JP5670836B2 - Method and apparatus for detecting peak power spectrum of short-time signal with reduced number of samples in Fourier transform - Google Patents

Description

  The present invention relates to a method and apparatus for detecting a peak power spectrum by cutting out a portion within a desired time width from a signal that changes according to time, and applying Fourier transform to the cut-out portion, In particular, the present invention relates to a method and an apparatus that can reduce the number of samples in Fourier transform while maintaining a desired frequency resolution capability, thereby shortening the calculation processing time and improving the frequency accuracy of a detected spectrum.

  It will be described later that only a portion having a desired time width is cut out from a signal having a predetermined frequency bandwidth and changes every moment, and the peak power spectrum of the signal in the cut portion is detected. For example, it is widely used in Doppler measurement. The desired time width here is sufficiently short when compared with the duration of the entire signal. For example, the start time is given or the start time can be automatically detected. Further, the detected peak power spectrum has the strongest power spectrum in the frequency spectrum of the signal in the cut out portion. For the detection of the power spectrum, Fourier transform is generally used, and FFT (Fast Fourier Transform) is used from the viewpoint of calculation amount.

  By the way, when a signal is emitted (transmitted) into a medium and a signal (echo signal) reflected from the medium is received, if the transmitted time is the start time, the echo signal from the start time is received until the echo signal is received. Is dependent on the propagation distance of the signal in the medium, that is, the distance to the object. Therefore, in consideration of the propagation speed of a signal (the speed of sound in the case of sound waves), an echo signal received when a desired time has elapsed from the start time is from an object located at a distance corresponding to the elapsed time. It becomes an echo signal. Application devices that display the intensity of the echo signal as an image according to the time (that is, distance) from the start time are, for example, a radar and a fish finder.

  Assuming that the object that reflects the signal is relatively moving, a frequency shift from the transmitted frequency is observed in the reflected echo due to the Doppler effect. This frequency difference, that is, the difference between the frequency when transmitted to the medium and the frequency observed by the reflected echo is called the Doppler frequency. In Doppler measurement, a signal having a constant frequency is emitted into a medium, a signal reflected by an object in the medium (reflection echo) is received, and the frequency analysis is performed to determine the Doppler frequency. Examples of Doppler measurements include Doppler radar, Doppler sonar, ADCP (acoustic Doppler current profiler), tide meter, sonic radar, and ultrasonic Doppler velocimeter, which are based on Doppler frequency. To determine the relative speed with the object.

A signal having a constant transmission frequency f _tx is generated by the transmission circuit, and this signal is emitted from the transducer to the medium. Assuming that the object (reflector) is moving in the medium, the Doppler frequency f _dop has the moving speed of the object as V (m / s) and the propagation speed of the signal in the medium as C (m / s). Then, when the propagation speed of the signal in the medium is sufficiently faster than the speed of the object (C >> V), it is expressed by the following approximate expression.

Here, θ is an angle formed by the direction when the transducer is viewed from the object and the moving direction of the object, and if the direction is the same (when the object is moving straight toward the transducer) ), Θ = 0. Accordingly, the Doppler frequency f _dop is positive (+) when the object is approaching, and is negative (−) when the object is moving away.

A frequency analysis of the echo signal is performed to obtain a Doppler frequency f _dop , and a Fourier transform method is generally used for this frequency analysis. As the Fourier transform, when performing power spectrum analysis, DFT (Discrete Fourier Transform) is used, or when the number of signal samples (number of samples) is a power of 2, high-speed arithmetic processing is possible. FFT (Fast Fourier Transform) is usually used. Both DFT and FFT repeat complex multiplication operations. If the number of samples is N, the number of complex multiplications in the DFT is N × N times (that is, N ² times), and N = 2 ⁿ , The number of complex multiplications in the FFT is 2 ⁿ × log ₂ 2 ⁿ times (that is, N × log ₂ N times), and the higher the N, the faster the FFT can perform operations compared to the DFT.

  In order to obtain a frequency from the received signal including the Doppler frequency by Fourier transform using a technique such as FFT or DFT, it is necessary to convert the received signal, which is an analog signal, into a digital signal. From the sampling theorem, the sampling frequency in this analog / digital (A / D) conversion must be at least twice the frequency of the input signal. In other words, the input signal to be subjected to A / D conversion must be ½ or less of the sampling frequency.

  By the way, in Doppler measurement, it is often desirable to acquire information on both the position and speed of an object. For example, in order to obtain the flow velocity profile by obtaining the direction and velocity of the tidal current at each depth in the ocean, a reflected echo is obtained by emitting a sound pulse in an oblique direction with respect to the ocean, and frequency analysis is performed. At this time, the reflected echo is cut out at a certain time width after a lapse of a predetermined time from the emission of the sound wave pulse, and the frequency analysis is performed on the cut out portion. The depth of flow to be measured is determined by the predetermined time after the sound pulse is emitted, and the flow velocity is calculated as an average over the depth range (thickness) according to the time width when the reflected echo is cut out. It will be decided whether or not. For example, if the time width at the time of cutting is large, an average flow velocity in a thick layer in the sea is obtained. On the other hand, if the time width is small, it is possible to obtain the flow velocity in a thin layer, and as a result, a fine flow velocity profile is obtained.

  However, a problem of Fourier transform as frequency analysis for obtaining the Doppler frequency is that the frequency resolution and the time (distance) resolution are in a contradictory relationship. Here, the frequency resolution is a resolution for obtaining the Doppler frequency, and is proportional to the resolution of the speed. The time resolution refers to how far the time width can be reduced when extracting the reflected echo, which is proportional to the distance or position resolution in Doppler measurement. If the time resolution is rough, in the case of the above-described flow velocity profile, only a rough average flow velocity in a layer having a large thickness in the depth direction can be obtained.

  The discrete Fourier transform (DFT) is expressed by the following equation.

When the sampling frequency in DFT or FFT is f _ft and the period of the fundamental wave of Fourier transform is T ₀ , the reciprocal of the period is called the fundamental frequency f _{0 in} Fourier transform,
f ₀ = 1 / T _0: Equation 1-4
It is expressed. The fundamental frequency f ₀ is the minimum resolution frequency in DFT or FFT, that is, the frequency resolution. If the total number of sampled signal points, ie the number of samples, is N,
T ₀ = N / f _ft : Formula 1-5
Of course, and the minimum resolution frequency f ₀ , which is the frequency resolution, is
_{f 0 = 1 / T 0 =} f ft / N: Equation 1-6
Will be expressed. Conversely, given the desired frequency resolution f ₀ , the required number of samples N is
N = f _ft / f ₀ : Formula 1-7
Will be expressed. In the Fourier transform, N samples are extracted at equal intervals from a signal having a time width equal to the period T _{0 of the} fundamental wave, so that T ₀ is a signal cutting time (cutting time width).

An example of a power spectrum obtained by FFT is shown in FIG. The power spectrum of the FFT is expressed as a spectrum in which values 14 and 15 are given for each frequency at a constant frequency interval from 0 to (N / 2) −1 with respect to the number N of samples. Here frequency interval is consistent with the above f _0, a f ₀ = 1 / T _0.

