JP2011038948A - Transmission waveform generation method in pulse compression, transmission waveform generation program, and pulse compression device manufactured by the transmission waveform generation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a transmission waveform generation method in pulse compression having little S/N loss, capable of further lowering a side-lobe level. <P>SOLUTION: If the waveform of Fourier transformed pulse compression waveform, wherein a range side lobe becomes a desired level is defined as P(f), and that the waveform of a power spectrum density of a linear chirp wave is defined as P'(f); a nonlinear chirp waveform whose chirp rate c(t) is proportional to P'(f(t))/P(f(t)) is calculated based on a linear chirp waveform and is then multiplied by a window function w(t) for suppressing rise and fall of the waveform. Furthermore, the waveform is subjected to Fourier expansion, corrected so that its amplitude spectrum agrees with an amplitude spectrum of the waveform P(f), and is then subjected to inverse-Fourier transformation so as to acquire the transmission waveform. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a transmission waveform generation method in pulse compression, a transmission waveform generation program, and a pulse compression apparatus such as a radar apparatus, an ultrasonic diagnostic apparatus, and an ultrasonic nondestructive inspection apparatus manufactured by the transmission waveform generation method.

  In a conventional pulse compression device, when the transmission power cannot be increased due to hardware restrictions, the pulse compression method is used as a technique for improving transmission performance in a pseudo manner and improving the long-range detection performance. It is known. As a pulse compression method, a typical method is to transmit a linear FM modulated wave (linear chirp wave), receive a reflected wave reflected by a target, and correlate a reference wave having the same waveform as the transmitted wave with the received wave. This is a method of making a pulse compression wave.

  As shown in FIG. 12, when the frequency is changed linearly with time, the power spectral density is rectangular. Since the pulse compression wave is an inverse Fourier transform of the power spectral density, it is obtained as a sinc function. Therefore, in addition to the main lobe, there is a problem that range side lobes appear on both sides thereof. In addition, the actual power spectral density is not an ideal rectangular shape, and ringing noise-like ripples are generated at the rising and falling parts of the frequency. This ripple further amplifies the range side lobe. The problem of becoming a tendency to be generated occurs.

Conventionally, the following method is known as a countermeasure for this range side lobe.
1) Range side lobe suppression processing is performed after pulse compression (for example, Patent Document 1, Non-Patent Documents 1 and 2).
2) A transmission wave having a low range sidelobe level subjected to amplitude modulation is used (for example, Patent Document 2 and Non-Patent Document 3).
3) A transmission wave having a low range sidelobe level subjected to frequency modulation is used (for example, Non-Patent Documents 4 and 5).

JP-A-11-142507 JP-A-5-27019

Merrill Skolnik, “RADAR HANDBOOK Third Edition”, 2008, McGraw-Hill J.R.Klauder, A.C.Price, S. Darlington, and W.J.Albersheim, “The Theory and Design of Chirp Radars”, 1960, The Bell System Technical Journal vol.39 Y. Takeuchi, “Chirped Excitation for <-100dB Time Sidelobe Echo Sounding”, 1995, IEEE Ultrasonics Symposium p1309-p1314 C.E.Cook, J.Paolillo, “A Pulse Compression Predistortion Function for Efficient Sidelobe Reduction in High-Power Radar”, 1964, Proc IEEE 52 p377-p389 Armin.W.Doerry, “Generating Nonlinear FM Chirp Waveforms for Radar”, 2006, SANDIA REPORT

  However, in the method 1), it is necessary to provide a range side lobe suppression circuit after the pulse compression, and there is a problem that the circuit scale increases. Further, there is a problem that the S / N loss is deteriorated as a result of the range side lobe suppression processing. For example, when the method of Non-Patent Document 2 is used, in order to make the range side lobe level about -40 dB, S / N is lost about 1 dB.

  In the method 2), a sufficiently low side lobe level can be obtained if the range to which amplitude modulation is applied is long, but transmission power is reduced and S / N loss is caused by applying amplitude modulation. For example, in Non-Patent Document 3, although a side lobe level of −100 dB or less is obtained, a loss of 6 dB occurs in the S / N due to the influence of amplitude modulation.

