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CN113541624B - Small signal processing method for power amplifier control - Google Patents

Small signal processing method for power amplifier control
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CN113541624B
CN113541624BCN202110747270.9ACN202110747270ACN113541624BCN 113541624 BCN113541624 BCN 113541624BCN 202110747270 ACN202110747270 ACN 202110747270ACN 113541624 BCN113541624 BCN 113541624B
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CN113541624A (en
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郑德智
李大鹏
惠乾鑫
那睿
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Beihang University
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Beihang University
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Abstract

The invention discloses a small signal processing method for power amplifier control, which is characterized in that by carrying out Hample filtering and autocorrelation operation on an analog sine wave small signal with smaller amplitude and lower signal-to-noise ratio and carrying out Fast Fourier Transform (FFT) frequency measurement on the result of the autocorrelation operation, the signal-to-noise ratio of the sine wave is effectively improved by comparing an ideal digital sine wave with a triangular wave generated by a built-in ROM, signal burrs are eliminated, and the problem of PWM wave output jump caused by abnormal fluctuation of the amplitude of the signal due to environmental noise and ADC quantization error when the analog sine wave small signal is input is solved, thereby ensuring stable output of PWM signals, leading the control signal of a power amplifier to be more stable and better in performance.

Description

Small signal processing method for power amplifier control
Technical Field
The invention belongs to the technical field of signal self-adaptive control, and particularly relates to a small signal processing method for controlling a power amplifier.
Background
A power amplifier is widely used in various fields such as aerospace, vehicle transportation, medical equipment, and industrial automation as a device for driving a load under a given distortion rate. Accordingly, there is also a higher requirement for the accuracy and stability of its control signals.
At present, most power amplifiers generate PWM signals to drive loads to work by adopting a method of comparing analog sine waves with different frequencies and amplitudes and digital triangular waves generated by a built-in ROM. However, the industrial environment is complex, when a sine wave with smaller amplitude is input into the power amplifier, the signal-to-noise ratio of the input sine wave signal is low due to the influence of environmental noise, and the signal is submerged in the noise and contains more burrs. In addition, due to the limited number of ADC bits, the generated quantization noise can further reduce the signal-to-noise ratio of the sinusoidal signal, so that irregular fluctuation is generated when the quantized digital sinusoidal wave is compared with the digital triangular wave, the PWM signal is output unstably, and the stable operation of a load is influenced.
Therefore, when sine waves with smaller amplitude and lower signal-to-noise ratio are input externally, how to realize stable control of the power amplifier signals, improve the driving performance of equipment and prolong the service life of the equipment has important engineering significance.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a small signal processing method for controlling a power amplifier, which can solve the problem of PWM output jump caused by abnormal fluctuation of signals generated by environmental noise and ADC quantization error when an analog sine small signal with smaller external amplitude and lower signal-to-noise ratio is input, thereby ensuring stable output of PWM signals, enabling the control signal of the power amplifier to be more stable, improving the driving performance of equipment and prolonging the service life of the equipment. The specific technical scheme of the invention is as follows:
a small signal processing method for power amplifier control, comprising the steps of:
s1: sampling the externally input continuous sine wave small signal by adopting a high-precision ADC, quantizing the continuous sine wave small signal into a digital sine wave signal, and inputting the digital sine wave signal into a processor;
s2: intercepting the digital sine wave signal obtained in the step S1, solving a signal variance, adaptively adjusting the window length of a Hample filter according to the signal variance, and carrying out Hample filtering treatment on the intercepted digital sine wave signal;
s3: performing discrete autocorrelation operation on the signal filtered in the step S2 to obtain a discrete autocorrelation sequence;
s4: performing FFT operation on the discrete autocorrelation sequence obtained in the step S3, and calculating the frequency of the autocorrelation sequence; the frequency of the autocorrelation sequence is the frequency of the input sine wave signal in the step S1, the discrete sine wave signal sequence with fixed sampling rate, frequency and amplitude is generated by the processor by utilizing the frequency of the obtained input sine wave signal, and the discrete sine wave signal sequence is retransmitted to the processor;
s5: generating triangular waves by using a ROM table, and then performing linear interpolation to ensure that the sampling rate of the triangular wave signals after interpolation is the same as that of the discrete sine signal sequences generated in the step S4, namely the quantization errors are the same;
s6: and (3) comparing the triangular wave signal processed in the step (S5) with the discrete sine sequence generated in the step (S4) by a comparator to generate a PWM signal P, and directly driving a power amplifier.
