Frequency analysis device

Abstract

The purpose of the present disclosure is to provide a frequency analysis device capable of determining the frequency of a signal of a weak desired wave with higher accuracy than frequency resolution. A frequency analysis device according to the present disclosure is configured to execute: a process of acquiring the frequency of a signal wave; a process of dividing the signal wave in a time domain into a plurality of sections at predetermined time intervals; a calculation process of calculating, for at least one set among the plurality of sections, a section phase difference which is the phase difference of the signal wave between adjacent sections; and a correction process of correcting the frequency using the section phase difference.

Description

Frequency analyzer

[0001] This disclosure relates to a technique for analyzing and measuring the frequency of a weak desired wave signal.

[0002] Non-patent document 1 describes a predetermined time (T o A technique has been disclosed in which a Discrete Fourier Transform (DFT) is performed on each of the waveforms extracted for each step, and the frequency of the weak desired wave signal (also called the target signal) is determined by averaging the Fourier-transformed waveform (also called the frequency spectrum) or its square (power).

[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 determine the exact frequency of a weak desired wave signal.

[0005] To solve the above-mentioned problems, this disclosure aims to provide a frequency analyzer capable of determining the frequency of a weak desired wave signal with higher accuracy than frequency resolution.

[0006] Preferably, the present disclosure is a frequency analyzer configured to perform: a process for acquiring the frequency of a signal wave; a process for dividing the time-domain signal wave into a plurality of intervals at predetermined time intervals; a calculation process for calculating interval phase differences, which are the phase differences of the signal wave in adjacent intervals, for at least one pair of the plurality of intervals; and a correction process for correcting the frequency using the interval phase differences.

[0007] 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 analyzer that can determine the frequency of a weak desired wave signal with higher accuracy than the frequency resolution.

[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 intervals according to Embodiment 1. Fourier transform vector r of the signal wave r(t) in the first to third intervals according to Embodiment 1 n ^(f) is a waveform example. Signal wave r according to Embodiment 1 n (t) and the waveform example of the phase-adjusted signal wave r n ’ (t). The waveform example of the synthesized signal wave r according to Embodiment 1 ad (t). The waveform example of the frequency spectrum r according to Embodiment 1 ad ^(f). The waveform example of the desired wave s according to Embodiment 1 n (t). It is a diagram showing the relationship between the desired wave s in the first to third intervals n (t) and the phase difference θ. Fourier transform vector s of the signal wave according to Embodiment 1 n+1 ^(f s ) and s n ^(f s ) shown on the complex plane. It is a diagram showing the state of rotating the Fourier transform vector r of the signal wave in the nth interval according to Embodiment 1 n ^(kΔf). It is a diagram summarizing the characteristics of the Fourier transform vector r in the first to nth intervals according to Embodiment 1 n ^(kΔf). It is the time-series data to be analyzed according to Embodiment 1. Fourier transform vector r of the analysis target according to Embodiment 1 n ^(kΔf) is a diagram summarizing the characteristics. Frequency spectrum r created from the time-series data to be analyzed according to Embodiment 1 ad ^(f). Frequency spectrum r of the comparative example created from the time-series data to be analyzed av ^(nΔt). It is a diagram explaining the reason why the SN ratio can be improved according to Embodiment 1. It is a diagram explaining the reason why the SN ratio can be improved according to Embodiment 1. It is a diagram showing the hardware configuration of the frequency analysis device 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 Store the waveform of ^(f).

[0020] The frequency determination circuit 12 obtains the provisional frequency of the signal wave r(t). The method for obtaining the provisional frequency is not limited, but for example, the Fourier transform vector r in at least one of the intervals from the first interval to the q-th interval. n The frequency may be obtained based on the peak position (kΔf) of ^(nΔt). Alternatively, it may be pre-stored in a memory circuit (not shown) as the frequency of the signal wave that may be received by antenna 1. The tentatively determined frequency is obtained from the discrete Fourier transform r of the signal wave. n It is expressed as (kΔf) using the frequency resolution Δf at ^(f).

[0021] 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 11) 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).

[0022]

[0023] 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 5.

[0024] 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 6.

[0025]

[0026] 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 r ad We obtain ^(f). Note that the frequency spectrum r ad See Figure 7 for an example of the ^(f) waveform.

