Frequency analysis device

Abstract

The purpose of the present disclosure is to provide a frequency analysis device capable of determining a frequency with a higher accuracy than a frequency resolution. A frequency analysis device according to the present disclosure divides a signal wave in the time domain into a plurality of sections at predetermined time intervals, and performs discrete Fourier transform on each of the plurality of sections into which the signal wave has been divided. Furthermore, the frequency analysis device calculates a frequency spectrum by combining the signal waves subjected to the discrete Fourier transform in the plurality of sections, and determines a provisionally determined frequency from the frequency spectrum. Furthermore, the frequency analysis device calculates a section phase difference, which is a phase difference between the signal waves in adjacent sections, for at least one set of the plurality of sections. The frequency analysis device corrects the provisionally determined frequency using the section phase difference.

Description

Frequency analyzer

[0001] This disclosure relates to a technique for analyzing frequency and detecting signals buried in noise.

[0002] Non-patent document 1 discloses a signal detection technique for determining frequency. In it, a predetermined time (T o For each waveform extracted, a Discrete Fourier Transform (DFT) is performed, and the Fourier-transformed waveform (also called the frequency spectrum) or its square (power) is averaged. This allows for the extraction of spectral characteristics and the detection of signals buried in noise.

[0003] Market Trends Report "History and Applications of FFT Analyzers," March 2014 issue, TechEyes Vol.04

[0004] However, the frequency determined by the method described above has a frequency resolution Δf = (1 / T o Due to the uncertainty caused by ( ), it is difficult to detect the exact frequency.

[0005] This disclosure aims to provide a frequency analyzer capable of determining frequencies with higher accuracy than frequency resolution in order to solve the above-mentioned problems.

[0006] Preferably, the present disclosure is a frequency analysis device configured to perform the following: dividing a time-domain signal wave into a plurality of intervals at predetermined time intervals; performing a discrete Fourier transform on each of the signal waves divided into the plurality of intervals; calculating a frequency spectrum by synthesizing the signal waves that have been discrete Fourier transformed in the plurality of intervals; determining a provisionally determined frequency from the frequency spectrum; calculating an interval phase difference, which is the phase difference between adjacent signal waves, for at least one pair of the plurality of intervals; and correcting the provisionally determined frequency using the interval phase difference.

[0007] In this disclosure, the interval phase difference θ is the phase difference of the signal wave r(t) in adjacent intervals. nUsing this, the provision of a frequency analysis device capable of determining a frequency with higher accuracy than the frequency resolution by correcting the provisionally determined frequency (kΔf) can be achieved.

[0008] It is a block diagram of the frequency analysis device according to Embodiment 1. It is a waveform example of the signal wave r(t) according to Embodiment 1. It is a waveform example of the signal wave r(t) in the first to third sections according to Embodiment 1. Fourier transform vector r n ^(f) waveform example. The first frequency spectrum r according to Embodiment 1 av ^(f) waveform example. The signal wave r according to Embodiment 1 n (t) and the phase-adjusted signal wave r n ’ (t) waveform example. The synthesized signal wave r according to Embodiment 1 ad (t) waveform example. The second frequency spectrum r according to Embodiment 1 ad ^(f) waveform example. The desired wave s according to Embodiment 1 n (t) waveform example. The relationship between the desired wave s n (t) and the phase difference θ in the first to third sections. Fourier transform vector s according to Embodiment 1 n+1 ^(f s ) and s n ^(f s ) shown on the complex plane. The Fourier transform vector r of the signal wave in the nth section according to Embodiment 1 n ^(kΔf) rotation state diagram. Fourier transform vector r from the first to nth sections according to Embodiment 1 n ^(kΔf) characteristics summary diagram. Time-series data to be analyzed according to Embodiment 1. The first frequency spectrum r created from the time-series data to be analyzed according to Embodiment 1 av ^(nΔt). Fourier transform vector r of the analysis target according to Embodiment 1 n ^(kΔf) characteristics summary diagram. The second frequency spectrum r created from the time-series data to be analyzed according to Embodiment 1 ad^(f). This is a diagram explaining the reason why the signal-to-noise ratio can be improved according to Embodiment 1. This is a diagram explaining the reason why the signal-to-noise ratio can be improved according to Embodiment 1. This is a diagram showing the hardware configuration of the frequency analyzer according to Embodiment 1.