  In the method 3), although there is no S / N loss, the obtained side lobe level is about −40 to −50 dB.

  As described above, each of the conventional methods has problems. In particular, when the S / N is lost as in 1) and 2), the influence on the cost is large, and in order to compensate for the lost S / N. There is a problem that the transmission power must be increased.

  When the required side lobe level is -50 dB or less, the method 3) has a limit.

  The present invention has been made in view of such a problem, and an object of the present invention is to provide a transmission waveform generation method, a transmission waveform generation program, and transmission in pulse compression that can reduce the S / N loss and further reduce the side lobe level. It is to provide a pulse compression device manufactured by a waveform generation method.

In order to solve the above-described problem, the invention according to claim 1 of the present invention transmits a transmission wave using a chirp wave, receives a reflected wave of the transmission wave, and pulse-compresses the received signal to generate a pulse compression waveform. A transmission waveform generation method for pulse compression to obtain
Linear chirp when the first target waveform of the Fourier transform of the pulse compression waveform at which the range side lobe is at a desired level is P ₁ (f) and the power spectral density waveform of the linear chirp waveform is P ′ (f). A frequency modulation step of calculating a non-linear chirp waveform based on the waveform such that its chirp rate c (t) is proportional to P ′ (f (t)) / P ₁ (f (t));
An amplitude modulation step of multiplying the window function w (t) for suppressing the rise and fall of the nonlinear chirp waveform calculated in the frequency modulation step;
The waveform obtained in the amplitude modulation process is further expanded in the Fourier series, and the amplitude spectrum is corrected so as to be the amplitude spectrum of the second target waveform P ₂ (f) of the power spectrum density of the transmission waveform, and is subjected to inverse Fourier transform. Correction process on the frequency axis to generate
And a transmission waveform generation method in pulse compression for generating a transmission waveform from a linear chirp waveform.

  According to a second aspect of the present invention, in the frequency modulation step according to the first aspect, a waveform is calculated such that the chirp rate c (t) is proportional to the square of the window function w (t) multiplied by the amplitude modulation step. It is characterized by.

According to a third aspect of the present invention, in the first or second aspect of the present invention, the first target waveform P ₁ (f) used in the frequency modulation step and the second purpose used in the correction step on the frequency axis. The waveform P ₂ (f) is the same.

According to a fourth aspect of the invention, in the first or second aspect of the invention, the second target waveform P ₂ (f) used in the correction step on the frequency axis is the waveform of the waveform obtained in the amplitude modulation step. The power spectral density waveform is smoothed.

The invention according to claim 5 is the invention according to any one of claims 1 to 4, wherein the first target waveform P ₁ (f) used in the frequency modulation step is a window function. To do.

The invention according to claim 6 is the invention according to any one of claims 1 to 5, wherein the correction step on the frequency axis is obtained by Fourier series expansion of the waveform obtained in the amplitude modulation step. When the obtained amplitude spectrum is A (f), the amplitude spectrum is corrected by multiplying the amplitude spectrum A (f) by √ (P ₂ (f)) / A (f).

The invention according to claim 7 is a transmission waveform generation program for pulse compression that transmits a transmission wave using a chirp wave, receives a reflected wave of the transmission wave, and pulse-compresses the received signal to obtain a pulse compression waveform. Because
On the computer,
Linear chirp when the first target waveform of the Fourier transform of the pulse compression waveform at which the range side lobe is at a desired level is P ₁ (f) and the power spectral density waveform of the linear chirp waveform is P ′ (f). A frequency modulation step of calculating a non-linear chirp waveform based on the waveform such that its chirp rate c (t) is proportional to P ′ (f (t)) / P ₁ (f (t));
An amplitude modulation step of multiplying the window function w (t) for suppressing the rise and fall of the nonlinear chirp waveform calculated in the frequency modulation step;
The waveform obtained in the amplitude modulation process is further expanded in the Fourier series, and the amplitude spectrum is corrected so as to be the amplitude spectrum of the second target waveform P ₂ (f) of the power spectrum density of the transmission waveform, and is subjected to inverse Fourier transform. Correction process on the frequency axis to generate
And a transmission waveform generation program in pulse compression for generating a transmission waveform from a linear chirp waveform.