[0027] Furthermore, the phase angle calculation circuit 14 corrects the provisionally determined frequency (kΔf) obtained by the frequency identification circuit 12 using a method described later, thereby correcting the true frequency f s Determine (correction process).

[0028] The display unit 15 shows the frequency spectrum r ad ^(f) and the true frequency f s Display the results.

[0029] As explained above, the frequency analyzer 100 of this disclosure corrects the provisionally determined frequency (kΔf) to obtain the true frequency f s We seek.

[0030] <The true frequency f of the desired wave (target signal) s Method for determining the true frequency f s This explains how to find it.

[0031] 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 8.

[0032]

[0033]

[0034] As shown in Figure 9, 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].

[0035]

[0036]

[0037] As shown in (Equation 7), 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.

[0038] 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:

[0039]

[0040]

[0041] As shown in Figure 10, 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.

[0042] Following (Equation 9), 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:

[0043]

[0044] 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.

[0045] The interval phase difference θ can be obtained from (Equation 11). n Since noise ξ is included in the effect, the interval phase difference θ applies to n from 2 to q. n It is preferable to perform an averaging process on the Fourier transform vector r. n Amplitude A of ^(kΔf) n A weighted average that takes this into account can be used. In this case, the Fourier transform vector r n Assume that ^(kΔf) is as follows:

[0046]

[0047] Fourier transform vector r n Amplitude A of ^(kΔf) n The averaged phase difference θ is calculated using a weighted average that takes this into account. av It can be calculated as follows.

[0048]

[0049]

[0050] Furthermore, the averaging method does not necessarily have to be a weighted average; the interval phase difference θ is also used. nIt may be a simple average or other methods. Also, in the averaging process, it is not always necessary to average all the interval phase differences θ from the second interval to the q-th interval. n It is not necessary to average all of them, and a part of them may be sufficient.

[0051] [[ID=*5]] Here, obtaining the averaged phase difference θ av means, as shown in FIG. 11, rotating the Fourier transform vector r n ^(kΔf) in the n-th interval (where n ranges from 2 to q) by ((n - 1)θ av ) so as to align it as closely as possible with the direction of the Fourier transform vector r1^(kΔf) in the first interval.

[0052] The true frequency f s is determined as follows from Equation (7) using the temporarily determined frequency (kΔf) and the averaged phase difference θ av .

[0053]

[0054] In FIG. 12, the amplitude A n of the Fourier transform vector r n ^(kΔf) from the first interval to the n-th interval, the phase angle Φ n , the interval phase difference θ n , and the interval phase difference A n weighted by the amplitude A n θ n are summarized. In the last row, the averaged phase difference θ av obtained by Equation (13) is shown. <E0002*91>

[0055] 〈Verification Results〉 The results of analyzing the frequency of the time series data obtained by adding noise ξ, which is Gaussian noise, to the desired wave (target signal) s(t) of a sine wave vibrating at the true frequency f s = 3.222 Hz will be described using the above method. Refer to FIG. 13 for the time series data to be analyzed. The sampling time Δt is 0.01 s.

[0056] In the frequency analysis, time T0 was set to 1 s. In this case, the frequency resolution is Δf = 1 / T0 = 1 Hz. The provisionally determined frequency (kΔf) was set to 3 Hz. Thus, the correct value of the phase difference θ can be found from (Equation 7) as (3.222 Hz - 3 Hz) / (1 × 360 (degrees)) = 80 degrees.

[0057] Figure 14 shows the Fourier transform vector r of the analysis target. n Amplitude A of ^(kΔf) n , phase angle Φ n , interval phase difference θ n , and amplitude A n Phase difference A weighted by n θ n This is a table summarizing the calculation results. The last row contains the averaged phase difference θ calculated by (Equation 13). 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.

[0058] Furthermore, (Equation 15) 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.

[0059] Figure 15 shows the frequency spectrum r created from the time-series data being analyzed. ad ^(f) is shown. Frequency spectrum r ad The signal-to-noise ratio of ^(f) is 0.102, and the frequency spectrum r of the comparative example assuming the method of Non-Patent Document 1 av The signal-to-noise ratio (SNR) was higher than that of ^(f), which was 0.0368.

