Frequency estimation device, frequency estimation method, and frequency estimation program

Abstract

To provide a frequency estimation device, a frequency estimation method, and a frequency estimation program which can estimate a frequency of an input signal without redesigning a filter for every time the frequency changes.SOLUTION: A frequency estimation device 10 includes: a filter section 20 for outputting a frequency of an input signal; a Hilbert transformation section 12 for performing Hilbert transformation on the input signal; an analytic signal generation section 14 for generating an analytic signal from the input signal and a conversion signal output from the Hilbert transformation section 12; an instantaneous frequency calculation section 16 for calculating an instantaneous frequency on the basis of the analytic signal; and a filter coefficient setting section 18 for setting a filter coefficient of the filter section 20 on the basis of the instantaneous frequency in such a manner that frequency components with an even multiple of the frequency of the input signal are removed.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The disclosed technology relates to a frequency estimation device, a frequency estimation method, and a frequency estimation program. [Background technology]

[0002] A sine wave is one of the most basic waveforms, and estimating its frequency is a problem that has been studied in fields such as radar, sonar, communications, medicine, etc. For example, in the field of electronic scales, tuning fork sensors that use a single frequency signal have been attracting attention in recent years due to their excellent resolution, stability, and repeatability.

[0003] A tuning fork sensor is a load sensor that utilizes the phenomenon that the frequency of vibration changes when a load is applied to a vibrator that is shaped like two connected tuning forks. It is made up of only a metal tuning fork and a ring structure that transmits the load to it, and the frequency of the sensor changes depending on the load. This frequency is measured and digital processing is performed on the obtained frequency to remove noise and convert it into a weight value.

[0004] The main methods for measuring such single frequencies are those using a frequency counter and those using instantaneous frequency. The former method, which is currently mainstream, is the reciprocal frequency counter, which measures one period of the signal to be measured using a reference clock and calculates the frequency from its reciprocal. With this method, if the frequency of the signal to be measured changes, the output intervals of the frequency, which is the measured value, become unequal. For this reason, in order to perform digital processing, some ingenuity such as interpolation processing is required.

[0005] The latter instantaneous frequency is generally found using a Hilbert transformer. In a method of estimating instantaneous frequency using a Hilbert transformer, it is possible to output an estimated value of the frequency for each sample, and to measure the change in frequency over time. For this reason, instantaneous frequency estimation is also used in fault diagnosis of rotating machines and in understanding nonlinear and non-stationary processes. A complex signal with the real part as the input of the Hilbert transformer and the imaginary part as the output is called an analytic signal, and the phase of the analytic signal at a certain moment is the instantaneous phase. The instantaneous frequency is determined by time-differentiating this instantaneous phase and dividing it by 2π.

[0006] In the case of digital signals, the time derivative of the phase can be calculated from the difference between adjacent samples, making it possible to estimate the frequency without calculating the period. Therefore, the obtained frequency is output for each sample. Instantaneous frequency is also used to understand the detailed mechanisms of nonlinear and nonstationary processes.

[0007] The Hilbert transformer used to obtain the analytic signal to be actually used must be designed with a finite order. Therefore, it has ripples as an approximation error with respect to the amplitude characteristics of an ideal Hilbert transformer. As a result, the instantaneous frequency estimated using the Hilbert transformer contains components derived from the ripples in addition to the original frequency components, which is a problem when estimating frequencies with high accuracy. This error can be suppressed by increasing the order of the Hilbert transformer, but increasing the order is problematic because it increases the delay time and increases the circuit size.

[0008] The inventors have shown that the frequency of the vibration component contained in the estimated instantaneous frequency is an even multiple of the frequency of the input signal, and have proposed that the estimation accuracy can be improved by removing this using an FIR (Finite Impulse Response) filter having transmission zeros (see Non-Patent Document 1). [Prior art documents] [Non-patent literature]

[0009] [Non-Patent Document 1] Keisuke Takao, Takahiro Natori, Tomoma Miyata, and Naoyuki Aikawa, “A High-Precision Estimation Method of Instantaneous Frequency Using Finite-Order Hilbert Transformer,” The 34th Signal Processing Symposium, vol.B2-2, pp.237-241, Nov. 2019. Summary of the Invention [Problem to be solved by the invention]

[0010] However, the method described in Non-Patent Document 1 has a problem in that the filter needs to be redesigned every time the frequency of the input signal changes.