  According to an eighth aspect of the present invention, there is provided a memory for storing the transmission waveform generated by the method according to any one of the first to sixth aspects, a waveform reading unit for reading out the transmission waveform signal from the memory, and a transmission waveform signal. A D / A converter that converts the signal into an analog transmission signal, an amplifier that amplifies the transmission signal, a transducer that radiates the amplified transmission signal as a transmission wave and receives a reflected wave of the transmission wave, and A pulse compression apparatus comprising: an A / D converter that A / D converts a received wave into a received waveform signal; and a pulse compression unit that obtains a pulse compressed waveform signal by correlating the received waveform signal and the reference waveform signal It is characterized by being.

  According to the present invention, when generating a transmission waveform for pulse compression, in the frequency modulation step, frequency modulation is performed based on the linear chirp waveform to form a non-linear chirp waveform, and the power spectral density is sufficiently high for the range side lobe. By performing frequency modulation so as to be a first target waveform that is a Fourier transform of an ideal pulse compression waveform that has a low desired level, and by multiplying the rising and falling edges of the nonlinear chirp waveform by a window function in the amplitude modulation process, Ripple of the power spectrum density of the nonlinear chirp waveform calculated in the frequency modulation process can be removed, and furthermore, in the correction process on the frequency axis, the spectrum is matched on the frequency axis so that it cannot be dropped in the amplitude modulation process Remove further ripple. When the transmission waveform generated in this way is used to perform transmission and reception and pulse compression, a pulse compression waveform with a small S / N loss and a desired low sidelobe level can be obtained.

  In the frequency modulation step, by making the chirp rate proportional to the square of the window function multiplied in the amplitude modulation step, it is possible to perform modulation in consideration of fluctuations in power spectral density due to suppression in the amplitude modulation step, The range side lobe of the pulse compression waveform can be set to a desired level.

Further, the first target waveform P ₁ (f) used in the frequency modulation step and the second target waveform P ₂ (f) used in the correction step on the frequency axis are made the same, so that the pulse compression waveform is A pulse compression waveform with a range side lobe at a desired level can be obtained. Alternatively, the second target waveform P ₂ (f) used in the correction process on the frequency axis is obtained by smoothing the waveform of the power spectrum density of the waveform obtained in the amplitude modulation process. The load in the correction process can be reduced.

Further, by selecting the first target waveform P ₁ (f) from an arbitrary window function, the inverse Fourier transformed waveform can be made a waveform having a low range side lobe.

It is a schematic block diagram showing the whole pulse compression device manufactured by the transmission waveform generation method in pulse compression by the present invention. It is a figure showing the relationship between the time of a linear chirp waveform and a non-linear chirp waveform, and an instantaneous frequency. It is a figure showing the relationship between the power spectrum density of a linear chirp waveform and a non-linear chirp waveform. It is explanatory drawing of the chirp wave after frequency modulation. It is a wave form diagram showing the transmission wave which applied the window function after amplitude modulation. It is a flowchart showing the procedure which produces | generates a transmission waveform and manufactures a pulse compression apparatus. It is a flowchart which calculates | requires a frequency coefficient. The target waveform (broken line) and generated waveform (solid line) of the pulse compression waveform are represented, (a) after the frequency modulation step, (b) after the amplitude modulation step, and (c) after the correction step on the frequency axis. . It represents the target waveform (broken line) and generated waveform (solid line) of the log scale of the power spectrum density of the transmission waveform, (a) after the frequency modulation step, (b) after the amplitude modulation step, and (c) on the frequency axis. After the correction process. The target waveform (dashed line) and generated waveform (solid line) of the power spectrum density of the transmission waveform are represented, (a) after the frequency modulation step, (b) after the amplitude modulation step, and (c) on the frequency axis. After the correction process. It is a figure showing the relationship between the time of the produced | generated transmission waveform, and an instantaneous frequency. (A) by the conventional linear chirp wave is a diagram showing the relationship between the time and the instantaneous frequency of the transmission wave, (b) is the transmission waveform, (c) is the power spectral density of the transmission wave, and (d) is shown by the linear scale. (E) is a pulse compression waveform indicated by a log scale.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 shows a pulse compression apparatus 10 manufactured by a transmission waveform generation method in pulse compression according to the present invention. The pulse compression device 10 may be a device that transmits and receives detection waves such as radio waves and ultrasonic waves, such as a radar device, an ultrasonic diagnostic device, and an ultrasonic nondestructive inspection device.

