本帖最后由 yszh0836 于 2017-2-28 17:40 编辑

案例场景：

现通过AD采集电网信号进行谐波分析的课题研究，电网为正弦波，周期50Hz(周期20ms)，AD采样率6400(即每个电网周期采样128个点)。

现在用matlab进行前期仿真分析来分析一个直流+50Hz+1500Hz的正弦波叠加后的波形。

代码基本按照matlab的fft帮助文件里的代码修改过来，代码可以正常运行。问题描述如下：

1：Fs=6400，L=128 或者更高的2^N时，分析没有问题，3条幅度从左往右依次是1，2，3。

2：Fs=6400，L=64，则分析后显示频谱幅值就有比较大的误差了，取32就更不对。

我的问题：

1：按理说，L取64时相当于刚好分析半个电网周期的数据，难道FFT分析时一定要分析至少一个完整周期的信号？

2：plot后频谱图上如果两个频率相差太近，可以在每条频谱线的X轴标上频率 值？

代码如下：

Fs = 6400;            % Sampling frequency

T = 1/Fs;             % Sampling period

L = 64;             % Length of signal

t = (0:L-1)*T;        % Time vector

%%

% Form a signal containing a 50 Hz sinusoid of amplitude 0.7 and a 120 Hz

% sinusoid of amplitude 1.

S = 1+2*sin(2*pi*50*t) + 3*sin(2*pi*1500*t);

%%

% Corrupt the signal with zero-mean white noise with a variance of 4.

X = S + 2*randn(size(t));

%%

% Plot the noisy signal in the time domain. It is difficult to identify

% the frequency components by looking at the signal |X(t)|.

% plot(1000*t(1:50),X(1:50))

title('Signal Corrupted with Zero-Mean Random Noise')

xlabel('t (milliseconds)')

ylabel('X(t)')

%%

% Compute the Fourier transform of the signal.

Y = fft(X);

%%

% Compute the two-sided spectrum |P2|.  Then compute the single-sided

% spectrum |P1| based on |P2| and the even-valued signal length |L|.

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2*P1(2:end-1);

%%

% Define the frequency domain |f| and plot the single-sided amplitude

% spectrum |P1|.  The amplitudes are not exactly at 0.7 and 1, as expected, because of the added

% noise. On average, longer signals produce better frequency approximations.

f = Fs*(0:(L/2))/L;

plot(f,P1)

title('Single-Sided Amplitude Spectrum of X(t)')

xlabel('f (Hz)')

ylabel('|P1(f)|')

%%

% Now, take the Fourier transform of the original, uncorrupted signal and

% retrieve the exact amplitudes, 0.7 and 1.0.

Y = fft(S);

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2*P1(2:end-1);

% plot(f,P1)

bar(f,P1,1)

title('Single-Sided Amplitude Spectrum of S(t)')

xlabel('f (Hz)')

ylabel('|P1(f)|')

N=128.png

(67.56 KB, 下载次数: 6)

2017-2-28 11:23 上传

N=128时正常的图

2.png

(70.26 KB, 下载次数: 1)

2017-2-28 11:25 上传

N=64时幅度不正常