As shown in Equation 1-4, the frequency resolution f _0, since the reciprocal of the cut-out duration T ₀ of the signal, in order to increase the frequency resolution (the lower f _0), the signal of the cut time width T ₀ Must be lengthened. As a result, if the frequency resolution is made twice as fine, the time resolution, that is, the position (distance) resolution becomes twice as coarse and deteriorates.

The Doppler frequency f _dop changes depending on the relative speed with the object. _Assuming that the range in which the Doppler frequency f _fop changes is Δf _p , assuming that the movement in the approaching direction and the moving away direction occur equally (this process is a reasonable assumption in applications such as tidal current meters). The center frequency f _c of the frequency range Δf _P of the Doppler signal, that is, the frequency of the received signal when the Doppler frequency f _dop is zero matches the transmission frequency f _tx (f _c = f _tx ).

  Consider a case where an ultrasonic pulse signal is transmitted into the sea under the following conditions and the Doppler frequency of a reflected echo from a moving object is measured.

Sound wave velocity in seawater C: C = 1500 (m / s)
Transmission frequency f _tx : f _tx = 120 kHz
Maximum detection speed (horizontal direction) V: V = 15 (m / s)
It is assumed that sound waves are transmitted and received in the oblique direction (θ = 60 °) from the horizontal direction. From Equation 1-1:

Next, if the detection maximum speed is 15 m / s, the frequency range Delta] f _p which is observed as Doppler signal is a 120 ± 1.2 (kHz).

  Since the measurement speed range, that is, the maximum detection speed is usually determined in advance, the frequency range of the Doppler signal is also determined in advance and measured.

If the speed accuracy by Doppler measurement is 0.1 m / s, the frequency resolution f ₀ required for this is 12 Hz. Assuming that the range (position resolution) of a position to be detected in Doppler measurement is 7.5 m, the signal extraction time width is multiplied by 2/1500 (m / s), which is the time for a sound wave to reciprocate 1 m in seawater. 7.5 × 2/1500 = 0.01, which is 10 ms.

However, if 12 Hz, which is the frequency resolution f ₀ , is substituted into Equation 1-4, T ₀ = 1 / f ₀ = 1 / 12≈83.3 ms, and 83.3 ms is the time required for the sound wave to reciprocate 1 m in seawater. When converted to a distance by dividing by 2/1500 (m / s), 83.3 (ms) × 1500 (m / s) /2≈62.5 (m).

That is, if the frequency resolution f _{0 is set} to 12 Hz in order to set the speed accuracy to 0.1 m / s, 83 ms is required as the signal extraction time width, which corresponds to 63 m in terms of distance, and the position (distance ) Cannot satisfy the requirement for a resolution of 7.5 m. On the other hand, if FFT is performed with a signal having a position-related resolution of 7.5 m, the frequency resolution f ₀ is 100 Hz according to Equation 1-4, and the request for the frequency resolution of 12 Hz determined from the speed accuracy cannot be satisfied.

  As described above, the Fourier transform has a basic problem that the frequency resolution and the time resolution related to the measurement target are not compatible. In the case of Doppler measurement, this is the frequency resolution or velocity resolution and the distance or position. This means that the resolution is not compatible.

FIG. 2 shows an example of a configuration of a general Doppler measuring device, in which only a portion having a desired time width is cut out from a received signal and a peak power spectrum of the signal in the cut portion is detected. The structure of a power spectrum detection apparatus is shown. Here, it is assumed that the signal is an acoustic signal and the medium through which the signal propagates is water (or seawater). The acoustic signal transducer 1 is connected to the output of the transmission circuit 3 and the input of the reception amplifier 4 via a transmission / reception switching circuit 2. The transmission circuit 3 generates a signal having a transmission frequency f _tx . The output of the reception amplifier 4 is provided with a modulator 5 that converts the received signal into an intermediate frequency signal. A signal having a local oscillation frequency f _loc is supplied from the local oscillation circuit 6 to the modulator 5. . The output of the modulator 5, that is, the intermediate frequency signal, is supplied to an analog / digital converter (A / D) 10 through a high-order analog filter 60 and converted into a digital signal. This digital signal has a predetermined number of samples ( In other words, the signal is supplied to the signal cut-out gate 11 for cutting out the signal by time width. The signal cut out by the signal cut-out gate 11 is then sent to the FFT processing unit 13 and subjected to frequency analysis by FFT. The calculated power spectrum is output from the FFT processing unit 13.

In this apparatus, when a sound wave pulse is emitted into water, a signal having a transmission frequency f _tx is supplied from the transmission circuit 3 to the transmitter / receiver 1 via the transmission / reception switching circuit 2, and then the transmission / reception switching circuit 2 is immediately set as the receiving side. The reflected echo from the medium (underwater) is received by the transducer 1 and converted into a received signal which is an electrical signal, and the received signal is supplied to the receiving amplifier 4 via the transmission / reception switching circuit 2. As a result, the received signal is amplified by the receiving amplifier 4 and supplied to the modulator 5.

FIG. 3 shows a relationship between frequencies such as a received signal and an intermediate frequency signal. It is assumed that the signal itself output from the receiving amplifier 4 has a frequency band as indicated by reference numeral 52 in FIG. Band of the received signal is part of a frequency band indicated by reference numeral 52, the Doppler signal to be detected is within the frequency range Delta] f _p indicated by reference numeral 51. The center of the frequency range Δf _p , that is, the frequency f _c (47) when the Doppler frequency is zero is the same as the transmission frequency f _tx (f _c = f _tx ). The local oscillation circuit 6 generates a local oscillation signal having a local oscillation frequency f _loc (45) higher than the frequency f _c by the intermediate frequency f _mid (that is, f _loc > f _c ), and supplies it to the modulator 5. As a result, the modulator 5 multiplies the received signal by the local oscillation signal to convert the received signal into an intermediate frequency signal having the intermediate frequency f _mid .

Of the frequency band of the received signal, if the upper limit of the frequency range Δf _p of interest for topler measurement is the upper limit frequency f _max (49) and the lower limit is the lower limit frequency f _min (48), the frequency range to be Fourier transformed Δf _p (51) is represented by Δf _p = f _max -f _min.

Generation of the signal of the intermediate frequency f _mid in the modulator 5 is expressed by the following equation, and the lower frequency is obtained from the two conversion frequencies by the high-order analog filter 60.

Frequency range Delta] f _p of the Doppler signal, centered on the intermediate frequency f _mid,

Will be transformed in the range, the frequency range Delta] f _p of the detection target is maintained even if the frequency converter. The above equation is shown a process when the f _loc> f _c, even when the f _loc <f _c, only decoding (code (±)) is reversed, the same processing is performed .

