MATLAB中方波的频谱

Question

我需要使用 MATLAB 绘制方波的频谱。波在 0 和 -2 之间为 HIGH (5mV)，在 0 和 2 之间为 LOW (omv)。我已经获得了傅里叶序列 对于这个函数，我有该系列的前十个组件。

(5/2) + ((10/pi)*sin((pi*t)/2)) + ((10/(3*pi))*sin((3*pi*t)/2 )) + ((10/(5*pi))*sin((5*pi*t)/2)) + ((10/(7*pi))*sin((7*pi*t)/2 ))+ ((10/(9*pi))*sin((9*pi*t)/2))+ ((10/(11*pi))*sin((11*pi*t)/2 ))+ ((10/(13*pi))*sin((13*pi*t)/2))+ ((10/(15*pi))*sin((15*pi*t)/2 ))+ ((10/(17*pi))*sin((17*pi*t)/2))+ ((10/(19*pi))*sin((19*pi*t)/2 ))

如何使用 MATLAB 绘制此波的频谱？我曾尝试使用 FFT，但我真的不知道它是如何绘制图形的。

Answer 1

这是直接改编自fft docs，但使用方波作为信号：

Fs = 1000;                    %// Sampling frequency
freq = 50;
T = 1/Fs;                     %// Sample time
L = 1000;                     %// Length of signal
t = (0:L-1)*T;                %// Time vector
A = 10;                       %// Amplitude

y = A*(sin(2*pi*freq*t) > 0); %// Make a square wave


plot(Fs*t,y);
xlabel('time (milliseconds)')

NFFT = 2^nextpow2(L);         %// Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);

%// Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2+1))) 
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)') %// probably would be more meaningful if you convert this to radians per second, check out the xtickmark and xtickmarklabel properties of plot
ylabel('|Y(f)|')