Further, the step S2 specifically includes:
s2-1: intercepting digital sine wave signal sequence X with length NN Is [ x ]0 ,x1 ,…,xi ,…,xN-1 ]Find signal XN Is a variance of (2);
s2-2: adaptive adjustment of Hample Filtering finger x based on variancei The number of surrounding samples k, where i=1, …, N, as shown in equation (1), determines a window length of l=2k+1, where,
wherein ,rounding down as a rounding function;
s2-3: select xi Surrounding sequence Y2k+1 Is [ x ]i-k ,xi-k+1 ,...,xi ,...,xi+k-1 ,xi+k ]Length l=2k+1, and sequence Y is determined2k+1 Median m of (2)i And absolute deviation sigmai As shown in the formula (2) (3):
mi =median(xi-k ,xi-k+1 ,…,xi ,…,xi+k-1 ,xi+k ) (2)
σi =1.4826·median(|xi-k -mi |,...,|xi+k -mi |) (3)
wherein media () represents a median sequence value;
s2-4: when sampling point xi The sampling point on the left or right is less than k, namely when the sampling point is at the head end or the tail end of the signal, the median m is calculated according to (4) and (5)i And absolute deviation sigmai
S2-5: processing the selected x according to equation (6)i
wherein ,nσ Is a specified multiple of the deviation.
Further, the step S4 specifically includes:
the autocorrelation sequence phi obtained in step S3 is checked by the IP of the FFT in the processorx (m) performing FFT operation, and then taking the frequency corresponding to the point with the highest amplitude in the frequency domain as the frequency of the input sine wave signal, as shown in the formulas (7) (8):
fsin =f(Yj =max(Y(k))) (8)
wherein ,Wn =e(-2πi)/n Y (k) is the amplitude corresponding to different frequency points after Fourier transformation, k is the frequency point sequence, fsin To be the required inputInto the frequency of the sinusoidal signal, Yj The frequency domain maximum amplitude value is j, the frequency point corresponding to the maximum amplitude value is j, and M is the length of the autocorrelation sequence;
using the obtained frequency f of the input sinusoidal signalsin Generating, by a processor, a sequence X of discrete sinusoidal signals of fixed sampling rate, frequency and amplitudesin And the discrete sine signal sequence is retransmitted to the processor through the serial port.
Further, the step S5 specifically includes:
s5-1: generating a sampling frequency f using ROM tables Peak-to-peak value of Vp-p Is a triangular wave signal of (2);
s5-2: let the frequency of the triangular wave to be generated be ftri Original adjacent two points xi and xi+1 Is required to be inserted betweenA p-th point, wherein the amplitude of the p-th point is xip
Guarantee triangular wave signal Xtri And sinusoidal signal Xsin The sampling rate of (a) is the same, i.e. the quantization error is the same.
The invention has the beneficial effects that:
1. compared with the Hample filter algorithm with the fixed-length window length, the Hample filter algorithm with the self-adaptive window length can still effectively delete peak outliers generated by environmental impact noise from signals under the condition of input sine wave frequency change without generating excessive smoothing.
2. According to the invention, the frequency is obtained by carrying out FFT (fast Fourier transform) on the autocorrelation sequence of the discrete signal after Hample filtering, and compared with the method for directly carrying out FFT on the discrete signal, the frequency measurement is more accurate. Meanwhile, the autocorrelation operation is adopted to replace the design of FIR, IIR and other digital filters, and the noise suppression is directly carried out in the time domain, so that the operation amount is reduced, the operation speed is improved, and the implementation is easier in the operation of the processing unit.
3. The invention uses a linear interpolation method to ensure that the sampling frequency of the triangular wave is the same as that of the sine wave, namely the quantization steps are the same, thereby avoiding abnormal jump of the PWM wave caused by quantization errors and ensuring the output stability of the PWM wave.