3, the right part represents the relationship between the signal of the received signal and the local oscillation frequency f _loc, where f _mid (46) satisfies the relationship of f _mid = f _loc -f _c. On the other hand, the left part of FIG. 3 shows the spectrum after being converted into the intermediate frequency signal, and here, the center frequency of the intermediate frequency signal is f _mid (50). The above-described frequency band 52 is also converted to the frequency band 54, and the frequency range Δf _p (51) to be detected is converted to the frequency range Δf _p (53) whose center frequency is f _mid . That band 53 is an intermediate frequency signal by removing only the frequency components of the lower and frequency conversion by a modulator 5, represents the band of Delta] f _p in the received signal which has passed through a high-order analog filter 60 Yes.

The high-order analog filter 60 selects the lower of the two conversion frequencies output from the modulator 5 and further prevents aliasing in A / D conversion. A band-pass filter (BPF) or a low-pass filter (LPF) is used. In the following, for the sake of explanation, it is assumed that a Butterworth LPF with little ripple in the passband is used for the high-order analog filter 60. Considering _{aliasing in} A / D conversion, when the data width of A / D conversion in the A / D converter 10 is 8 bits, the frequency is ½ of the sampling frequency f _2ad of the A / D converter 10. That is, if the signal level at f _2ad / 2 is −48 dB or less with reference to the signal level in the pass band of the filter, aliasing does not occur completely. Similarly, in the case of 16-bit width A / D conversion, if the signal level is −96 dB or less, aliasing does not occur completely. Therefore, the high-order analog filter 60 includes the frequency band of _interest in the intermediate frequency signal (range Δf _p centered on the frequency f _mid ) in its pass band, and at the frequency f _2ad / 2, the above-described attenuation amount (8 It is necessary to have −48 dB for A / D conversion with a bit width and −96 dB for 16 bit width. In other words, it is necessary to increase f _ft / 2 until the attenuation reaches this value, and to increase the sampling frequency f _{2ad accordingly} .

  In the following description, it is assumed that the data width of A / D conversion is 8 bits. FIG. 4 shows an example of the frequency characteristic of the LPF. Hereinafter, the frequency band of the received signal will be described with reference to FIG.

Frequency f _c of the received signal is 120 kHz, the Doppler maximum frequency is 1200 Hz, the frequency resolution required to Fourier transform to be 12 Hz. As shown in Equation 2-3, even when converting the received signal into an intermediate frequency signal, it does not change the frequency range Delta] f _p itself Doppler frequency. On the other hand, it is necessary to select the local oscillation frequency f _loc so that the received signal and the local oscillation frequency signal do not crosstalk or cause cross modulation. Here, it is assumed that a local oscillation frequency f _loc that is 10% or more away from the received signal at that frequency is selected, and is separated by 17 KHz. The local oscillation frequency f _loc is f _loc = f _c +17 kHz = 137 KHz, and the intermediate frequency f _mid is 17 KHz. At this time, the passband (all bands) W of the analog LPF is

It is necessary to. Δf _p / 2 = 1200 Hz, and adding an appropriate α (attenuation region) and f _mid to this, the LPF only needs to pass signals up to 20 KHz completely as shown in FIG. . In FIG. 4, reference numeral 74 indicates the characteristics of the second-order LPF, reference numeral 73 indicates the characteristics of the fourth-order LPF, and reference numeral 72 indicates the characteristics of the eighth-order LPF. In an analog LPF, it is not practical from the viewpoint of cost to configure an 8th order LPF because of the accuracy of components, temperature coefficient, and the like, and therefore a 4th order LPF is used for the high order analog filter 26.

As described above, in the 8-bit width A / D conversion, if the signal level at half the sampling frequency is −48 dB compared to the pass band, the aliasing problem does not occur. FIG. 5 shows the relationship between the signal converted to the intermediate frequency and the sampling frequency of A / D conversion. In FIG. 5, the sampling frequency is indicated by f _2ad (78). Since the fourth-order LPF is used here, the frequency of −48 dB is 80 kHz, and the frequency f _2ad / 2 (77) which is half the sampling frequency f _2ad is also set to 80 kHz. Therefore, A / D conversion is performed at a sampling frequency f _2ad of ₁₆₀ kHz.

As a result, from Equation 1-6, the number N of samples that satisfy the resolution condition is N = f _2ad / f ₀ = _16000/16 = 10000. Since the number of FFT data points should be a power of 2, the number of samples in the FFT is 16384 (= 2 ¹⁴ ), and the frequency resolution f _{0 at} this time is f ₀ = 16000/16384 = 9.77 [ Hz]. At this time, the number of complex multiplications performed in the FFT is
Number of FFT complex multiplications: 2 ¹⁴ × log ₂ 2 ¹⁴ = 229376
It becomes. If frequency analysis is performed using DFT instead of FFT, the number of data points does not need to be a power of 2 in DFT, so that complex multiplication when DFT calculation is performed under the same conditions as in FFT The number of times
Number of DFT complex multiplication: 10000 × 10000 = 100000
It becomes. In DFT, the required number of complex multiplications is as extremely large as 1 × 10 ⁸ , which is not practical for frequency analysis as in the present invention. Even when using FFT, enormous computations are required, requiring high processing capability and long processing time for the FFT computing unit. As a result, powerful DSP (digital signal processor) and software computing capability CPU is required, which increases the cost of the frequency detection device.

FIG. 6 shows a case where a reflected echo is received by emitting a sound wave pulse in a direction of θ = 60 ° from the observation ship (a direction facing 60 ° downward from the horizontal direction) in order to measure a flow velocity profile in a tidal current. An example of the received waveform is shown. In the figure, the horizontal axis represents time. Here, the reflected echo 16 is shown as a signal after being converted into an intermediate frequency signal. The large-amplitude signal 17 immediately after time 0 is due to the reception of the transmitted sound wave pulse itself by the transducer. A waveform 18 having a large amplitude indicates an echo reflected from the seabed (seafloor echo). In seabed echo, according to the ship speed of research ship, it includes Doppler shift in the frequency range of ± Δf _p / 2.

Here, considering the case where the peak power spectrum is detected with a frequency resolution of 12 Hz in the band of 120 ± 1.2 (kHz), the above-mentioned will be described if the ease of frequency conversion and the realization of the high-order analog filter are taken into consideration. As a result, the intermediate frequency f _mid (that is, the center frequency of the frequency-converted signal) is 17 kHz, the sampling frequency in the analog / digital conversion and the sampling frequency f _ft in the FFT is 160 kHz, and the number of samples N in the Fourier transform is N N = 2 ¹⁴ = 16384. At this time, the frequency resolution is 9.766 Hz, which is finer than the above-described frequency resolution of 12 Hz corresponding to the speed accuracy of 0.1 m / s and satisfies the requirements.

In FIG. 6, reference numeral 20 represents a time T ₀ required to acquire 16384 signal samples necessary for FFT, assuming that acquisition is started simultaneously with the transmission of the sound wave pulse. From Equation 1-5, T ₀ becomes T ₀ = 102.4 ms. In the period T ₀ , a signal 17 resulting from the wraparound of the transmitted sound wave pulse is included in addition to the waveform 18 caused by the sea bottom echo. Since the amplitude of the signal 17 is larger than that of the waveform 18, the amplitude of the transmission signal itself having the largest power is detected as the peak power spectrum even in the result of taking the signal sample within the time width T ₀ and performing the FFT. Therefore, the Doppler shifted frequency included in the seafloor echo cannot be detected as the peak power spectrum. This is because performing FFT for a time width T _{0 of} 102.4 ms is essentially the FFT target from the position of the transducer to the seabed. That is, for an FFT input signal having a strong signal outside the desired time range, it is not possible to obtain the spectrum or frequency that is the peak power within the desired time range.