[0060] Here, in the method of Non-Patent Document 1, the Fourier transform vector r calculated by the DFT calculation circuit 9 as described in this disclosure nThe waveform of ^(f) is stored in the second memory circuit 10 as described in this disclosure. Then, in the method of Non-Patent Document 1, the Fourier transform vector r from the first interval to the q interval is stored. n The frequency spectrum r obtained by averaging the amplitude of ^(f) 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.

[0061] <Frequency spectrum of the comparative example> Figure 16 shows the frequency spectrum of the comparative example created from the time-series data of the subject of analysis. av ^(f) is shown. The frequency spectrum r of the comparative example av ^(f) is the Fourier transform vector r from the first interval to the qth interval. n It can be obtained by averaging the amplitude of ^(f).

[0062]

[0063] <Reasons why the signal-to-noise ratio can be improved> As shown in Figure 17, 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 18, 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 Phase angle of (t) with a phase difference θ AB The signal wave r is phase-adjusted (in-phase) by adding it. B Calculate (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 2The 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

[0064] Thus, the frequency spectrum r of Non-Patent Document 1 av ^(f) 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 n By considering the phase angle of (t), the signal-to-noise ratio of the frequency spectrum can be improved.

[0065] Figure 19 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.

[0066] The frequency analysis program may be provided on a storage medium or via a network.

[0067] 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.

[0068] 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.

[0069] The communication unit 42 is, for example, a communication interface that communicates with a transmitter.

[0070] 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.

[0071] 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 and the second memory circuit 10 described above.

[0072] 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.

[0073] Note that the architecture of the frequency analyzer 100 is not limited to the example shown in the figure.

[0074] 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 analyzer that can determine the frequency of a weak desired wave signal with higher accuracy than the frequency resolution Δf.

[0075] 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 frequency of the desired wave is tentatively determined to be kΔf) in the adjacent interval. n-1 (t) and r n (t) interval phase difference θ n This 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. avThe frequency is determined. Furthermore, the desired frequency of the wave is determined by correcting the provisionally determined frequency (kΔf) based on (Equation 15). 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). This allows for the provision of a frequency analyzer that can determine the frequency of a weak desired wave signal with higher accuracy than the frequency resolution.

[0076] <Variation 1> Note that the true frequency f s When calculating this, it is not always necessary to use (Equation 15). For example, the interval phase difference θ n If the calculation accuracy is good, the averaged phase difference θ in (Equation 15) 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.

[0077] <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, 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.

[0078] <Variation 3> In the above, the interval phase difference θ was used for all combinations from the first interval to the q-th interval in the calculation process. 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.

[0079] <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.

[0080] 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.

[0081] <Correspondence with terms used in the claims> The true frequency f obtained by (Equation 15) s In the claims, this is referred to as the corrected frequency.

[0082] 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, 12: Frequency identification 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: a process for acquiring the frequency of a signal wave; a process for dividing the signal wave in the time domain into a plurality of intervals at predetermined time intervals; a calculation process for calculating the interval phase difference, which is the phase difference of the signal wave in adjacent intervals, for at least one pair of the plurality of intervals; and a correction process for correcting the frequency using the interval phase difference.

2. The frequency analyzer according to claim 1, wherein the calculation process includes: a process of performing a discrete Fourier transform on each of the signal waves in adjacent intervals; and a process of determining the interval phase difference as the phase difference of the signal waves that have been discrete Fourier transformed in adjacent intervals.

3. The calculation process includes a process of calculating multiple sets of interval phase differences for different intervals, and the correction process includes a process of calculating an averaged phase difference by averaging the interval phase differences for the multiple sets, where the predetermined time is T0, the frequency is kΔf, k is an integer, the frequency resolution of the discrete Fourier transformed signal wave is Δf = 1 / T0, and the averaged phase difference is θ av The frequency f corrected by the following formula s A frequency analyzer according to claim 2, which determines the following.

4. A frequency analyzer according to claim 1, configured to perform the following steps:

4. A process of calculating a signal wave that has been phase-adjusted to match the signal wave in a specific section of the plurality of sections for each of the other sections of the plurality of sections; 5. A process of calculating a synthesized signal wave by adding the amplitude of the phase-adjusted signal wave in each of the other sections to the amplitude of the signal wave in the specific section; and 6. A process of calculating a frequency spectrum by performing a discrete Fourier transform on the synthesized signal wave.

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