[0009] Embodiments of this disclosure will be described with reference to the drawings. The same or corresponding components will be denoted by the same reference numerals, and repetition of the description may be omitted.

[0010] Embodiment 1 Figure 1 is a block diagram of a frequency analysis device 100 according to Embodiment 1. The signal wave received by antenna 1 passes through a high-frequency (RF) band-pass filter (BPF) 2 and is amplified by amplifier 3. The amplified signal wave is input to a quadrature demodulator 20 equipped with a 90-degree splitter 4 and an AC power supply. In the quadrature demodulator 20, the signal wave and the local oscillator wave are complex multiplied by a multiplier 5 and output a signal wave with an intermediate frequency between the I component and the Q component.

[0011] The I component and Q component signal waves pass through separately provided band-pass filters 6, and are sampled at a sampling time Δt by separately provided AD converters 7. The waveforms of the digitized signal waves are stored in the first memory circuit 8.

[0012] Hereafter, the time-domain signal wave demodulated by the quadrature demodulator 20 will be denoted as r(t), where n is an integer from 0 to (T0 / Δt). The digitized I component signal wave will be denoted as Re[r(nΔt)], and the digitized Q component signal wave will be denoted as Im[r(nΔt)]. For an example of the signal wave r(t), please refer to Figure 2.

[0013] The DFT calculation circuit 9 divides the signal wave r(nΔt) into predetermined time intervals T0 from the first interval to the q interval. For examples of the waveforms of the signal wave r(t) divided into the first to third intervals, please refer to Figure 3.

[0014] Furthermore, the DFT calculation circuit 9 performs a discrete Fourier transform on each of the signal waves r(nΔt) from the first interval to the q-th interval. The discrete Fourier transform of the signal wave r(nΔt) in the n-th interval is expressed by the following (Equation 1).

[0015]

[0016] Here, N is the number of samples of the signal wave r(nΔt) at time T0, k is an integer, and Δf is the frequency resolution.

[0017]

[0018] Hereafter, we will discuss the discrete Fourier transform r in the nth interval. n ^(f) is called the Fourier transform vector in the nth interval. The hat symbol "^" indicates that it is a vector. Note that the Fourier transform vector r from the first to the third interval is also shown. n See Figure 4 for an example of the waveform of ^(f).

[0019] The second memory circuit 10 stores the Fourier transform vector r calculated by the DFT calculation circuit 9. n The waveform of ^(f) is stored. The averaging circuit 11 calculates the Fourier transform vector r from the first interval to the q interval. n By averaging the amplitude of ^(f), the first frequency spectrum r av Find ^(f).

[0020]

[0021] Note that the first frequency spectrum r av See Figure 5 for an example of the waveform of ^(f) and its enlarged view. The frequency resolution is Δf = (1 / T o )

[0022] Note that the first frequency spectrum r av In calculating ^(f), in (Equation 3), the Fourier transform vector r n Alternatively, instead of using the absolute value of ^(f), we can average the square of the absolute value (power). Also, the Fourier transform vector r n ^(f) does not necessarily have to be averaged; it can be simply added together or combined in other ways.

[0023] The third memory circuit 13 is the first frequency spectrum r av The waveform of ^(f) is stored. The frequency identification circuit 12 determines the first frequency spectrum r avThe frequency of the signal wave r(t) is tentatively determined from the peak position (kΔf) of ^(nΔt). The tentatively determined frequency (kΔf) has uncertainty due to the frequency resolution Δf.

[0024] The phase angle calculation circuit 14 calculates the signal wave r in adjacent intervals. n-1 (t) and r n The phase difference of (t) is the interval phase difference θ n (See Equation 12) is calculated for all combinations from the first interval to the qth interval (calculation process). Furthermore, the phase angle calculation circuit 14 calculates the interval phase difference θ n By averaging, the averaged phase difference θ av The averaging process calculates the r of the signal wave r in the nth interval (where n is 2 to q). n With respect to (t), the phase angle is ((n-1)θ av ) By advancing, the signal wave r is phase-adjusted (composite phase). n ’ Calculate (t).