In FIG. 6, it is also conceivable to perform the FFT by shifting only the signal in the time range T ₁ (21) including only the peak 18 by shifting the transmission time of the sound wave pulse by the time t ₁ (22). Assuming T ₁ = 6.4 ms, the frequency resolution f ₀ is f ₀ = 1 / 0.0064≈156 Hz, which is a coarse accuracy that is 156 Hz different if the FFT step is shifted by one. This frequency resolution is extremely coarse compared to the required resolution of 12 Hz and cannot meet the requirements.

In conventional Doppler measurement, when obtaining the peak power frequency within a desired time interval, first, the distance (time) resolution is prioritized, and the necessary range T ₁ is extracted from the received signal until the frequency resolution is coarse. Perform frequency analysis by FFT. Interpolate from the sampling point with the highest value in the analysis result, the sampling point with the next largest value, the sampling point with the next largest value, etc. by a method such as curve fitting that assumes the peak shape in the spectrum The method of estimating a true peak power frequency by performing was used. Because of interpolation, the true peak power frequency can be calculated with a finer resolution than the frequency resolution in FFT.

  However, in such a conventional method, a circuit and an estimation algorithm for obtaining the peak power frequency by interpolation become complicated, and as a result, it is necessary to spend calculation power for processing other than FFT, and the calculation speed is reduced. It was a factor of cost increase. Moreover, since frequency estimation is performed after FFT, there is also a problem that measurement accuracy is likely to deteriorate.

  In the end, the conventional peak power spectrum detection method in Doppler measurement easily realizes an analog filter for preventing aliasing in A / D conversion even if the Doppler frequency, that is, the bandwidth of Doppler shift is small, and performs frequency conversion. The sampling frequency must be set high due to the necessity of performing it reliably, and as a result, the number of samples increases, the number of times of complex multiplication of Fourier transform becomes enormous, and calculation processing may become difficult. . Moreover, in order to perform enormous complex operations, an extremely high-speed arithmetic processor is required, and there is a problem that a great cost is required.

  In addition, the Fourier transform has a basic problem that the frequency resolution and the distance (time) resolution of the measurement range are not compatible. In the conventional peak power spectrum detection method, in order to solve this problem, the distance (time) resolution is prioritized to cut out the necessary range, and the FFT of the coarse frequency resolution is performed, and the sampling point that has the highest value in the analysis result is obtained. The true peak power frequency can be calculated by interpolating from the sampling point with the next largest value, the sampling point with the next largest value, etc. using a method such as curve fitting that assumes the shape of the peak in the spectrum. I was estimating. Because of interpolation, the true peak power frequency can be calculated with a finer resolution than the frequency resolution in FFT.

  However, in such a conventional method, a circuit and an estimation algorithm for obtaining the peak power frequency by interpolation become complicated, and as a result, it is necessary to spend calculation power for processing other than FFT, and the calculation speed is reduced. It was a factor of cost increase. Moreover, since frequency estimation is performed after FFT, there is also a problem that measurement accuracy is likely to deteriorate.

  Patent Document 1 discloses a signal processing method that increases the frequency resolution while reducing the number of calculation points in FFT.

WO2006 / 043511

  When performing Fourier transform to obtain the Doppler frequency for the received signal obtained by receiving the reflected echo, the sampling frequency becomes high and the number of complex multiplications in the Fourier transform becomes enormous, which makes computation difficult. In addition, there is a problem caused by the fundamental problem of Fourier transform that the improvement of the frequency resolution and the improvement of the resolution for the time (or distance) of the range to be measured are not compatible. Arise.

  The object of the present invention is to solve the above-mentioned problems in the Fourier transform, increase the frequency resolution while increasing the resolution of the time range to be measured, and lower the sampling frequency in the Fourier transform to reduce the number of samples. It is an object of the present invention to provide a detection method and apparatus that can reduce the number of complex multiplications in Fourier transform.

The detection method of the present invention is a method for detecting a peak power frequency of a received signal within a predetermined frequency bandwidth including a first frequency in a time-varying received signal and within a desired time width. After converting the received signal to an intermediate frequency signal different from the first frequency, applying an analog filter to remove high frequency components from the frequency converted signal, and after applying the analog filter A signal is sampled at a second frequency and A / D converted, and a digital bandpass filter is applied to the digital signal obtained by A / D conversion, corresponding to a predetermined frequency bandwidth. a step of extracting a signal only, the two first frequency powers fraction of a second frequency as a down-sampling frequency, within a desired time width, the digital bandpass filter Down-sampling stage to extract and output the signal output from the signal, and the number of samples required in the fast Fourier transform to satisfy the required frequency resolution, and to reach this reference sample number An addition step of adding zero data to the digital data sequence output from the down-sampling step; an FFT step of performing fast Fourier transform using a third frequency as a sampling frequency on the digital data sequence to which zero data is added; has a peak in the down-sampling phase, disposed bandwidth frequency band of the signals extracted by the down-sampling is equivalent from zero frequency to a predetermined frequency bandwidth, the frequency showing the maximum value in the result of the fast Fourier transform Detect as power frequency.

The detection device of the present invention is a device that detects a peak power frequency of a received signal within a predetermined frequency bandwidth including a first frequency in a time-varying received signal and within a desired time width. , A frequency converting means for converting the frequency of the received signal into a signal having an intermediate frequency different from the first frequency, an analog filter for removing a high frequency component from the frequency converted signal, and a signal output from the analog filter as a second An A / D converter that samples and performs A / D conversion at a frequency, and a digital bandpass filter that is connected to the output of the A / D converter and outputs a digital signal including only a signal corresponding to a predetermined frequency bandwidth When the two first frequency powers fraction of a second frequency as a down-sampling frequency, within a desired time width, of the output from the digital bandpass filter Down-sampling means for down-sampling and extracting the signal to be sampled, and down-sampling means to reach this reference sample number with the number of samples required in the Fast Fourier Transform to satisfy the required frequency resolution as the reference sample number And zero adding means for adding zero data to the digital data string output from the digital data string, and FFT means for performing fast Fourier transform using a third frequency as a sampling frequency for the digital data string to which zero data is added. The frequency band of the signal in the digital data sequence output from the down-sampling means is arranged in the bandwidth corresponding to the predetermined frequency bandwidth from the frequency zero, and the frequency showing the maximum value in the result of the fast Fourier transform is the peak power frequency. Detect as.

  According to the present invention, the peak power frequency can be obtained directly from the FFT with a desired frequency resolution without performing post-FFT interpolation or estimation, and the number of samples in the FFT can be greatly reduced to reduce the computation load. Therefore, the peak power frequency can be obtained with high accuracy and high speed at a low cost with a simple configuration without requiring a complicated circuit or algorithm.