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For a clearer description of an embodiment of the invention or of the solutions of the prior art, reference will be made to the accompanying drawings, which are used in the embodiments and which are intended to illustrate, but not to limit the invention in any way, the features and advantages of which can be obtained according to these drawings without inventive labour for a person skilled in the art. Wherein:
FIG. 1 is an ideal sinusoidal small signal waveform and a sinusoidal small signal waveform with Gaussian white noise and spike noise added, wherein (a) is a sinusoidal time domain continuous waveform, (b) is a sinusoidal time domain step waveform, (c) is a sinusoidal time domain waveform with Gaussian white noise and spike noise added, and (d) is a sinusoidal time domain step waveform with Gaussian white noise and spike noise added;
FIG. 2 is a digital triangular time domain waveform, wherein (a) is a triangular time domain waveform and (b) is a triangular time domain staircase waveform;
FIG. 3 shows the result of the process when the signal-to-noise ratio of the added Gaussian white noise is 10dB, wherein (a) is an ideal PWM time domain waveform, (b) is a PWM time domain waveform after the noise is added, and (c) is a PWM time domain waveform after the process of the invention;
FIG. 4 shows the result of the process when the signal-to-noise ratio of the added Gaussian white noise is 5dB, wherein (a) is an ideal PWM time domain waveform, (b) is a PWM time domain waveform after the noise is added, and (c) is a PWM time domain waveform after the process of the invention;
fig. 5 is a flow chart of the method of the present invention.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. It should be noted that, without conflict, the embodiments of the present invention and features in the embodiments may be combined with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
As shown in fig. 5, a small signal processing method for power amplifier control includes the steps of:
s1: sampling the externally input continuous sine wave small signal by adopting a high-precision ADC, quantizing the continuous sine wave small signal into a digital sine wave signal, and inputting the digital sine wave signal into a processor;
s2: intercepting the digital sine wave signal obtained in the step S1, solving a signal variance, adaptively adjusting the window length of a Hample filter according to the signal variance, and carrying out Hample filtering treatment on the intercepted digital sine wave signal; the peak abnormality generated by random noise is filtered, the waveform is smoothed, and the signal to noise ratio is improved.
S3: performing discrete autocorrelation operation on the signal filtered in the step S2 to obtain a discrete autocorrelation sequence;
s4: performing FFT operation on the discrete autocorrelation sequence obtained in the step S3, and calculating the frequency of the autocorrelation sequence; the frequency of the autocorrelation sequence is the frequency of the input sine wave signal in the step S1, the discrete sine wave signal sequence with fixed sampling rate, frequency and amplitude is generated by the processor by utilizing the frequency of the obtained input sine wave signal, and the discrete sine wave signal sequence is retransmitted to the processor;
s5: generating triangular waves by using a ROM table, and then performing linear interpolation to ensure that the sampling rate of the triangular wave signals after interpolation is the same as that of the discrete sine signal sequences generated in the step S4, namely the quantization errors are the same;
s6: and (3) comparing the triangular wave signal processed in the step (S5) with the discrete sine sequence generated in the step (S4) by a comparator to generate a PWM signal P, and directly driving a power amplifier.
In some embodiments, step S2 is specifically:
s2-1: intercepting digital sine wave signal sequence X with length NN Is [ x ]0 ,x1 ,…,xi ,…,xN-1 ]Find signal XN Is a variance of (2);
s2-2: adaptive adjustment of Hample Filtering finger x based on variancei The number of surrounding samples k, where i=1, …, N, as shown in equation (1), determines a window length of l=2k+1, where,
wherein ,rounding down as a rounding function;
s2-3: select xi Surrounding sequence Y2k+1 Is [ x ]i-k ,xi-k+1 ,...,xi ,...,xi+k-1 ,xi+k ]Length l=2k+1, and sequence Y is determined2k+1 Median m of (2)i And absolute deviation sigmai As shown in the formula (2) (3):
mi =median(xi-k ,xi-k+1 ,…,xi ,…,xi+k-1 ,xi+k ) (2)
σi =1.4826·median(|xi-k -mi |,...,|xi+k -mi |) (3)
wherein media () represents a median sequence value;
s2-4: when sampling point xi The sampling point on the left or right is less than k, namely when the sampling point is at the head end or the tail end of the signal, the median m is calculated according to (4) and (5)i And absolute deviation sigmai
S2-5: processing the selected x according to equation (6)i When the deviation is large, the median value is used instead of:
wherein ,nσ Is a specified multiple of the deviation.
Preferably, nσ Taken as 3.