[0025]

[0026] Note that the signal wave r n (t) and the phase-adjusted (in-phase) signal wave r n ’ For an example of the waveform of (t), please refer to Figure 6.

[0027] Furthermore, the phase angle calculation circuit 14 calculates the phase-adjusted (in-phase) signal wave r from the first section to the q section. n ’ The signal wave r is synthesized by weighting the amplitudes of (t). ad Calculate (t). Note that the signal wave r is synthesized by common-mode addition. ad For an example of the waveform of (t), please refer to Figure 7.

[0028]

[0029] Furthermore, the phase angle calculation circuit 14 calculates the combined signal wave r ad By performing a discrete Fourier transform on (t), the synthesized signal wave r is obtained. ad(t) frequency spectrum (second frequency spectrum r ad We obtain ^(f)). Note that the second frequency spectrum r ad See Figure 8 for an example of the waveform of ^(f).

[0030] Furthermore, the phase angle calculation circuit 14 corrects the provisionally determined frequency (kΔf) using a method described later to obtain the true frequency f s Calculate (correction process).

[0031] The display unit 15 shows the second frequency spectrum r ad ^(f) and the true frequency f s Display the results.

[0032] As explained above, the frequency analyzer 100 of this disclosure analyzes the first frequency spectrum r av By correcting the provisional frequency (kΔf) obtained from ^(nΔt), the true frequency f s We seek.

[0033] <The true frequency f of the signal buried in noise> s Method for determining the true frequency f s This explains how to find it.

[0034] Signal wave r in the nth section n (t) is the true frequency f s The desired wave s that vibrates n It is expressed as the sum of (t) and noise ξ. Note that the desired wave s n An example of the waveform for (t) is shown in Figure 9.

[0035]

[0036]

[0037] As shown in Figure 10, the desired wave s for the (n+1)th interval n+1 Phase angle Φ of (t) n+1 This is the desired wave s of the nth interval. ｎ Phase angle Φ of (t) n It is delayed by a phase difference θ compared to [the previous state].

[0038]

[0039]

[0040] As shown in (Equation 8), the phase difference θ is the difference between the tentatively determined frequency (kΔf) and the true frequency f s This is the angle resulting from the difference with the true frequency f. s To find this, we need to find the phase difference θ.

[0041] The Fourier transform vector s of the desired wave in the (n+1)th interval. n+1 ^(f s ) and the Fourier transform vector s of the desired wave in the nth interval n ^(f s Using ), the phase difference θ is expressed as follows:

[0042]

[0043]

[0044] As shown in Figure 11, the Fourier transform vector s of the desired wave in the (n+1)th interval is in the complex plane. n+1 ^(f s ) is the Fourier transform vector s of the desired wave in the nth interval. n ^(f s ) with respect to the phase difference θ = 2π(f s It is rotating by -kΔf)T0.

[0045] Following (Equation 10), the Fourier transform vector r of the signal wave in the nth interval is obtained. n ^(kΔf) and the Fourier transform vector r of the signal wave in the (n-1)th interval n-1 ^(kΔf) interval phase difference θ n It can be expressed as follows:

[0046]

[0047] Furthermore, without using the Fourier transform vector, the signal wave r in the nth interval n (t) and the signal wave r in the (n-1)th interval n-1 (t) interval phase difference θ n It is also possible to find the interval phase difference θ by using the Fourier transform vector. n This can improve the accuracy of the calculation.

[0048] The interval phase difference θ obtained from (Equation 12)n Since it includes the influence of noise ξ, it is preferable to average the interval phase difference θ n for n from 2 to q. As an example, the weighted average considering the amplitude A n of the Fourier transform vector r n ^(kΔf) is given. In that case, the Fourier transform vector r n ^(kΔf) is assumed as follows.

[0049]

[0050] The Fourier transform vector r n ^(kΔf) amplitude A n The averaged phase difference θ av is obtained as follows.

[0051]

[0052]

[0053] Note that the method of averaging is not necessarily a weighted average, and it may be a simple average of the interval phase difference θ n or other methods. Also, in the averaging process, it is not necessary to average all the interval phase differences θ n from the second interval to the q-th interval, and a part of them may be used.