It is a graph which shows the frequency spectrum analysis result by FFT. It is a block diagram which shows an example of a structure of the conventional peak power spectrum measuring apparatus. It is a spectrum figure explaining conversion etc. to the intermediate frequency of a received signal. It is a graph which shows an example of the characteristic of analog LPF used when performing frequency conversion to an intermediate frequency. It is a spectrum figure which shows the relationship between the sampling frequency in A / D conversion, and an intermediate frequency. It is a wave form diagram which shows an example of the received waveform of the reflective echo when an acoustic signal is transmitted in the sea in the diagonal direction. It is a block diagram which shows the structure of the peak power spectrum detection apparatus of one Embodiment of this invention. It is a spectrum figure explaining the conversion to the intermediate frequency signal of the received signal in the apparatus shown in FIG. It is a spectrum figure which shows the signal used as the object of FFT in the apparatus shown in FIG. It is a spectrum figure explaining the signal when down-sampling by the power of 2. It is a spectrum figure which shows the signal after deleting an unnecessary frequency component by digital BPF (band pass filter). It is a spectrum figure which shows the relationship between an intermediate frequency and the sampling frequency of an A / D converter. It is a wave form diagram explaining the input signal to FFT.

  The peak power spectrum detection apparatus according to the embodiment of the present invention shown in FIG. 7 shortens the FFT operation time by minimizing the number of complex multiplications by minimizing the number of samples in the Fourier transform, and the Fourier transform of the Fourier transform. This solves the basic problem that the frequency resolution and the distance (time) resolution of the measurement range are not compatible. First, how the number of samples in the Fourier transform is reduced in the apparatus shown in FIG. 7 will be described.

Consider a case in which a sound wave signal or radio wave signal having a certain frequency with respect to a medium is emitted (transmitted), reflected by an object (target) in the medium, and a reflected signal (reflected echo) is received. Due to the Doppler effect, the frequency of the reflected echo deviates from the frequency of the original sound wave signal or radio wave signal, but the magnitude of the deviation, that is, the frequency bandwidth of the Doppler frequency, is such that the relative movement speed between the object and the object is Is sufficiently smaller than the original signal frequency. For example, when θ = 60 °, an ultrasonic signal of f _tx = 120 kHz is reflected in water, and the maximum measurement speed V is 15 m / s, the maximum value of the Doppler frequency f _{dop is obtained} from the above equation 1-1. 1200 Hz. Since the moving direction of the object in some cases in the direction away as in the direction to approach, the frequency bandwidth Delta] f _p of the Doppler frequency becomes a 2400 Hz, which is sufficiently smaller than the transmission frequency f _tx is 120 kHz. If not considering the attenuation band adjacent to the frequency bandwidth Delta] f _p, and extracts only the frequency components within this Delta] f _p from the received signal are arranged within the range 0 to 2400 Hz, the Fourier transform to this If done, a sufficient frequency resolution should be obtained with a sufficiently small sampling frequency, and a Fourier transform should be able to be performed with a minimum number of samples to obtain the required frequency resolution. In the prior art, due to the difficulty of frequency conversion to an extremely low frequency and the difficulty of realizing an analog filter for removing high-frequency components with steep characteristics, the frequency is obtained by performing a Fourier transform with a minimum number of samples. Analysis could not be performed.

It should be noted that the frequency resolution f ₀ by the Fourier transform itself is the period T ₀ of the fundamental wave of the Fourier transform, that is, the length of the signal cut-out as shown in FIG. This is expressed by the reciprocal of T ₀ and does not depend on the sampling frequency f _ft . If the frequency resolution f ₀ is constant and the sampling frequency f _ft is increased, the number of samples N also increases based on Equation 1-7 and the amount of calculation increases. However, the increased number of samples N itself can be detected by frequency analysis. This contributes to extending the frequency range to the higher frequency side, but does not contribute to the improvement of the frequency resolution. A high sampling frequency means that the frequency analysis is practically performed over a wide frequency range beyond the possible change range of the Doppler frequency.

  Therefore, the peak power spectrum detection apparatus shown in FIG. 7 performs A / D conversion by oversampling, then extracts a necessary frequency band through a digital bandpass filter (D-BPF), and then performs downsampling. The frequency band subject to frequency analysis in the received signal is substantially moved from the zero frequency to the lowest frequency range. This makes it possible to perform Fourier transform at a sampling frequency corresponding to twice the frequency bandwidth to be frequency analyzed, and to perform frequency analysis by performing Fourier transform with the minimum number of samples. That is, according to the peak power spectrum detection device of the present embodiment, power spectrum analysis can be performed for a frequency band to be subjected to frequency analysis with a desired frequency resolution, and since the number of samples is minimum, Fourier transform can be performed.

  Next, how the frequency resolution and the distance (time) resolution are made compatible in the apparatus shown in FIG. 7 will be described.

As shown in Expression 1-6, the frequency resolution f ₀ itself by the Fourier transform is expressed by the period T ₀ of the fundamental wave of the Fourier transform, that is, the reciprocal of the signal cut-out length T ₀ as shown in FIG. It does not depend on the number. On the other hand, the distance (time) resolution is determined by the length of signal clipping. Therefore, in this embodiment, when downsampling is performed by performing A / D conversion by oversampling and frequency band extraction by digital BPF, a time width T _d (where T _d <T ₀ ) only in the case of downsampling and extracting the sample into a digital data string, and then adding a sample with a value of zero to the digital data string to satisfy the frequency resolution, and adding zero data to the time FFT is performed on the digital data string whose width becomes T ₀ .

  Hereinafter, the peak power spectrum detection apparatus shown in FIG. 7 will be described.

The peak power spectrum detection device shown in FIG. 7 is removed from the high-order analog filter 60 and the A / D converter 10 in the device shown in FIG. 2, and instead, the output of the modulator 5 is converted into a digital signal by oversampling. an a / D converter 61 which, from the digital signal output from a / D converter 61, a digital BPF62 to extract only the component of the predetermined frequency band Delta] f _p around the intermediate frequency f _mid as described below A downsampling unit 63 for downsampling the digital signal output from the digital BPF 62 is provided, and a digital data string output from the downsampling unit 63 is supplied to the signal cutout gate 11. Further, a zero adding unit 12 is inserted between the signal cut-out gate 11 and the FFT processing unit 13. The signal cutout gate 11 cuts out only a part corresponding to the time range _Td to be measured from the digital data sequence from the downsampling unit 63, and the zero addition unit 12 performs FFT to satisfy the required frequency resolution. Assuming that the required number of samples is the reference sample number, zero data is added to the digital data string from the signal cutout gate 11 so as to reach this reference sample number. Details of processing in the zero adding unit 12 will be described later.

  First, the operation from the transducer 1 to the downsampling unit 63 will be described.