The Hampel filter works in a similar manner to a median filter, but it replaces only the values corresponding to a few standard deviations away from the local median. The discrete sine wave signal is subjected to the Hample filtering processing by using the Hample filtering algorithm with the self-adaptive window length, so that peak abnormal values can be still effectively deleted from the signal under the condition of changing the frequency of the input sine wave, excessive smoothing phenomenon can not be generated, noise can be effectively reduced, the signal to noise ratio is improved, and preparation is made for the next step of signal autocorrelation operation.
In some embodiments, step S3 is specifically:
performing autocorrelation operation on the Hample filtered signal with the adaptive window length to obtain a discrete autocorrelation sequence phix (m) as shown in formula (7):
where m=0, 1,..n-1, since the discrete signal is a periodic signal, the autocorrelation signal is thus also a periodic signal of the same frequency. Because the correlation between the signal and the noise is different, the signal is strengthened after the autocorrelation is obtained, the noise is weakened, namely, the noise is inhibited to a certain extent, so that the signal-to-noise ratio can be increased, and the frequency measurement precision is improved. Meanwhile, the digital filters such as FIR and IIR are replaced, noise suppression is directly carried out in a time domain, the operation amount is reduced, and the operation speed is improved.
In some embodiments, step S4 is specifically:
the autocorrelation sequence phi obtained in step S3 is checked by the IP of the FFT in the processorx (m) performing FFT operation, and then taking the frequency corresponding to the point with the highest amplitude in the frequency domain as the frequency of the input sine wave signal, as shown in equations (8) (9):
fsin =f(Yj =max(Y(k))) (9)
wherein ,Wn =e(-2πi)/n Y (k) is the amplitude corresponding to different frequency points after Fourier transformation, k is the frequency point sequence, fsin For the frequency of the input sinusoidal signal, Yj The frequency domain maximum amplitude value is j, the frequency point corresponding to the maximum amplitude value is j, and M is the length of the autocorrelation sequence;
using the obtained frequency f of the input sinusoidal signalsin Generating, by a processor, a sequence X of discrete sinusoidal signals of fixed sampling rate, frequency and amplitudesin And the discrete sine signal sequence is retransmitted to the processor through the serial port.
In some embodiments, step S5 is specifically:
s5-1: generating a sampling frequency f using ROM tables Peak-to-peak value of Vp-p Is a triangular wave signal of (2);
s5-2: let the frequency of the triangular wave to be generated be ftri Original adjacent two points xi and xi+1 Is required to be inserted betweenA p-th point, wherein the amplitude of the p-th point is xip
Guarantee triangular wave signal Xtri And sinusoidal signal Xsin The sampling rate of (a) is the same, i.e. the quantization error is the same.
In some embodiments, step S6 is specifically:
the interpolated triangular wave signal Xtri And the sinusoidal signal X generated in step S4sin The signal is fed to a comparator, as shown in equation (11), which generates a PWM signal P to directly drive the power amplifier.
In summary, the invention provides a small signal processing method based on power amplifier control, which is characterized in that by carrying out Hample filtering and autocorrelation operation on an analog sine wave small signal with smaller amplitude and lower signal-to-noise ratio and carrying out Fast Fourier Transform (FFT) frequency measurement on the result of the autocorrelation operation, an ideal digital sine wave is generated and compared with a triangular wave generated by a built-in ROM, so that the signal-to-noise ratio of the sine wave is effectively improved, signal burrs are eliminated, the problem of PWM wave output jump caused by abnormal fluctuation of signal amplitude due to environmental noise and ADC quantization error when the analog sine wave small signal is input is solved, and the stable output of PWM signals is ensured, so that the control signal of the power amplifier is more stable and has better performance.
In order to facilitate understanding of the above technical solutions of the present invention, the following detailed description of the above technical solutions of the present invention is provided by specific embodiments.
Example 1
Simulation was performed using Matlab by adding gaussian white noise and spike noise to a single frequency sinusoidal signal to simulate an external input sine wave when the power amplifier is actually operating, as shown in fig. 1.
Fig. 2-4 show effective results obtained after the processing of the small signal processing method based on the control of the power amplifier according to the present invention.