  As shown in the figure, the pulse compression apparatus 10 includes a memory 12 in which a transmission waveform signal and a reference waveform signal are stored, a waveform readout unit 14 that reads out a transmission waveform signal stored in the memory 12, and a digital transmission that is read out in the waveform readout unit 14. The D / A converter 16 that converts the waveform signal into an analog transmission signal, the amplifier 18 that amplifies the analog transmission signal from the D / A converter 16, and the signal amplified by the amplifier 18 is radiated as a transmission wave and reflected from the target. The antenna 20 that receives the reflected wave, the transducer 20 such as an ultrasonic transducer, the A / D converter 24 that converts the received wave from the transducer 20 into a digital received waveform signal, and the reference waveform signal stored in the memory 12 are read and received. A pulse compression unit 26 that obtains a pulse compression waveform by correlating with the waveform signal , Comprising a. In a radar device that performs frequency conversion, a modulation circuit is added immediately after the D / A converter and immediately before the A / D converter.

  In principle, the transmission waveform signal and the reference waveform signal stored in the memory 12 are the same waveform signal.

  The waveform readout unit 14 and the pulse compression unit 26 can be configured by a microcomputer or FPGA.

  Here, when the pulse compression device 10 is a radar device, an amplified signal from an amplifier 18 such as a semiconductor amplifier can be used without using a conventional magnetron that oscillates microwaves. The transmission power is lower than the transmission power to be used, and this low transmission power can be artificially improved by pulse compression.

  In the pulse compression performed by the pulse compression unit 26, correlation processing between the received waveform signal and the reference waveform signal is performed, and a convolution operation is performed.

で表される。ここで、Ｘ（ｔ）はパルス圧縮波形、ｘ（ｔ）は受信波形、ｒ*（ｔ）は参照波形で、送信波形の複素共役波形、Ｔは送信パルス幅である。パルス圧縮を離散系で表せば、単純なＦＩＲフィルタ処理となる。
送信波が反射されて戻ってきたときは、（１）式は、

It is represented by Here, X (t) is a pulse compression waveform, x (t) is a reception waveform, r * (t) is a reference waveform, a complex conjugate waveform of the transmission waveform, and T is a transmission pulse width. If the pulse compression is expressed in a discrete system, it becomes a simple FIR filter process.
When the transmitted wave is reflected back, equation (1) becomes

となる。即ち、パルス圧縮部２６で出力されるパルス圧縮波形は送信波の自己相関関数となる。ウィナー・ヒンチンの定理により、送信波の自己相関関数は送信波のパワースペクトル密度を逆フーリエ変換した波形である。

It becomes. That is, the pulse compression waveform output from the pulse compression unit 26 is an autocorrelation function of the transmission wave. According to Wiener Hinchin's theorem, the autocorrelation function of the transmitted wave is a waveform obtained by inverse Fourier transform of the power spectral density of the transmitted wave.

  For example, in the case of linear chirp, the power spectral density of the transmission waveform can be regarded as a rectangle approximately, so that the pulse compression waveform has a high range sidelobe level. Therefore, it can be seen that in order to lower the range side lobe, it is preferable to select a waveform that has a low side lobe level when the power spectrum density is subjected to inverse Fourier transform.