[0011] The disclosed technology has been made in consideration of the above-mentioned circumstances, and aims to provide a frequency estimation device, a frequency estimation method, and a frequency estimation program that are capable of estimating a frequency without having to redesign a filter every time the frequency of an input signal changes. [Means for solving the problem]

[0012] In order to achieve the above object, a frequency estimation device according to a first aspect includes a filter unit that outputs a frequency of an input signal, a Hilbert transform unit that performs a Hilbert transform on the input signal, an analytic signal generation unit that generates an analytic signal from the input signal and the transformed signal output from the Hilbert transform unit, an instantaneous frequency calculation unit that calculates an instantaneous frequency based on the analytic signal, and a filter coefficient setting unit that sets a filter coefficient of the filter unit based on the instantaneous frequency so that frequency components that are even multiples of the frequency of the input signal are removed.

[0013] In the frequency estimation device according to the first aspect, when the instantaneous frequency is a frequency higher than a Nyquist frequency corresponding to a sampling frequency at which the input signal is sampled, the filter coefficient setting unit may set the filter coefficients so as to remove aliasing noise of the instantaneous frequency and frequency components that are even multiples of a frequency of the input signal.

[0014] In the frequency estimation device according to the first aspect, the transformed signal may be a signal including an error based on an order of the Hilbert transform.

[0015] A frequency estimation method according to a second aspect includes a process in which a computer performs a Hilbert transform on an input signal, generates an analytic signal from the input signal and the Hilbert transformed signal, calculates an instantaneous frequency based on the analytic signal, sets filter coefficients of a filter section that outputs the frequency of the input signal based on the instantaneous frequency so that frequency components that are even multiples of the frequency of the input signal are removed, and outputs the frequency of the input signal based on the filter coefficients.

[0016] A frequency estimation program according to a third aspect causes a computer to execute a process of performing a Hilbert transform of an input signal, generating an analytic signal from the input signal and the Hilbert transformed signal, calculating an instantaneous frequency based on the analytic signal, setting filter coefficients of a filter section that outputs a frequency of the input signal based on the instantaneous frequency so that frequency components that are even multiples of the frequency of the input signal are removed, and outputting the frequency of the input signal based on the filter coefficients. Effect of the Invention

[0017] The disclosed technique has an advantage that it is possible to estimate the frequency without redesigning the filter every time the frequency of the input signal changes. [Brief description of the drawings]

[0018] [Figure 1] FIG. 2 is a diagram showing the amplitude characteristic of a Hilbert transformer. [Diagram 2] FIG. 2 is a diagram showing an instantaneous frequency estimated using a Hilbert transformer having the characteristics of FIG. 1; [Diagram 3] FIG. 13 is a diagram showing the Fourier spectrum of the instantaneous frequency estimated using a 42nd-order Hilbert transformer. [Figure 4] FIG. 13 is a diagram for explaining transmission zero points. [Diagram 5]FIG. 2 is a functional block diagram of a frequency estimation device. [Figure 6] FIG. 11 is a flowchart of a frequency estimation process. [Figure 7] FIG. 4 is a diagram showing the amplitude characteristics of a tunable filter. [Figure 8] FIG. 4 is a diagram showing the amplitude characteristics of a tunable filter. [Figure 9] FIG. 13 is a diagram showing an estimation result of an instantaneous frequency. [Figure 10] FIG. 10 is an enlarged view of a portion of FIG. [Figure 11] FIG. 10 is an enlarged view of a portion of FIG. [Figure 12] FIG. 13 is a diagram showing an estimation result of the instantaneous frequency of a chirp signal. [Figure 13] FIG. 13 is an enlarged view of a part of FIG. [Figure 14] FIG. 13 is a diagram for explaining aliasing noise. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings.