From the processing results, the method of the invention can fundamentally improve the signal-to-noise ratio of the sine wave, eliminate burrs, solve the problem of PWM wave output jump caused by abnormal fluctuation of signals generated by environmental noise and ADC quantization error when the sine wave small signal with smaller amplitude and lower signal-to-noise ratio is input, and eliminate the influence of the environmental noise on the sine wave, thereby eliminating the abnormal jump of PWM in the comparison process and ensuring the stable output of PWM signals.
The analog sine wave small signal with smaller external input amplitude and lower signal-to-noise ratio is subjected to Hample filtering, autocorrelation operation and Fast Fourier Transform (FFT) frequency measurement processing, so that an ideal digital sine wave signal is generated, the problem that PWM wave output jumps due to abnormal fluctuation of signal amplitude generated by environmental noise and ADC quantization error when the analog sine wave small signal is input is solved, and stable output of the PWM signal is ensured, and the control signal of the power amplifier is more stable.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

Translated fromChinese
1.一种用于功率放大器控制的小信号处理方法,其特征在于,包括以下步骤:1. A small signal processing method for power amplifier control, characterized in that it includes the following steps:S1:采用高精度ADC对外部输入的连续正弦波小信号采样,并量化为数字正弦波信号,输入处理器;S1: Use a high-precision ADC to sample the externally input continuous sine wave small signal, quantize it into a digital sine wave signal, and input it into the processor;S2:截取步骤S1得到的数字正弦波信号,求信号方差,根据信号方差自适应调整Hample滤波器的窗口长度,并对所截取的数字正弦波信号进行Hample滤波处理;S2: Intercept the digital sine wave signal obtained in step S1, find the signal variance, adaptively adjust the window length of the Hample filter according to the signal variance, and perform Hamle filtering on the intercepted digital sine wave signal;S3:对步骤S2滤波后的信号进行离散自相关运算,得到离散自相关序列;S3: Perform discrete autocorrelation operation on the signal filtered in step S2 to obtain a discrete autocorrelation sequence;S4:对步骤S3得到的离散自相关序列进行FFT运算,计算自相关序列的频率;自相关序列的频率即为步骤S1中输入正弦波信号的频率,利用得到的输入正弦波信号的频率,通过处理器产生固定采样率、频率与幅度的离散正弦信号序列,并将离散正弦信号序列再传输给处理器;S4: Perform FFT operation on the discrete autocorrelation sequence obtained in step S3, and calculate the frequency of the autocorrelation sequence; the frequency of the autocorrelation sequence is the frequency of the input sine wave signal in step S1, and use the obtained frequency of the input sine wave signal to calculate The processor generates a discrete sinusoidal signal sequence with a fixed sampling rate, frequency and amplitude, and then transmits the discrete sinusoidal signal sequence to the processor;S5:利用ROM表产生三角波,再进行线性插值,保证插值后三角波信号与步骤S4中产生的离散正弦信号序列的采样率相同,即量化误差相同;S5: Use the ROM table to generate a triangular wave, and then perform linear interpolation to ensure that the interpolated triangular wave signal has the same sampling rate as the discrete sinusoidal signal sequence generated in step S4, that is, the quantization error is the same;S6:将步骤S5处理后的三角波信号与步骤S4产生的离散正弦序列输入比较器比较,产生PWM信号P,直接驱动功率放大器;S6: Compare the triangular wave signal processed in step S5 with the discrete sinusoidal sequence input comparator generated in step S4 to generate a PWM signal P to directly drive the power amplifier;所述步骤S2具体为:The step S2 is specifically:S2-1:截取长度为N的数字正弦波信号序列XN为[x0,x1,…,xi,…,xN-1],求信号XN的方差;S2-1: Intercept the digital sine wave signal sequence XN of length N into [x0 ,x1 ,…,xi ,…,xN-1 ], and find the variance of the signal XN ;S2-2:根据方差自适应调整Hample滤波时指定点xi周围的样本数k,其中,i=1,…,N,如式(1)所示,确定的窗口长度为l=2k+1,其中,S2-2: Adaptively adjust the number of samples k around the specified point xi when performing Hample filtering according to the variance, where i=1,...,N, as shown in equation (1), the determined window length is l=2k+1 ,in,其中,为取整函数,向下取整;in, It is a rounding function, rounded down;S2-3:选择xi周围的序列Y2k+1为[xi-k,xi-k+1,...,xi,...,xi+k-1,xi+k],长度为l=2k+1,求序列Y2k+1的中值mi和绝对偏差σi,如式(2)(3)所示:S2-3: Select the sequence Y2k+1 aroundxi as [xik ,xi-k+1 ,...,xi ,...,xi+k-1 ,xi+k ], The length is l=2k+1. Find the median mi and absolute deviation σi of the sequence Y2k+1 , as shown in equations (2) and (3):mi=median(xi-k,xi-k+1,…,xi,…,xi+k-1,xi+k) (2)mi =median(xik ,xi-k+1 ,…,xi ,…,xi+k-1 ,xi+k ) (2)σi=1.4826·median(|xi-k-mi|,...,|xi+k-mi|) (3)σi =1.4826·median(|xik -mi |,...,|xi+k -mi |) (3)其中,median()表示求序列中值;Among them, median() means finding the median value of the sequence;S2-4:当采样点xi左边或右边的采样点数不足k,即采样点在信号的首端或尾端时,则按式(4)(5)计算中值mi和绝对偏差σiS2-4: When the number of sampling points to the left or right of the sampling point xi is less than k, that is, when the sampling point is at the beginning or end of the signal, the median value mi and the absolute deviation σi are calculated according to equations (4) and (5). :S2-5:根据式(6),处理选择的xiS2-5: Process the selected xi according to equation (6):其中,nσ为指定的偏差倍数。Among them, nσ is the specified deviation multiple.2.根据权利要求1所述的一种用于功率放大器控制的小信号处理方法,其特征在于,所述步骤S4具体为:2. A small signal processing method for power amplifier control according to claim 1, characterized in that the step S4 is specifically:利用处理器中自带的FFT的IP核对步骤S3求得的自相关序列φx(m)进行FFT运算,然后取频域中幅值最高的点所对应的频率作为输入正弦波信号的频率,如式(7)(8)所示:Use the FFT IP that comes with the processor to check the autocorrelation sequence φx (m) obtained in step S3 for FFT operation, and then take the frequency corresponding to the point with the highest amplitude in the frequency domain as the frequency of the input sine wave signal, As shown in formula (7) (8):fsin=f(Yj=max(Y(k))) (8)fsin =f(Yj =max(Y(k))) (8)其中,Wn=e(-2πi)/n,Y(k)为傅里叶变换后不同频率点对应的幅值,k为频率点序列,fsin为所求输入正弦信号的频率,Yj为频域最大幅值,j为最大幅值对应的频率点,M为自相关序列的长度;Among them, Wn =e(-2πi)/n , Y(k) is the amplitude corresponding to different frequency points after Fourier transform, k is the frequency point sequence, fsin is the frequency of the input sinusoidal signal, Yj is the maximum amplitude in the frequency domain, j is the frequency point corresponding to the maximum amplitude, and M is the length of the autocorrelation sequence;利用得到的输入正弦信号频率fsin,通过处理器产生固定采样率、频率与幅度的离散正弦信号序列Xsin,并将离散正弦信号序列通过串口再传输给处理器。Using the obtained input sinusoidal signal frequency fsin , the processor generates a discrete sinusoidal signal sequence Xsin with a fixed sampling rate, frequency and amplitude, and then transmits the discrete sinusoidal signal sequence to the processor through the serial port.3.根据权利要求1所述的一种用于功率放大器控制的小信号处理方法,其特征在于,所述步骤S5具体为:3. A small signal processing method for power amplifier control according to claim 1, characterized in that the step S5 is specifically:S5-1:利用ROM表产生采样频率为fs,峰峰值为Vp-p的三角波信号;S5-1: Use the ROM table to generate a triangular wave signal with a sampling frequency of fs and a peak-to-peak value of Vpp ;S5-2:设需生成三角波的频率为ftri,则原有的相邻两点xi和xi+1之间需要插入个点,其中,第p个点的幅值为xipS5-2: Assuming that the frequency of the triangular wave to be generated is ftri , then the original two adjacent points xi and xi+1 need to be inserted. points, where the amplitude of the p-th point is xip ,保证三角波信号Xtri与正弦信号Xsin的采样率相同,即量化误差相同。It is guaranteed that the sampling rates of the triangular wave signal Xtri and the sine signal Xsin are the same, that is, the quantization errors are the same.
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