 11, wherein the window function does not have a low-order cosine function term that contributes to the deterioration of the frequency resolution. [13] A signal processing method according to claim 11 or 12, wherein the window function reduces a side lobe to be reduced by superimposing a main lobe corresponding to a cosine function term in the frequency domain on the side lobe to be reduced. [14] A signal processing method according to claim 11 or 12, wherein the window function is obtained by determining a cosine function term of each degree depending on a reduction amount in the side lobe in the frequency domain. [15] A signal processing method according to claim 14, wherein the window function does not comprise a constant term but comprises a cosine function term. [16] A signal processing method according to any one of claims 11 to 15, wherein the window function has a characteristic shape in which a central part is recessed in comparison. [17] A signal processing method of a signal processing device, the signal processing method comprising: a step of acquiring an input signal by a signal acquiring unit; a step of extracting a specific signal by a signal extraction unit by multiplying the input signal by a window function; a step of performing frequency conversion of the extracted signal by a frequency conversion unit; and a step of outputting the frequency-converted signal by a signal output unit, where the window function has a characteristic shape in which a central part is recessed compared to the two end parts. [18] A signal processing method according to any one of claims 11 to 17, wherein the signal output unit extracts and outputs a minimum intensity signal from a signal obtained by performing frequency conversion on the signal extracted from the input signal by multiplying the window function. [19] A signal processing method according to any one of claims 11 to 17, wherein the signal output unit extracts and outputs a signal having a minimum intensity from a signal obtained by performing frequency conversion on the signal extracted from the input signal by multiplying the window function and a signal obtained by frequency converting the input signal. [20] Signal processing method according to claim 11, wherein the frequency conversion unit performs frequency conversion of the input signal, and the signal output unit extracts a frequency-converted specific signal from the frequency-converted input signal using a finite impulse response filter adjusted so that both the frequency resolution and the side lobe reduction amount are within the allowable ranges, and outputs the specific signal.

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