  Hereinafter, a waveform having a range side lobe at a desired low level is set as an ideal pulse compression waveform, and a waveform obtained by Fourier transform thereof is set as a target waveform of the power spectrum density of the transmission waveform. The target waveform can be an arbitrary window function, and the window function can be a Hanning window, a Hamming window, a Gaussian window, or the like.

  The present invention proposes a method for shaping the power spectral density of this transmission waveform into a target waveform. In order to shape the target waveform, in the preferred embodiment, three steps of 1) frequency modulation, 2) amplitude modulation, and 3) correction on the frequency axis are sequentially performed on the linear chirp wave. The processing of each of these steps will be described sequentially.

1) Frequency modulation In frequency modulation, as shown in FIG. 2, the linear chirp waveform is deformed to form a non-linear chirp waveform whose power spectral density is close to the target waveform.

  For this reason, the fact that the chirp rate and the intensity of the power spectral density are in an inversely proportional relationship is utilized (FIG. 3). When a linear chirp with a pulse width T and a frequency sweep width B is considered, the chirp rate is constant at c = B / T. On the other hand, if the target waveform of the power spectrum density is P (f) and the power spectrum of the linear chirp is P ′ (f), the chirp rate c (t) is

とすれば、目的波形のパワースペクトルが得られる。ここで、Ｃは周波数掃引幅Ｂに関する制約条件である

Then, the power spectrum of the target waveform can be obtained. Here, C is a constraint on the frequency sweep width B

を満足させるための定数である。このＣを周波数定数と呼ぶ。離散系においては、ｋ番目のサンプリング点の時刻をｔ_k、サンプリング間隔をΔｔとして、チャープ率ｃ（ｔ_k）を、

Is a constant for satisfying This C is called a frequency constant. In a discrete system, the time of the _kth sampling point is t _k , the sampling interval is Δt, and the chirp rate c (t _k ) is

とすれば、目的波形のパワースペクトルが得られることになる。

Then, the power spectrum of the target waveform can be obtained.

However, since the amplitude modulation is performed in the next stage, it is necessary to consider in advance the influence of the amplitude modulation of the power spectral density. That is, the frequency interval whose amplitude is w times, the power can be regarded as approximately to be ^doubled w. Therefore, in order to shape the power spectral density to the target waveform, considering the power drop due to amplitude modulation in advance,

とする。ここでｗ_kは、ｋ番目のサンプリング点における振幅変調量である。

And Here, w _k is an amplitude modulation amount at the k-th sampling point.

2) Amplitude modulation When the waveform shaping of the power spectral density is performed only by the frequency modulation of 1), ripples occur and the waveform of the power spectral density is distorted. The cause of this ripple will be briefly described. FIG. 4 is a chirp wave model after frequency modulation in a discrete system. The chirp rate c _k , frequency f _k , phase φ _k , power spectrum density target waveform P (f) at the k-th discrete point, linear chirp power spectrum density P ′ (f), frequency coefficient C To do.
Here, the waveform from time t _{k to} t _{k + 1} is linear chirp,

と書ける。周波数変調によりパワースペクトルを整形したノンリニアチャープ波形Ｘ（ｔ）は、各微小時間のリニアチャープの和で、

Can be written. The non-linear chirp waveform X (t) whose power spectrum is shaped by frequency modulation is the sum of the linear chirps of each minute time,

である。（８）式からＸ（ｔ）の周波数特性は、

It is. From the equation (8), the frequency characteristic of X (t) is

となる。（９）式の積分項はｘ_k（ｔ）の周波数特性で、（７）式を代入すると、

It becomes. The integral term of equation (9) is the frequency characteristic of x _k (t), and when equation (7) is substituted,

となる。（１０）式をさらに書き直すと、

It becomes. Rewriting equation (10) further,

となる。ここで、Ｚ（ｕ）は複素フレネル積分で

It becomes. Where Z (u) is the complex Fresnel integral

である。よって、

It is. Therefore,

は（１１）式の複素フレネル積分の寄与を受け、この複素フレネル積分の寄与により、Ｘ（ｔ）の周波数特性は、目的波形に対してリプルとして生じることになる。

Receives the contribution of the complex Fresnel integral of equation (11), and the contribution of this complex Fresnel integral causes the frequency characteristic of X (t) to occur as a ripple with respect to the target waveform.