In this peak power spectrum detection device, when an ultrasonic pulse is emitted into the water, a signal having a transmission frequency f _tx is supplied from the transmission circuit 3 to the transmitter / receiver 1 via the transmission / reception switching circuit 2, and then the transmission / reception switching circuit immediately thereafter. 2 is a reception side, a reflected echo from a medium (underwater) is received by the transducer 1 and converted into a reception signal which is an electrical signal, and the reception signal is supplied to the reception amplifier 4 via the transmission / reception switching circuit 2. As a result, the received signal is amplified by the receiving amplifier 4 and converted into an intermediate frequency signal by the modulator 5.

FIG. 8 shows the relationship between the received signal, the signal of the local oscillation frequency f _loc (45) supplied from the local oscillation circuit 6 to the modulator 5 and the signal of the intermediate frequency f _mid (46) after frequency conversion. Yes. The signal itself output from the receiving amplifier 2 has a frequency band as indicated by reference numeral 52. The band 51 of the received signal is a part of the frequency band indicated by reference numeral 52, and the center of the frequency band of the received signal is the center of the Doppler frequency to be measured. This is the frequency f _c (47) when the Doppler frequency is zero, and is the same as the transmission frequency f _tx (f _c = f _tx ). The modulator 5 multiplies the received signal by the signal having the local oscillation frequency f _loc and frequency-converts the received signal to a signal having the intermediate frequency f _mid . Here, as in the case of FIG. 3 described above, the local oscillation frequency f _loc is set to a frequency higher than the received signal, that is, f _loc > f _c + Δf _p / 2. Assuming that the upper limit frequency of the received signal is f _max (49) and the lower limit frequency is f _min (48), the frequency range Δf _p (51) in which the Fourier transform is to be performed is expressed as Δf _p = f _max −f _min. The In the peak power spectrum detection device of the present embodiment, in order to achieve a minimum number of samples in the Fourier transform, as shown in FIG. 9, so as fit in the final minimum frequency range variation range Delta] f _p of the Doppler frequency . In other words, the maximum frequency of interest in the Fourier transform as f _bs, such that f _bs = Δf _p, so as accommodate the range Delta] f _p of frequency analysis in the range from zero frequency up to a frequency f _bs. In other words, the maximum frequency of interest in the Fourier transform as f _bs, such that f _bs = Δf _p, so as accommodate the range Delta] f _p of frequency analysis in the range from zero frequency up to a frequency f _bs. The following describes placing a range of Delta] f _p in this way.

In the spectrum diagram of FIG. 9, the desired frequency analysis range is Δf _p (71), and the highest frequency is f _bs (69), so the sampling frequency f _ft of the Fourier transform may be twice this. . The center frequency f _mf range Δf _p (71) is represented by reference numeral 70. (As the sampling frequency f _ft , a frequency slightly higher than twice Δf _p may be used, and the frequency range Δf _p only needs to be within a range where aliasing does not occur during A / D conversion.

First, the intermediate frequency f _mid will be described. Figure 10 is a diagram illustrating a signal when downsampling power of 2, a band 53 of Delta] f _p when the frequency conversion of the received signal into a signal of intermediate frequency f _mid, minimum frequency band of interest It shows a band 71 of Delta] f _p when projected onto. If the highest frequency 69 of the band 71 is f _bs , f _mid may be determined as shown in the following equation.

f _bs and (69) and by setting the same as the bandwidth Delta] f _p,

Is obtained. After determining the intermediate frequency f _mid in this way, the local oscillation frequency f _loc is determined. The intermediate frequency f _mid (50) shown in the left part of FIG. 8 is equal to f _mid (46) of the right part, since f _mid = f _loc −f _c ,
f _loc = f _c + f _mid = f _tx + 3.5 × Δf _p : Equation 3-3
And f _loc may be determined.

Next, the sampling frequency _fadc by oversampling in the A / D converter 61 will be described. 11, frequency-converts the received signal into a signal of intermediate frequency f _mid, by the A / D converter 61 into a digital signal, then only the range of Delta] f _p by removing unnecessary frequency components by digital BPF62 The relationship between the extracted signal 53 and the sampling frequency f _adc (64) of the A / D converter 61 is shown. Here, placing the upper limit frequency 66 ranging Delta] f _p after converting into a signal of intermediate frequency f _mid and f _mm, consider the downsampling described later, as shown in FIG. 10 and Formula 3-2,
f _mm = 4 × f _bs : Formula 3-4
You can see that. Since f _mm is the highest frequency of the input signal to the A / D converter 61, m is oversampling with m being a power of 2 (that is, m = 2 ^{n where n is} an integer of 1 or more). Then, from equation 3-1, the sampling frequency f _adc is
f _adc = f _mm × m = 4 × m × f _bs : Formula 3-5
It will be represented by

Next, characteristics required for the analog filter 7 will be described. FIG. 12 shows the relationship between the intermediate frequency f _mid (50) and the sampling frequency f _adc (64) by oversampling.

The high frequency component of the input signal supplied to the A / D converter 61 must be attenuated in advance by the analog filter 7 in accordance with the sampling theorem. As described above, since f _mm (66) is the highest frequency of the signal, this is set as the upper limit of the pass band in the analog filter 7, and the frequency f _adc / 2 (65) which is half the sampling frequency f _adc (64). It is sufficient that the signal is sufficiently attenuated (for example, −48 dB in the case of 8-bit width A / D conversion). Since f _mm (66) is also f _adc / m according to the expression 3-5, it is only necessary to secure sufficient attenuation at a frequency that is m / 2 times higher than the maximum frequency f _{mm of the} signal. By performing m-times oversampling, the attenuation per octave required in the analog filter can be reduced to 1 / m, and the design of the analog filter becomes easy. When m = 8, a filter having an attenuation characteristic corresponding to a fourth-order Butterworth LPF can be used for the analog filter 7, and the analog filter 7 can be easily configured.

Next, the digital BPF 62 will be described. The signal that is input to the A / D converter 61 via the analog filter 7 and is oversampled and converted into a digital signal is obtained from the frequency range Δf _p (53) to be analyzed, as indicated by reference numeral 54 in FIG. Has a wide frequency band. Therefore, the digital BPF 62 removes unnecessary signal components from the signal in the frequency range indicated by reference numeral 54, extracts only the desired band Δf _p (53) as shown in FIG. 11, and supplies it to the downsampling unit 63. As the digital BPF 62, an FIR (finite impulse response) digital filter having a BPF characteristic can be used.

Next, the downsampling performed by the downsampling unit 63 will be described. The received signal frequency-converted to the intermediate frequency f _mid by processing by the digital BPF 62 is a signal having only a component in the desired band Δf _p (53). The downsampling unit 63 downsamples this signal by m. In other words, the signal sampled by _fadc , which is m times oversampling, is downsampled so that the number of samples becomes 1/2 m. Numeral 66 of FIG. 10 and FIG. 11, but represents the highest frequency f _mm band Delta] f _p, because it is from equation _{3-5 (f adc / m) =} f mm, frequency down-sampled to 1 / m f _adc / m is equal to the maximum frequency f _mm (66) that does not cause aliasing during A / D conversion.

