Matlab perform fft to obtain amplitude and phase

本文介绍如何利用Matlab的FFT函数分析周期信号,并获取其幅度和相位信息。通过示例代码展示了如何设置采样频率、创建周期信号、进行快速傅立叶变换以及绘制频谱图。

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In this article, we imposed Matlab fft on a periodic function and to get its amplitude and phase

code

sampleFreq=100;
x=[-100:1/sampleFreq:100-1/sampleFreq];
nLength=length(x);%20000
fftLength=floor(nLength/2);
frequencyVector=(0:1/nLength*sampleFreq:(nLength-1)/nLength*sampleFreq);
y1=1.7*cos(10*2*pi*x+pi/4);
result=fft(y1,nLength);
result1=result(1:fftLength);
phase=atan2(imag(result1),real(result1));
result=2*abs(result)/nLength;
%plot(y1);
figure;
plot(frequencyVector(1:fftLength),result(1:fftLength));
xlabel("frequency")
ylabel("amplitude")
grid on;
%hold on;
%plot(frequencyVector(1:fftLength),phase(1:fftLength));
maxAmpli=max(result)
index=find(result==maxAptil)
thisPhase=phase(index(1))
freq=frequencyVector(index(1))

result

result 1:
在这里插入图片描述
result 2:

maxAmpli =
    1.7000
index =
        2001       18001
thisPhase =
    0.7854
freq =
    10

Note:

  1. If the function is relating to sin(), the correct phase should plus pi/2 due to the fft function is powered by cos() in matlab.
  2. To get right phase, the number of sample points should be even due to unknown error.
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