  In order to remove such ripples, amplitude modulation is performed to suppress the rise and fall of the transmission waveform.

As the amplitude modulation waveform, a function that smoothly attenuates such as a window function as shown in FIG. 5 may be used. Since the influence of the difference in the window function on the performance is small, an arbitrary window function w (t) or w _k can be used.

3) Correction on the frequency axis The transmission waveform generated by performing the frequency modulation of 1) and the amplitude modulation of 2) cannot avoid a slight ripple or distortion remaining in the waveform of the power spectral density. This slight residual ripple or distortion can cause range side lobes of the pulse compression waveform. Further, in order to remove ripples or distortion from the remaining waveform of the power spectrum density so as to obtain the target waveform, correction on the frequency axis is performed, and the amplitude spectrum of the transmission waveform becomes the target waveform P ( Correction is made so as to coincide with the amplitude spectrum √ (P (f)) of f).

It is assumed that the transmission wave x (t), the amplitude spectrum A (f) of the transmission wave, and the phase spectrum φ (f) of the transmission wave.
First, the transmission wave x (t) is expanded in the Fourier series. At this time,

である。
次に、フーリエ級数の項それぞれに、

It is.
Next, for each Fourier series term,

を乗じる。即ち、

Multiply That is,

とする。

And

  The spectrum whose amplitude is corrected by the equation (16) is subjected to inverse Fourier transform to return to the time-axis waveform to obtain a transmission waveform.

   Next, a method of producing the pulse compression device 10 by generating a transmission waveform based on the above-described principles 1) to 3) will be described based on the flowchart of FIG. This process can be executed by a computer using a transmission waveform generation program.

(1) First, a transmission pulse width T, a frequency sweep width B, a sampling interval Δt, and a power spectrum target waveform P (f) (= first target P ₁ (f)) are set (step S10).
For example, when a Hanning window is used as the target waveform, P (f) is

である。ここで、便宜上、時刻Ｔ／２における周波数ｆ_C、及び位相φは０とし、周波数ｆは−Ｂ／２→Ｂ／２と変化させることとする。このとき、

It is. Here, for convenience, the frequency f _C and the phase φ at time T / 2 are set to 0, and the frequency f is changed from −B / 2 to B / 2. At this time,

となり、Ｔ／２を中心に対称となるので、Ｔ／２〜Ｔの範囲についてのみ計算を行うことで、計算を簡略化することができる。

Therefore, the calculation is simplified by performing the calculation only for the range of T / 2 to T.

(2) The frequency coefficient C is calculated in the state where the above preparation is completed (step S12).
The frequency coefficient C satisfies the expression (4), and when the function B (C) having the frequency coefficient C as a variable is used, the expression (6) to B (C) are expressed by the following expressions. .

Here, C is represented by C = kBP ′ (f) / T, and k is a constant. Since P ′ (f), which is the power spectrum of the linear chirp, is considered as a rectangle, P ′ (f) can also be regarded as a constant.
Therefore, when P ′ (f) is included in k and C = kB / T, B (C) is a monotonically increasing function with respect to C.

となるＣ_lとＣ_uを考えると、Ｂ（Ｃ）＝ＢとなるＣは、Ｃ_lとＣ_uの区間に存在する。よって、図７に示すフローチャートで示す２分探査を行えば、Ｂ（Ｃ）＝ＢとなるＣを求めることができる。

Considering C _l and C _u , C where B (C) = B exists in the interval between C _l and C _u . Therefore, if the binary search shown in the flowchart of FIG. 7 is performed, C where B (C) = B can be obtained.

(3) Next, calculated C and the following formula

を用いて、チャープ率ｃ（ｔ_k）と周波数ｆ（ｔ_k）を算出する（ステップＳ１４）。算出区間はＴ／２〜Ｔである。

Is used to calculate the chirp rate c (t _k ) and the frequency f (t _k ) (step S14). The calculation interval is T / 2 to T.