[0020] <Summary of the disclosed technology>

[0021] In this embodiment, a method for removing vibration components using a low-pass FIR filter with variable transmission zeros will be described, which addresses the problem in the method described in Non-Patent Document 1 mentioned above that the filter needs to be redesigned every time the frequency of the input signal changes.

[0022] The low-pass FIR filter with variable transmission zeros described below is a filter in which the transmission zeros change by an even multiple of the change in the frequency of the input signal by changing the stopband characteristics.

[0023] Zero-phase amplitude characteristic H0(e jω ) is expressed by the following formula:

[0024] JPEG0007603304000001.jpg56124...(1)

[0025] where h(n) is the filter coefficient.

[0026] Figure 1 shows the amplitude characteristics of the 42nd and 60th order Hilbert transformers designed using the Remez algorithm described in Reference 1 below. The sampling frequency is 50 kHz, and the low pass band edge frequency and high pass band edge frequency are 1.25 kHz and 27.75 kHz. As is clear from Figure 1, the ripple of a finite order Hilbert transformer becomes smaller as the order increases.

[0027] (Reference 1)

[0028] J. McClellan, T. Parks, and L. Rabiner, “A computer program for designing optimal FIR linear phase digital filters,” IEEE Transactions on Audio and Electroacoustics, vol.21, no.6, pp.506-526, Dec. 1973. Conference Name:IEEE Transactions on Audio and Electroacoustics.

[0029] The sinusoidal input signal x(t) is expressed by the following equation.

[0030] JPEG0007603304000002.jpg1372...(2)

[0031] Here, A is the amplitude and ω1 is the angular frequency. As shown in Figure 1, the difference between the ideal amplitude characteristic and the actual amplitude characteristic at a certain angular frequency ω is δ. Then, the analytic signal obtained by using a finite-order Hilbert transformer for the input signal x(t) in the above equation (2) is JPEG0007603304000003.jpg1021 is expressed by the following equation. Note that below, the analytic signal may be expressed as x^(t).

[0032] JPEG0007603304000004.jpg21118...(3)

[0033] However, x h (t) is the output of the Hilbert transformer. From this analytic signal, the instantaneous phase is expressed by the following equation:

[0034] JPEG0007603304000005.jpg2295...(4)

[0035] And the instantaneous frequency (instantaneous angular frequency) JPEG0007603304000006.jpg1117 is expressed by the following equation. Note that in the following, it may be expressed as ω~(t).

[0036] JPEG0007603304000007.jpg30111...(5)

[0037] It can be seen that the instantaneous frequency estimated from the above equation (5) contains a cosine term at angular frequencies other than ω1 where the Hilbert transformer ripple is δ=0, and is not the true angular frequency ω1. Therefore, it can be seen that the instantaneous frequency obtained using a finite-order Hilbert transformer contains an oscillatory component in addition to the true angular frequency. As described in Non-Patent Document 1 above, the relationship between the true angular frequency ω1 and other angular frequencies can be expressed by the following equation.

[0038] JPEG0007603304000008.jpg2076...(6)

[0039] However, a n is expressed by the following equation.

[0040] JPEG0007603304000009.jpg2092...(7)

[0041] Also, a nis found using the following recurrence formula:

[0042] JPEG0007603304000010.jpg1452...(8) however, JPEG0007603304000011.jpg4756

[0043] From the above equations (6) to (8), it can be seen that the estimated instantaneous angular frequency ω~(t) has the angular frequency ω1 of the input signal as a DC component, and can be expressed as the sum of cosine components whose angular frequencies that depend on δ are even multiples of ω1. Therefore, when δ ≠ 0, the instantaneous angular frequency estimated using a finite-order Hilbert transformer includes angular frequency components that are even multiples of the input signal angular frequency. Therefore, to perform highly accurate angular frequency estimation using a finite-order Hilbert transformer, it is sufficient to remove angular frequency components that are even multiples of the estimated instantaneous angular frequency.