[0054] Here, obtaining the averaged phase difference θ av means, as shown in Fig. 12, rotating the Fourier transform vector r n ^(kΔf) in the n-th interval (n from 2 to q) by ((n - 1)θ av ) so as to align it as much as possible with the direction of the Fourier transform vector r1^(kΔf) in the first interval.

[0055] The true frequency f s is determined as follows from (Equation 8) using the temporarily determined frequency (kΔf) and the averaged phase difference θ av .

[0056]

[0057] Fig. 13 shows the Fourier transform vector r from the first interval to the n-th intervaln Amplitude A of ^(kΔf) n , phase angle Φ n , interval phase difference θ n , and amplitude A n Weighted interval phase difference A n θ n This is summarized. The last line shows the averaged phase difference θ obtained by (Equation 14). av This is shown.

[0058] <Verification Results> True frequency f s This section explains the results of frequency analysis using the method described above for time-series data obtained by adding Gaussian noise ξ to a desired sinusoidal wave s(t) oscillating at 3.222 Hz. Please refer to Figure 14 for the time-series data analyzed. The sampling time Δt is 0.01 s.

[0059] In the frequency analysis, time T0 was set to 1 s. In this case, the frequency resolution is Δf = 1 / T0 = 1 Hz.

[0060] Figure 15 shows the first frequency spectrum r created from the time-series data being analyzed. av ^(f) is shown. The first frequency spectrum r av The provisional frequency (kΔf) obtained by ^(f) was 3 Hz. The true frequency f s Given that the correct answer is 3.222 Hz and the frequency resolution Δf is 1 Hz, the determined provisional frequency (kΔf) can be considered a reasonable result.

[0061] Furthermore, using the result of the provisionally determined frequency (kΔf), the correct value of the phase difference θ can be found from (Equation 8) as (3.222Hz - 3Hz) / 1 × 360(degrees) = 80 degrees.

[0062] Figure 16 shows the Fourier transform vector r of the subject of analysis. n Amplitude A of ^(kΔf) n , phase angle Φ n , interval phase difference θ n , and amplitude A n Weighted interval phase difference A n θ n This is a table summarizing the calculation results. The last row shows the averaged phase difference θ calculated by (Equation 14).av This is shown. Averaged phase difference θ av The calculation result was 80.505232 degrees. Considering that the correct value for the phase difference θ is 80 degrees, the obtained averaged phase difference θ av This can be considered a reasonable result.

[0063] Furthermore, (Equation 16) gives the true frequency f s The true frequency f was calculated as (3 + 80.505232 / 360) = 3.22362564444. s Since the correct answer is 3.222 Hz, this result can be considered reasonable. The method disclosed herein allows for the true frequency f with higher precision than the frequency resolution Δf. s It is clear that this has been determined.

[0064] Figure 17 shows the second frequency spectrum r created from the time-series data being analyzed. ad ^(f) is shown. The second frequency spectrum r ad The signal-to-noise ratio of ^(f) is 0.102, and the first frequency spectrum r av It was higher than the signal-to-noise ratio of ^(f), which is 0.0368.

[0065] Here, in the method of Non-Patent Document 1, the first frequency spectrum r as referred to in this disclosure av ^(f) is calculated. However, this method has the problem that the signal-to-noise ratio of the frequency spectrum cannot be improved by analysis. In this disclosure, the signal wave r in each section is calculated. n By considering the phase angle of (t), the signal-to-noise ratio of the frequency spectrum can be improved.

