非平稳信号的频谱分析方法—（短时傅立叶变换）

f0 = 150e3;            %定义LFM信号的中心频率
d_f = 100e3;            %定义LFM信号的频率变化大小
fs = 5*f0;             %定义采样率
points = 2^15;         %采样点数
SNR = 40;              %信噪比
 
nTs = (0:points-1)/fs;
Delta_f = (0:points-1)*fs/points;
%生成LFM信号
signal = sin(2*pi*(f0 + (d_f*fs)/(2*points)*(nTs - points/(2*fs))).*(nTs - points/(2*fs))) + ...  %频率由小变大
         sin(2*pi*(f0 + (-d_f*fs)/(2*points)*(nTs - points/(2*fs))).*(nTs - points/(2*fs)));      %频率由大变小                                                                    
%加入一定功率的白噪声
signal_noise = signal + 10^(-SNR/20)*randn(1,points);

N = 2^8;                                          %截取信号片段点数
window = hanning(N);                              %窗函数类型
Noverlap = N - N/2;                               %相邻两段之间重叠的点数
[S,F,T] = specgram(signal_noise,N,fs,window,Noverlap);
abs_S = abs(S);
max_abs_S = max(max(abs_S));
abs_S = abs_S/max_abs_S;
log10_abs_S = 20*log10(abs_S);
[tt,ff] = meshgrid(T,F/1000);
figure;
surf(tt,ff,log10_abs_S);
xlabel('时间/s');
ylabel('频率KHz');
zlabel('归一化功率谱P(w,t)/dB');
string = ['短时傅里叶变换，采样点数=',num2str(points),',LFM信号中心频率f0=',num2str(f0/1000),...
          'KHz,信号频率变化量d_f=',num2str(d_f/1000),'KHz,采样率fs=',num2str(fs/1000),'KHz,信噪比SNR=',...
          num2str(SNR),'dB'];
title(string);