[0044] As an example, when an input signal x(t) of 1800 Hz is input, the instantaneous frequency estimated using a Hilbert transformer having the characteristics of FIG. 1 is shown in FIG. 2. This shows that the actual estimated instantaneous frequency oscillates around the true frequency of 1800 Hz. Furthermore, FIG. 3 shows the Fourier spectrum of the instantaneous frequency estimated using a 42nd order Hilbert transformer. This graph also shows that the estimated instantaneous frequency has components of 3600 Hz, which is twice the frequency of the input signal, and 7200 Hz, which is four times the frequency. The method described in Non-Patent Document 1 makes it possible to improve the estimation accuracy by removing these oscillation components. However, with this filter, it is necessary to redesign the filter every time the frequency changes.

[0045] A filter for removing even-multiple vibration components contained in the instantaneous angular frequency will be described below. The angular frequency of the single sine wave input to the Hilbert transformer is unknown, and it is necessary to consider changes in the angular frequency, such as when performing fault diagnosis of a rotating machine. In addition, when filters having transmission zeros are simply cascaded, there is a possibility that signals will be amplified in a certain frequency band, which is a problem when handling signals containing noise. Therefore, in this embodiment, a low-pass FIR filter with variable transmission zero positions as shown in Figure 4 is used as a filter for efficiently removing vibration components contained in the estimated value. The amplitude characteristic of the filter shown in Figure 4 is given by the following equation.

[0046] JPEG0007603304000012.jpg30121...(9)

[0047] Here, B is the number of transmission zeros, and M is half the filter order. Here, c(k, α) is the filter coefficient, and since the filter coefficient c(k, α) changes when the variable parameters change, it is approximated as an L-th order polynomial using the variable parameters as follows:

[0048] JPEG0007603304000013.jpg2494...(10)

[0049] Here, g(k, l) is a polynomial coefficient, and α is the lower limit of the normalized angular frequency of the expected input signal, ω' min From the upper limit ω' max The transmission zeros are placed at even multiples of the range. The above equations (9) and (10) can be expressed in the form of a matrix as follows:

[0050] JPEG0007603304000014.jpg1457...(11)

[0051] Here, T represents a transposition, and C, A, P, and G are respectively expressed by the following equations (12) to (16).

[0052] JPEG0007603304000015.jpg14164...(12) JPEG0007603304000016.jpg2353...(13) JPEG0007603304000017.jpg31164...(14) JPEG0007603304000018.jpg24164...(15) JPEG0007603304000019.jpg26112...(16)

[0053] Here, the ideal characteristics of the filter are defined by the following equation based on FIG.

[0054] JPEG0007603304000020.jpg3387...(17)

[0055] However, ω p , ω s are the normalized angular frequency at the passband edge and the normalized angular frequency at the stopband edge, respectively.

[0056] In this case, the error function e(ω, α) is expressed by the following equation.

[0057] e(ω, α)=D(ω)-A(ω,α) ···(18)

[0058] Therefore, the filter design problem in the frequency domain can be expressed as follows:

[0059] JPEG0007603304000021.jpg1681...(19)

[0060] However, Ω is the frequency range of the approximation band, and the transition band is not evaluated, so Ω is expressed by the following equation.

[0061] JPEG0007603304000022.jpg1264...(20)

[0062] Here, when α is discretized into Q points to solve the above design problem using a computer, the above equation (18) is expressed as follows:

[0063] e(ω, α q )=D(ω)-A(ω,α q ) ···(twenty one)

[0064] Here, 1≦q≦Q. Here, λ(ω,α q ) is the positive maximum allowable error, the design problem in (19) above can be transformed into the following equation:

[0065] minimize λ(ω,α q ) ···(twenty two)

[0066] subject to e(ω, α q ) 2 ≦λ(ω,α q ) ···(twenty three)

[0067] Furthermore, the above equation (23) can be transformed into the following equation.