[0066] <Reasons why the signal-to-noise ratio can be improved> As shown in Figure 18, in this disclosure, the time-domain signal wave r(t) is divided into multiple sections (here, section A and section B). As shown in Figure 19, the signal wave r in section B B (t) is the signal wave r in section A. A With respect to (t), the phase difference θ AB It is delayed by only that much. Therefore, the signal wave r in section B B The phase angle of (t) has a phase difference θ. AB The signal wave r is phase-adjusted (in-phase) by adding it. BCalculate (t). The signal wave r in section A. A (t) and the phase-adjusted (in-phase) signal wave r in section B B By adding (t), the signal waves r are combined (in-phase added) to match the phase. ad (t) is obtained. The signal wave r is synthesized q times. ad In (t), the signal strength is q 2 The signal wave r is multiplied by two, while the noise intensity is multiplied by q. Therefore, the signal wave r is obtained by combining (common-mode addition) q times. ad The frequency spectrum r created from (t) ad ^(t) represents the frequency spectrum r of the comparative example. av Compared to ^(f), the signal-to-noise ratio is q times (=q 2 / q) To improve

[0067] Thus, the frequency spectrum r of Non-Patent Document 1 av While method (f) cannot improve the signal-to-noise ratio of the frequency spectrum, this disclosure can improve the signal-to-noise ratio of the frequency spectrum.

[0068] Figure 20 shows the hardware configuration of the frequency analysis device 100. The processing performed by the frequency analysis device 100 may be executed by a program using a computer equipped with a CPU and memory, in which a frequency analysis program is stored.

[0069] The frequency analysis program may be provided on a storage medium or via a network.

[0070] The frequency analyzer 100 has an input unit 40, an output unit 41, a communication unit 42, a CPU (Central Processing Unit, also called a processor) 43, a memory 44, and an HDD (Hard Disk Drive) 45 connected via a bus 46, and functions as a computer. The frequency analyzer 100 is also configured to input and output data to and from a storage medium 47 that can be read by a computer.

[0071] The input unit 40 is, for example, a keyboard and mouse. The output unit 41 is, for example, a display device such as a display.

[0072] The communication unit 42 is, for example, a communication interface that communicates with a transmitter.

[0073] Memory 44 refers to volatile or non-volatile semiconductor memory such as RAM, ROM, and flash memory, or magnetic disks, flexible disks, optical disks, and DVDs.

[0074] The CPU 43 controls each component of the frequency analysis device 100 and performs predetermined processing. The memory 44 and HDD 45 are, for example, the first memory circuit 8, the second memory circuit 10, and the third memory circuit 13 described above.

[0075] The storage medium 47 is capable of storing frequency analysis programs and the like that which execute the functions of the frequency analysis device 100. The storage medium 47 can be a USB (Universal Serial Bus) memory, a CD-ROM (Compact Disc Read Only Memory), or the like.

[0076] Note that the architecture of the frequency analyzer 100 is not limited to the example shown in the figure.

[0077] As explained above, in this disclosure, the interval phase difference θ is the phase difference of the signal wave r(t) in adjacent intervals. n The provisionally determined frequency (kΔf) is corrected using this method. This makes it possible to provide a frequency analysis device that can determine the frequency with higher accuracy than the frequency resolution Δf.

[0078] Specifically, in this disclosure, the sampling interval Δt corresponds to time T o The terms r1(t), r2(t), ..., r are separated into segments. q The time series signals (t) are each subjected to a discrete Fourier transform, and the frequency at which the absolute value is maximized in all intervals (k is an integer, -T) is obtained. o / Δt≦k≦T o / Δt,Δf=1 / T o The kΔf) in the interval is tentatively determined as the frequency of the desired wave to be detected, which is buried in noise. Furthermore, the signal wave r in the adjacent interval is also determined. n-1 (t) and r n (t) interval phase difference θ nThis is obtained by taking the difference in the complex phase angles of the discrete Fourier transform. Furthermore, the interval phase difference θ over the entire interval is obtained. n The phase difference θ is obtained by weighting and averaging the values. av The frequency is determined. Furthermore, the desired frequency of the wave is determined by correcting the provisionally determined frequency (kΔf) based on (Equation 16). Furthermore, the phase difference θ of the signal wave in each section is averaged. av The signals are shifted and adjusted (in-phase), and then combined (in-phase addition). Furthermore, the signal obtained by adding the signals q times through in-phase addition has a signal-to-noise ratio (SNR) that is improved by a factor of q. This allows for better extraction of spectral characteristics and improved SNR compared to signal detection by averaging the spectrum. This makes it possible to provide a frequency analyzer that can determine frequencies with higher accuracy than the frequency resolution.