Incidentally, represented by reference numeral 53, the band Delta] f _p of after being converted to an intermediate frequency f _mid as a whole, than the half of the down-sampling frequency f _adc / m (66) frequency f _adc / 2m (67) Is in the high frequency region and is in the aliasing region due to downsampling. As a result, by performing the down-sampling, band Delta] f _p represented by reference numeral 53 is folded back in mirror symmetry about the frequency f _adc / 2m (67), moves to a region represented by reference numeral 71 in FIG. 12 It will be. f _mm (66) shifts to the frequency indicated by reference numeral 68 by this folding. Here, since Δf _p = f _bs = f _adc / 4m, the frequency indicated by reference numeral 68 is 0 Hz. Therefore, the band Δf _p (71) to be subjected to frequency analysis for Doppler frequency measurement has finally shifted to the frequency range from 0 Hz to f _bs .

Incidentally, in FIG. 9 and FIG. 10, the maximum frequency of the band Δf _p (71) is a f _bs represented by reference numeral 69. Since digital filtering by the digital BPF 62 is performed, no component exceeding the frequency f _bs appears in the output from the downsampling unit 63. Therefore, the frequency f _adc / 2m (67) which is twice f _bs can be set as the sampling frequency f _ft of the Fourier transform.

  Next, the operation from the signal cut-out gate 11 to the FFT processing unit 13 will be described.

From the down-sampling unit 63, a digital data string composed of digital values representing instantaneous values in the received signal whose frequency is shifted so as to have the frequency f _mf (70) as the center frequency is sequentially set with the clock frequency being f _adc / m. It is output. Therefore, the signal cut-out gate 11 outputs from the down-sampling unit 63 in a desired time range, for example, when obtaining a flow velocity distribution of a tidal current in the depth direction in the sea, in a time range corresponding to the desired depth. The digital data string to be cut out. The number of samples of the extracted data is defined as the number of cut samples. The zero adding unit 12 calculates the number of FFT samples corresponding to the required frequency resolution as the reference sample number, and the number of zeros corresponding to the difference between the reference sample number and the cut sample number so as to reach the reference sample number. Data (sample with a value of zero) is added to the extracted digital data string. Then, the FFT processing unit 13 performs FFT on the digital data string in which zero data is added and the number of samples is the reference number of samples, and calculates a peak power spectrum. The calculated peak power spectrum is for the range cut out by the signal cut-out gate 11 and indicates the peak power frequency in the time range of the signal. In addition, by adding zero data, the time width to be subjected to FFT in the signal is substantially expanded, and the reciprocal of this time width corresponds to the frequency resolution, so the frequency resolution is improved. . As described above, according to the present embodiment, the peak power spectrum in a desired time range (or distance range) in the received signal can be detected by satisfying the desired frequency accuracy only by the FFT calculation. .

  Hereinafter, the frequency resolution in this embodiment and the sampling frequency in FFT will be described by giving numerical examples.

Consider a case where an ultrasonic pulse signal is transmitted into the sea under the same conditions as described in the background art section, and the Doppler frequency of a reflected echo from a moving object is measured. That is, the sound wave propagation speed C in seawater is C = 1500 (m / s), the transmission frequency f _tx is f _tx = 120 kHz, the maximum detection speed (horizontal direction) V is V = 15 (m / s), It is assumed that sound waves are transmitted and received in a diagonal direction (θ = 60 °) from the horizontal direction.

At this time, the Doppler signal is in the range of 120 ± 1.2 (kHz), and if the speed accuracy is required to be 0.1 m / s, the frequency resolution f ₀ is 12 Hz. In addition, the range (position resolution) of a position to be detected in Doppler measurement is set to 7.5 m.

The frequency band Δf _p to be observed must be Δf _p ≧ 2 × 1200 = 2400. Further, the maximum frequency f _bs of the Fourier transform and f _bs = Δf _p.

Considering the signal attenuation band (1300Hz),
Δf _p = (1200 + 1300) × 2 = 2500 × 2 = 5000
And Outside the 1300 Hz attenuation band, the signal may be considered almost zero, so at 5 kHz (ie, f _bs ), the signal is almost zero.

From Formula 3-1 and Formula 3-3,
Center of the intermediate frequency: f _mid = 3.5 × f _bs = 17500
Local oscillation frequency: f _loc = f _tx + f _mid = 120,000 + 17500 = 137500
It becomes. Further, if the oversampling coefficient m is m = 4, the sampling frequency f _adc of the A / D conversion is expressed by the equation 3-5:
A / D conversion: f _adc = 4 × m × f _bs = 16 × 5000 = 80000
The sampling frequency f _ft of the Fourier transform is

Thus, the number of samples N in the Fourier transform satisfying the frequency resolution f ₀ is N = f _ft / f ₀ ≈833.3. Since the power of 2 that is equal to or larger than 834 and is closest to 834 is 2 ¹⁰ = 1024, the number of samples N in FFT is 1024. By setting the number of samples to 1024, a frequency resolution of 10,000 / 1024≈9.77 Hz is achieved.

  In FIG. 6 which shows a waveform after emitting a sound wave pulse in the sea, observing a received signal, and converting the received signal into an intermediate frequency signal, reference numeral 16 represents a reflected echo, and reference numeral 17 represents transmission. The signal represents the signal itself, and reference numeral 18 represents a seabed echo. Consider a case where the frequency of the seafloor echo 18 is analyzed and the speed of the ship is obtained from the Doppler frequency based on Formula 1-1. Here, in order to prevent unnecessary signals such as transmission signals from being included, only the seafloor echo 18 is cut out and subjected to FFT to obtain the Doppler frequency for the reflected wave from the seabed.

FIG. 13 shows a signal 19 obtained by cutting out only the sea bottom echo from the signal waveform shown in FIG. However, in FIG. 6, the sampling frequency in FFT is 160 kHz, whereas in this embodiment, the sampling frequency in FFT is 10 kHz. Therefore, in FIG. 13, FIG. 6 and FIG. In order to match, the horizontal axis is also set to 1/16 in the sample number display in accordance with the sampling frequency ratio. Here, it is assumed that the time width T ₂ (24) is cut out after the elapse of time t ₂ (26) from the transmission of the sound wave pulse as the portion of the seabed echo 19. The signal cut out here is 50 samples.

The frequency resolution f ₀ when the Fourier transform is performed using only 50 samples having the time width T ₂ is f ₀ = 10000 Hz / 50 = 200 Hz, which does not satisfy the required frequency resolution of 12 Hz.

Therefore, in this embodiment, the FFT is executed with the number of samples N = 1024 so as to satisfy the frequency resolution f _0, and the number of samples corresponding to the seafloor echo signal 19 is 50. Insert a sample of zero values. In FIG. 13, T ₀ (23) is a time corresponding to 1024 samples and is a time width to be subjected to FFT analysis.