(4) Next, a phase is calculated | required using following Formula and a waveform is calculated (step S16).

  In step S14 and step S16, when the total number of sampling points is an even number (2N), the data position at time T / 2 is a position between the Nth sampling point and the (N + 1) th sampling point. Become. In this case, it may be calculated as the time when the center of the data is shifted by Δt from T / 2. This is because even if the calculation error is small, this error causes a range side lobe.

(5) Next, a waveform of 0 to T / 2 is determined using the following equation (step S18).

(6) Fourier series expansion of x (t) (step S20).

(7) The amplitude spectrum is corrected with the power spectrum density P (f) (= second target P ₂ (f)) of the target waveform, and the corrected amplitude spectrum is subjected to inverse Fourier transform to return to the time axis waveform (step S22). .

(8) The waveform x (t) obtained in step S22 is stored in the memory 12, and the pulse compression apparatus 10 is configured (step S23).

   8 to 10, the pulse width T = 12.8 μsec, the sweep width B = 28 MHz (−14 MHz to 14 MHz), and the target waveform P (f) is a Gaussian window.

とし、振幅変調工程における窓関数をハニング窓

And the Hanning window as the window function in the amplitude modulation process

とした場合の各工程におけるパルス圧縮波形、パワースペクトル密度のログスケール、リニアスケールの波形をそれぞれ表しており、破線が目的波形、実線が生成波形を表している。また、図１１は、生成された送信波形の周波数遷移を表している。

The pulse compression waveform, the log scale of the power spectrum density, and the linear scale waveform in each step are respectively represented, the broken line represents the target waveform and the solid line represents the generated waveform. FIG. 11 shows the frequency transition of the generated transmission waveform.

  As can be seen from FIG. 8 to FIG. 10, since the modulation is performed with the amplitude modulation added in advance only by performing the frequency modulation step 1), the target waveform and the generation are respectively generated in the pulse compression waveform and the transmission waveform. There is a big difference with the waveform, and after the amplitude modulation process of 2), the generated waveform can be close to the target waveform, but there is still a difference, and there is a range sidelobe in the pulse compression waveform. Appears. After the correction process on the frequency axis of 3), the generated waveform becomes almost the same as the target waveform, and the side lobe level of the pulse compression waveform can be lowered. In this example, the S / N loss is 0.30 dB, and the side lobe level is approximately −90 dB.

  As described above, according to the present invention, when transmission / reception is performed and pulse compression is performed using the generated transmission waveform, a pulse compression waveform with a low S / N loss and a desired low sidelobe level is obtained. be able to.

In the embodiment described above, the generation is performed so that the waveform of the power spectrum density matches the predetermined target waveform. However, the present invention is not limited to this, and the predetermined target waveform (= first target P _{1) is used.} (F)) and the final target waveform (= second target P ₂ (f)) can also be made different. Specifically, a waveform obtained by smoothing the waveform of the power spectral density obtained through the frequency modulation step 1) and the amplitude modulation step 2) is defined as the final goal (= second goal P ₂ (f)). In particular, the correction amount in the correction process on the frequency axis of 3) can be made small. Even if the waveform obtained through the frequency modulation process of 1) and the amplitude modulation process of 2) is smoothed, if the ripple is removed, a low side lobe is obtained when the inverse Fourier transform is performed on the waveform. This is because it can be a level. The waveform that can be smoothed can be any window function or other function in which the deviation from the waveform obtained in the amplitude modulation step takes a least square value.

  It is preferable that the correction amount on the frequency axis is small. This is because multiplication on the frequency axis results in convolution on the time axis, and if the multiplication on the frequency axis is large, the waveform returned to the time axis may be greatly collapsed. Therefore, the correction on the frequency axis needs to be performed as close as possible to the target waveform in the frequency modulation step 1) and the amplitude modulation step 2).