[0079] <Variation 1> Note that the true frequency f s When calculating this, it is not always necessary to use (Equation 16). For example, interval phase difference θ n If the calculation accuracy is good, the averaged phase difference θ in (Equation 16) av Instead, a specific interval phase difference θ n The true frequency f is obtained using the value of f s You may also request this.

[0080] <Modification 2> The signal wave r(t) to be analyzed by the frequency analysis device 100 of this disclosure is not limited to the received wave received by the antenna 1, but can be any signal wave in the time domain. Therefore, the frequency analysis device 100 only needs to include at least a DFT calculation circuit 9, an averaging circuit 11, a frequency identification circuit 12, and a phase angle calculation circuit 14, and in this case as well, the same effects as described above can be obtained.

[0081] <Variation 3> In the above, in the calculation process, the interval phase difference θ is used for all combinations from the first interval to the qth interval. n We explained how to calculate the interval phase difference θ. n It is not necessary to find this for all combinations; it is sufficient to find it for at least one pair from the first to the qth interval. Interval phase difference θ n If calculations are performed for multiple sets, the averaging process described above may be performed only for those multiple sets.

[0082] <Modification 4> In the above, the phase angle calculation circuit 14 calculates the signal wave r in the nth interval (where n is from 2 to q). n With respect to (t), the phase angle is ((n-1)θ av ) By advancing, the phase-adjusted signal wave r n ’ We explained how to calculate (t). This involves calculating the signal wave r in the nth interval (from n = 2 to q) so that it is phase-matched to the signal wave r1(t) in the first interval. n This means adjusting the phase of (t). However, the signal wave to be phase-matched does not necessarily have to be the signal wave r1(t) in the first section; it can be any signal wave in a specific section.

[0083] This disclosure is not limited to the embodiments described above, and various modifications can be made during implementation without departing from its essence. Furthermore, each embodiment and its modifications may be combined as appropriate, and in that case, the combined effects can be obtained.

[0084] <Correspondence with terms used in the claims> The true frequency f obtained by (Equation 16) s The corrected frequency f s It is called the first frequency spectrum r av In the claims, ^(f) is simply referred to as the frequency spectrum.

[0085] 1: Antenna, 2: Bandpass filter, 3: Amplifier, 5: Multiplier, 6: Bandpass filter, 7: AD converter, 8: First memory circuit, 9: DFT calculation circuit, 10: Second memory circuit, 11: Averaging circuit, 12: Frequency identification circuit, 13: Third memory circuit, 14: Phase angle calculation circuit, 15: Display, 20: Quadrature demodulator, 40: Input section, 41: Output section, 42: Communication section, 43: CPU, 44: Memory, 45: HDD, 46: Bus, 47: Storage medium, 100: Frequency analyzer

Claims

1. A frequency analyzer configured to perform the following: dividing a time-domain signal wave into a plurality of intervals at predetermined time intervals; performing a discrete Fourier transform on each of the signal waves divided into the plurality of intervals; calculating a frequency spectrum by synthesizing the signal waves that have been discrete Fourier transformed in the plurality of intervals; determining a provisional frequency from the frequency spectrum; calculating an interval phase difference, which is the phase difference between the signal waves in adjacent intervals, for at least one pair of the plurality of intervals; and correcting the provisional frequency using the interval phase difference.

2. The frequency analyzer according to claim 1, wherein the calculation process includes a process for calculating multiple sets of interval phase differences for different intervals, the correction process includes an averaging process for calculating an averaged phase difference by averaging the multiple sets of interval phase differences, and the provisionally determined frequency is corrected based on the averaged phase difference.

3. The frequency analyzer according to claim 2, wherein the averaging process includes: a process of calculating the amplitudes of the Fourier transform vectors in adjacent intervals for multiple sets of intervals; and a process of calculating the averaged phase difference by weighting the interval phase difference in adjacent intervals by the amplitudes in those intervals and then averaging them.

4. In the correction process, let the predetermined time be T0, the provisionally determined frequency be kΔf, where k is an integer, the frequency resolution of the frequency spectrum be Δf = 1 / T0, and the averaged phase difference be θ av and obtain the corrected frequency f s by the following formula. The frequency analysis device according to claim 2 or 3

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