Here, the relationship of T ₀ = T ₂ + T ₃ holds, and the duration of the zero value signal added so as to satisfy the number N of samples necessary for FFT analysis by cutting out the signal 19 in the range to be measured is T _3. It will correspond to. The insertion position of the time width T ₃ may be before or after the time width T _2, that is, the extracted signal 19. Alternatively, the time width T ₀ (27) for FFT analysis may be set by arranging a time width for inserting the zero value signal by dividing the signal 19 before and after the signal 19 therebetween.

In the example shown here, the elapsed time t ₂ (symbol 26 in FIG. 13) and the time width T ₂ (symbol 24 in FIG. 13) from the transmission of the sound wave pulse to the start of signal clipping are determined in advance. If a reflected echo having a high intensity such as a sea bottom echo is to be detected, it is possible to automatically detect and determine the elapsed time t ₂ until the cutout and the time width T _{2 of the} cutout. When obtaining the flow velocity of the tidal current at each depth, automatic detection cannot be performed, and t ₂ and T ₂ are set in advance.

  Here, addition of zero value data by the zero addition unit 12 will be described.

In general, in FFT, the target number of samples needs to be a power of two. On the other hand, the number of samples in the target data to be analyzed by FFT is often not a power of two. Therefore, adding zero data samples so that the number of samples is a power of 2 is called zero padding. In that case, it is sufficient that the number of samples is enough to perform the FFT anyway. Therefore, when the number of samples of the target data is N _{s and} there is a natural number L that satisfies 2 ^L−1 <N _s ≦ 2 ^L , 2 ^L -N _s zero value data will be added. On the other hand, in the present embodiment, zero value data is not added so that the FFT can be executed, but the zero value is obtained so that a desired frequency resolution can be obtained in consideration of the sampling frequency f _ft in the FFT. Append data. Therefore, the number of zero value data added may be much larger than simply allowing the FFT to be performed. In the above-described example, assuming that the number of samples is 50 by cutting out the sea bottom echo, it is only necessary to add 14 zero-value data because 2 ⁶ = 64 only for executing FFT. However, as many as 974 zero value data are added to satisfy the desired frequency resolution.

  In this embodiment, since the number of samples in the FFT is 1024, the number of complex multiplication operations is only 10240. In the conventional example shown in FIGS. 2 to 5, in order to obtain the same frequency resolution as in the present embodiment, 229376 complex multiplications must be performed in the FFT. Therefore, according to the present embodiment, the same frequency is used. It can be seen that the number of complex multiplications required to obtain the resolution is greatly reduced. In the conventional example shown in FIGS. 2 to 5, the frequency resolution when the FFT is performed by cutting out only the sea bottom echo portion is 156 Hz, whereas in the present embodiment, the frequency resolution is 9.77 Hz. Is maintained.

  As described above, according to the present embodiment, it is possible to achieve both frequency resolution and position resolution, and it is possible to greatly reduce the number of computations by greatly reducing the number of samples necessary for Fourier transform.

  The preferred embodiment of the present invention has been described above by taking the detection of the Doppler frequency in the reflected echo as an example, but the scope of the present invention is not limited to this. The present invention is widely and generally applicable when a portion of a short time range is cut out from a signal that can assume a frequency range to be detected and analyzed by FFT.

DESCRIPTION OF SYMBOLS 1 Transmitter / receiver 2 Transmission / reception switching circuit 3 Transmission circuit 4 Reception amplifier 5 Modulator 6 Local oscillation circuit 7 Analog filter 10,61 A / D converter 11 Signal extraction gate 12 Zero addition part 13 FFT processing part 60 High-order analog filter 62 Digital BPF (band pass filter)
63 Downsampling unit

Claims (6)

A method for detecting a peak power frequency of the received signal within a predetermined frequency bandwidth including a first frequency in a time-varying received signal and within a desired time width,
Transforming the received signal to a signal having an intermediate frequency different from the first frequency;
Applying an analog filter to remove high frequency components from the frequency converted signal;
Sampling the signal after applying the analog filter at a second frequency and performing A / D conversion;
Applying a digital bandpass filter to a digital signal obtained by A / D conversion, and extracting only a signal corresponding to the predetermined frequency bandwidth;
A downsampling step of downsampling and extracting a signal output from the digital bandpass filter within the desired time width, with a frequency that is a power of 2 of the second frequency being a downsampling frequency;
Zero data is added to the digital data sequence output from the downsampling stage so that the number of samples required in the fast Fourier transform to satisfy the required frequency resolution is set as the reference sample number so as to reach the reference sample number. An additional stage;
An FFT stage for performing a fast Fourier transform using a third frequency as a sampling frequency on the digital data sequence to which the zero data is added;
Have
In the down sampling step, the frequency band of the signals extracted by said down-sampling is disposed to a bandwidth corresponding to the predetermined frequency bandwidth from zero frequency,
A method of detecting a frequency showing a maximum value as a result of the fast Fourier transform as the peak power frequency. The frequency width of the predetermined frequency bandwidth is Δf, the second and third frequencies are f ₂ and f ₃ , the intermediate frequency is f _mid, and n is an integer greater than or equal to 1 and m = 2 ⁿ ,
f _mid = 3.5 × Δf,
f ₂ = 4 × m × Δf,
f ₃ = f ₂ / (2 × m)
The method according to claim 1.   The method according to claim 1 or 2, wherein the reference sample number is at least twice the number of samples of the digital data sequence obtained in the sampling stage. An apparatus for detecting a peak power frequency of the received signal within a predetermined frequency bandwidth including a first frequency in a time-varying received signal and within a desired time width,
Frequency conversion means for converting the frequency of the received signal into a signal having an intermediate frequency different from the first frequency;
An analog filter for removing high-frequency components from the frequency-converted signal;
An A / D converter that samples the signal output from the analog filter at a second frequency and performs A / D conversion;
A digital bandpass filter connected to the output of the A / D converter and outputting a digital signal including only a signal corresponding to the predetermined frequency bandwidth;
Downsampling means for downsampling and extracting a signal output from the digital bandpass filter within the desired time width, with a frequency that is a power of 2 of the second frequency being a downsampling frequency;
Zero data is added to the digital data sequence output from the down-sampling means so that the number of samples required in the fast Fourier transform to satisfy the required frequency resolution is set as the reference sample number so as to reach the reference sample number. Zero addition means;
FFT means for performing a fast Fourier transform using a third frequency as a sampling frequency for the digital data sequence to which the zero data is added;
Have
The frequency band of the signal in the digital data string output from the down-sampling means is arranged in a bandwidth corresponding to the predetermined frequency bandwidth from frequency zero,
The apparatus which detects the frequency which shows the maximum value in the result of the said fast Fourier transform as said peak power frequency. The frequency width of the predetermined frequency bandwidth is Δf, the second and third frequencies are f ₂ and f ₃ , the intermediate frequency is f _mid , and n is an integer greater than or equal to 1 and m = 2 ⁿ ,
f _mid = 3.5 × Δf,
f ₂ = 4 × m × Δf,
f ₃ = f ₂ / (2 × m)
The apparatus according to claim 4.   6. The apparatus according to claim 5, wherein the reference sample number is at least twice the number of samples of the digital data sequence obtained by the sampling means.

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