[0068] λ(ω, α q )-e(ω,α q ) 2 ≧0 (24)

[0069] The above equations (22) and (23) can be expressed in matrix form as follows:

[0070] JPEG0007603304000023.jpg2974...(25)

[0071] From the above equation (25), Γ(ω,α q ) is the polynomial coefficient G and the maximum positive allowable error λ(ω,α q ) and is positive semidefinite. Furthermore, the positive semidefinite condition when the approximation band Q in the above equation (25) is discretized into M divisions and α into Q divisions is expressed by the following equation:

[0072] JPEG0007603304000024.jpg2091...(26)

[0073] Here, m is a value within the range of 1≦m≦M. Therefore, when the optimization problems (22) and (23) above are discretized with respect to ω and α, they are formulated as follows:

[0074] minimaize dx T (27)

[0075] subject to U(x)≧0 ···(28)

[0076] Here, d and x are expressed by the following formula.

[0077] JPEG0007603304000025.jpg2283...(29) JPEG0007603304000026.jpg1778...(30)

[0078] Since the matrix U(x) is linear with respect to x, the above equations (27) to (30) are positive semidefinite problems.

[0079] <Configuration and Action of Frequency Estimation Device>

[0080] Fig. 5 is a diagram showing the functional configuration of the frequency estimation device 10. As shown in Fig. 5, the frequency estimation device 10 includes a Hilbert transform unit 12, an analytic signal generation unit 14, an instantaneous frequency calculation unit 16, a filter coefficient setting unit 18, and a filter unit 20.

[0081] The Hilbert transform unit 12 performs a Hilbert transform on the input signal x(t). The input signal x(t) is expressed by the above formula (2). The Hilbert transform unit 12 is configured with the above-mentioned finite-order Hilbert transformer. The converted signal x h (t) is a signal including an error based on the order of the Hilbert transform, that is, the error δ described above.

[0082] The analytic signal generator 14 receives the input signal x(t) and the transformed signal x(t) output from the Hilbert transformer 12. h The analytic signal x^(t) is generated from (t) using the above equation (3).

[0083] The instantaneous frequency calculating section 16 calculates the instantaneous frequency ω~(t) based on the analytic signal x^(t) generated by the analytic signal generating section 14 using the above equation (5).

[0084] The filter coefficient setting unit 18 sets the filter coefficient c(k,α) of the filter unit 20 using the above equation (10) based on the instantaneous frequency ω~(t) so that frequency components that are even multiples of the frequency of the input signal (t) are removed.

[0085] The filter unit 20 outputs the frequency of the input signal x(t) based on the filter coefficient c(k, α) set by the filter coefficient setting unit 18. The filter unit 20 is configured with the low-pass FIR filter with variable transmission zero positions as described above. Specifically, the filter unit 20 is configured with an FIR filter whose amplitude characteristics are A(ω, α) expressed by the above formula (9).

[0086] Each functional unit included in the frequency estimation device 10 is configured, for example, with an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), etc., but is not limited thereto. For example, the frequency estimation device 10 may be configured with a computer including a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), an input / output interface (I / O), etc. In this case, a frequency estimation program may be stored in the ROM in advance, and the CPU may read the frequency estimation program from the ROM and execute a frequency estimation process to realize each functional unit.

[0087] Next, as an operation of this embodiment, a frequency estimation process executed by the frequency estimation device 10 will be described with reference to the flowchart shown in Fig. 6. Note that the frequency estimation process in Fig. 6 is repeatedly executed while the input signal x(t) is being input.

[0088] In step S100, the input signal x(t) is subjected to the Hilbert transform.

[0089] In step S102, the input signal x(t) and the Hilbert transformed signal x(t) in step S100 are h The analytic signal x^(t) is generated from (t) using the above equation (3).