DESCRIPTION OF SYMBOLS 10 Pulse compression apparatus 12 Memory 14 Waveform reading part 16 D / A converter 18 Amplifier (amplifier)
20 Transducer 24 A / D converter 26 Pulse compression section

Claims (8)

A transmission waveform generation method for pulse compression that transmits a transmission wave using a chirp wave, receives a reflection wave of the transmission wave, and pulse-compresses the received signal to obtain a pulse compression waveform,
Linear chirp when the first target waveform of the Fourier transform of the pulse compression waveform at which the range side lobe is at a desired level is P ₁ (f) and the power spectral density waveform of the linear chirp waveform is P ′ (f). A frequency modulation step of calculating a non-linear chirp waveform based on the waveform such that its chirp rate c (t) is proportional to P ′ (f (t)) / P ₁ (f (t));
An amplitude modulation step of multiplying the window function w (t) for suppressing the rise and fall of the nonlinear chirp waveform calculated in the frequency modulation step;
The waveform obtained in the amplitude modulation process is further expanded in the Fourier series, and the amplitude spectrum is corrected so as to be the amplitude spectrum of the second target waveform P ₂ (f) of the power spectrum density of the transmission waveform, which is then subjected to inverse Fourier transform. The correction process on the frequency axis to generate
A transmission waveform generation method in pulse compression that generates a transmission waveform from a linear chirp waveform.   The transmission waveform generation method according to claim 1, wherein in the frequency modulation step, a waveform is calculated such that the chirp rate c (t) is proportional to the square of the window function w (t) multiplied by the amplitude modulation step. The first target waveform P ₁ (f) used in the frequency modulation step and the second target waveform P ₂ (f) used in the correction step on the frequency axis are the same. Transmission waveform generation method. The second target waveform P ₂ (f) used in the correction step on the frequency axis is obtained by smoothing the waveform of the power spectrum density of the waveform obtained in the amplitude modulation step. Transmission waveform generation method. 5. The transmission waveform generation method according to claim _1, wherein the first object P ₁ (f) used in the frequency modulation step is a window function. 6. In the correction step on the frequency axis, when the amplitude spectrum obtained by Fourier series expansion of the waveform obtained in the amplitude modulation step is A (f), √ (P _2. The transmission waveform generation method according to claim 1, wherein the amplitude spectrum is corrected by multiplying by (f)) / A (f). A transmission waveform generation program for pulse compression that transmits a transmission wave using a chirp wave, receives a reflected wave of the transmission wave, and pulse-compresses the received signal to obtain a pulse compression waveform,
When the first target waveform of the Fourier transform of the pulse compression waveform at which the range side lobe reaches a desired level is P ₁ (f) and the power spectral density waveform of the linear chirp waveform is P ′ (f), A frequency modulation step of calculating a non-linear chirp waveform based on the linear chirp waveform such that the chirp rate c (t) is proportional to P ′ (f (t)) / P ₁ (f (t));
An amplitude modulation step of multiplying the window function w (t) for suppressing the rise and fall of the nonlinear chirp waveform calculated in the frequency modulation step;
The waveform obtained in the amplitude modulation process is further expanded in the Fourier series, and the amplitude spectrum is corrected so as to be the amplitude spectrum of the second target waveform P ₂ (f) of the power spectrum density of the transmission wave, and the inverse Fourier transform is performed. Correction process on the frequency axis to generate
Is a transmission waveform generation program in pulse compression that generates a transmission waveform from a linear chirp waveform. A memory for storing a transmission waveform generated by the method according to any one of claims 1 to 6, a waveform reading unit for reading a transmission waveform signal from the memory, and an analog signal obtained by D / A converting the transmission waveform signal A D / A converter for converting to a transmission signal, an amplifier for amplifying the transmission signal, a transducer for radiating the amplified transmission signal as a transmission wave and receiving a reflected wave of the transmission wave, and A / D conversion of the reception wave A pulse compression apparatus comprising: an A / D converter that converts the received waveform signal into a received waveform signal; and a pulse compression unit that obtains a pulse compressed waveform signal by correlating the received waveform signal and the reference waveform signal.

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