[0090] In step S104, the instantaneous frequency ω~(t) is calculated by the above equation (5) based on the analytic signal x^(t) generated in step S102.

[0091] In step S106, the filter coefficient c(k, α) of the filtering process is set by the above equation (10) based on the instantaneous frequency ω~(t) so that frequency components that are even multiples of the frequency of the input signal (t) are removed.

[0092] In step S108, a filter process is executed based on the filter coefficient c(k, α) set in step S106, and the frequency of the input signal x(t) is output.

[0093] In this manner, in this embodiment, the frequency of the input signal x(t) is estimated using a low-pass FIR filter with variable transmission zeros, in which the stopband characteristics are changed so that the transmission zeros change by an even multiple of the change in the frequency of the input signal. This makes it possible to estimate the frequency of the input signal x(t) without redesigning the filter every time the frequency of the input signal x(t) changes.

[0094] <Example>

[0095] Examples will now be described.

[0096] Here, it is shown by simulation that the instantaneous frequency can be estimated with high accuracy by using the low-pass FIR filter (hereinafter referred to as a variable filter) with variable transmission zero points as described above. In this simulation, a signal with an amplitude of 1 and a frequency that changes discontinuously in the range of 1600 Hz to 2000 Hz was used as the input signal. The sampling frequency was set to 50 kHz, the order of the Hilbert transformer was set to 42, and the low-passband edge frequency and the high-passband edge frequency were set to 1.25 kHz and 27.75 kHz, respectively. The passband edge frequency and the stopband edge frequency of the variable filter were set to 2.5 Hz and 3000 Hz, respectively, and the various parameters were set to the order 2N=12, the polynomial order L=3, the number of transmission zero points B=2, 3, and the range of the variable parameter α was set to the range where the frequency of the input signal was 1600 to 2000 Hz. For these design specifications, the evaluation points were divided into 10 equal parts in the passband and 990 equal parts in the stopband, and the design was performed by discretizing the change in the variable parameters into 10 equal parts. In this case, the amplitude characteristics of the tunable filter designed with the number of notches B = 3 are shown in Figures 7 and 8. These are the amplitude characteristics when the frequencies of the sine wave input signals are 1680Hz and 1900Hz, respectively. Therefore, the positions of the transmission zeros are 2, 4, and 6 times the frequencies of these input signals, which are shown by the dashed lines. It can be seen that the tunable filter obtained has quasi-equal ripple characteristics.

[0097] In addition, the parameters of the variable filter must be changed using the estimated instantaneous frequency. However, if the instantaneous frequency before filtering is used, the transmission zero point position will also fluctuate due to the influence of vibration components. Therefore, we used the ω calculated by the above formula (5) as the initial value, and then used the frequency output from the variable filter as the parameter.

[0098] Figure 9 shows the results of estimating the instantaneous frequency for an input signal. Here, the instantaneous frequency estimated using a Hilbert transformer and the results when the vibration component is removed using a variable filter are shown superimposed. Enlarged graphs of the estimation results are shown in Figures 10 and 11. These show that the ripple, or error δ, of the Hilbert transformer differs depending on the frequency of the input signal, and therefore the estimation accuracy also differs. For example, 1700 Hz shown in Figure 10 is ω1 in Figure 1, and in that case δ = -12.18 × 10 -3 In addition, 1900Hz shown in Figure 11 is ω2 in Figure 1, and then δ = -2.35 × 10 -3 As can be seen from Figs. 10 and 11, the number of transmission zeros needs to be determined depending on the magnitude and accuracy of the error δ.

[0099] Fig. 12 shows the results of estimating frequency by applying the technology of the present disclosure to a chirp signal whose frequency increases with time. Fig. 13 shows an enlarged view of a part of Fig. 12. As shown in Figs. 12 and 13, it was found that the ideal frequency could be tracked in both cases of B=2 and B=3, compared to the case where only the Hilbert transform was performed (HT only).

[0100] From the above, it has been confirmed that the technology disclosed herein can effectively remove vibration components contained in instantaneous frequencies.

[0101] <Modification>

[0102] As described above, the frequency of the vibration component generated in the instantaneous frequency is an even multiple of the frequency of the input signal, and it is necessary to remove the vibration component of this even multiple instantaneous frequency. Here, if the instantaneous frequency is a frequency higher than the Nyquist frequency corresponding to the sampling frequency for sampling the input signal, so-called aliasing noise occurs.

[0103] For example, as shown in FIG. 14, the frequency of the input signal x(t) is f0=4 kHz, and the sampling frequency f S = 10kHz, Nyquist frequency f NIn this case, it is necessary to remove the vibration components with instantaneous frequencies of 8 kHz, which is twice the frequency f0, and 16 kHz, which is four times the frequency f0.

[0104] For example, for an instantaneous frequency of 8 kHz, the Nyquist frequency f N Since aliasing noise occurs at a frequency of 2 kHz with respect to the axis of symmetry, the aliasing noise at the frequency of 2 kHz must also be removed.

[0105] Therefore, when the instantaneous frequency is higher than the Nyquist frequency corresponding to the sampling frequency for sampling the input signal, the filter coefficient setting unit 18 may set the filter coefficient so as to remove aliasing noise of the instantaneous frequency and frequency components that are even multiples of the input signal frequency, thereby enabling the frequency to be estimated with high accuracy.

[0106] Note that the present embodiment does not limit the invention according to the claims, and not all of the combinations of features described in the embodiment are necessarily essential to the solution of the invention. The above-mentioned embodiment includes inventions at various stages, and various inventions are extracted by combining the multiple components disclosed. Even if some components are deleted from all the components shown in the embodiment, as long as the effect can be obtained, the configuration from which these some components are deleted can be extracted as an invention. [Explanation of symbols]

[0107] 10 Frequency Estimation Device 12 Hilbert transform section 14 Analysis signal generation section 16 Instantaneous frequency calculation section 18 Filter coefficient setting section 20 Filter section

Claims

1. A filter unit that outputs a frequency of an input signal; a Hilbert transform unit that performs a Hilbert transform on the input signal; an analytic signal generator that generates an analytic signal from the input signal and a transformed signal output from the Hilbert transformer; an instantaneous frequency calculation unit that calculates an instantaneous frequency based on the analytic signal; a filter coefficient setting unit that sets a filter coefficient of the filter unit based on the instantaneous frequency so that frequency components that are even multiples of the frequency of the input signal are removed; Equipped with The transformed signal is a signal including an error based on the order of the Hilbert transform. Frequency estimator.

2. When the instantaneous frequency is a frequency higher than a Nyquist frequency corresponding to a sampling frequency for sampling the input signal, the filter coefficient setting unit sets the filter coefficient so as to remove aliasing noise of frequency components that are even multiples of the instantaneous frequency and the frequency of the input signal.

2. The frequency estimation device according to claim 1.

3. The computer The input signal is subjected to a Hilbert transform, generating an analytic signal from the input signal and the Hilbert transformed signal; Calculating an instantaneous frequency based on the analytic signal; setting a filter coefficient of a filter unit that outputs a frequency of the input signal based on the instantaneous frequency so that a frequency component that is an even multiple of the frequency of the input signal is removed; Outputting the frequency of the input signal based on the filter coefficient Execute the process, The transformed signal is a signal including an error based on the order of the Hilbert transform. Frequency estimation method.

4. On the computer, The input signal is subjected to a Hilbert transform, generating an analytic signal from the input signal and the Hilbert transformed signal; Calculating an instantaneous frequency based on the analytic signal; setting a filter coefficient of a filter unit that outputs a frequency of the input signal based on the instantaneous frequency so that a frequency component that is an even multiple of the frequency of the input signal is removed; Outputting the frequency of the input signal based on the filter coefficient Execute the process, The transformed signal is a signal including an error based on the order of the Hilbert transform. A frequency estimation program.

Images