时域信号的频谱、功率谱和功率谱密度计算

以高斯信号为例，计算幅度谱、相位谱、双边功率谱、双边功率谱密度、单边功率谱、单边功率谱密度。（转载请注明出处）

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MATLAB程序代码：

%==========================================================================
%Name:      spectrum_analysis.m
%Desc:      以高斯信号为例，求解其频谱、双边功率谱、单边功率谱、双边功率谱密度、
%           单边功率谱密度，这里高斯信号的半波全宽FWHM=50ps，中心点位于2.5ns处。
%Parameter: 
%Return:    
%Author:    yoyoba([e-mail])
%Date:      2015-4-28
%Modify:    2015-4-29
%=========================================================================
clc;
clear;
FWHM=50e-12;            %高斯信号FWHM宽度，为50ps
time_window=100*FWHM;   %高斯信号的采样窗口宽度，该值决定了傅里叶变换后的频率分辨率
Ns=2048;                %采样点
dt=time_window/(Ns-1);  %采样时间间隔
t=0:dt:time_window;     %采样时间
gauss_time=exp(-0.5*(2*sqrt(2*log(2))*(t-2.5e-9)/FWHM).^2); %高斯脉冲，中心位于2.5ns处。
plot(t*1e+9,gauss_time,'linewidth',2.5);
xlabel('Time/ns');
ylabel('Amplitude/V');
title('Gauss pulse');
%===========以下计算双边谱、双边功率谱、双边功率谱密度=================
gauss_spec=fftshift(fft(ifftshift(gauss_time)));    %傅里叶变换，并且进行fftshift移位操作。
gauss_spec=gauss_spec/Ns;   %求实际的幅度值；
df=1/time_window;               %频率分辨率
k=floor(-(Ns-1)/2:(Ns-1)/2);    
% k=0:Ns-1;
double_f=k*df;   %双边频谱对应的频点


figure; %幅度谱
plot(double_f*1e-9,abs(gauss_spec),'linewidth',2.5);
xlabel('Frequency/GHz');
ylabel('Amplitude/V');
title('double Amplitude spectrum');


figure; %相位谱
plot(double_f*1e-9,angle(gauss_spec),'linewidth',2.5);
xlabel('Frequency/GHz');
ylabel('Phase/rad');
title('double Phase spectrum');


figure; %功率谱
double_power_spec_W=abs(gauss_spec).^2;                 %双边功率谱，单位W；
double_power_spec_mW=double_power_spec_W*1e+3;          %双边功率谱，单位mW；
double_power_spec_dBm=10*log10(double_power_spec_mW);   %双边功率谱，单位dBm；
plot(double_f*1e-9,double_power_spec_dBm,'linewidth',2.5);
xlabel('Frequency/GHz');
ylabel('Power/dBm');
title('double Power spectrum');


figure; %功率谱密度
double_power_specD_W=abs(gauss_spec).^2/(df);       %双边功率谱密度,单位W/Hz
double_power_specD_mW=double_power_specD_W*1e+3;    %双边功率谱密度,单位mW/Hz
double_power_specD_dBm=10*log10(double_power_specD_mW);%双边功率谱密度,单位dBm/Hz
plot(double_f*1e-9,double_power_specD_dBm,'linewidth',2.5);
xlabel('Frequency/GHz');
ylabel('Power/(dBm/Hz)');
title('double power spectrum Density');


%==========以下计算单边谱、单边功率谱及单边功率谱密度=========
gauss_spec=fft(ifftshift(gauss_time));  %计算单边谱无需fftshift
gauss_spec=gauss_spec/Ns;       %计算真实的幅度值
single_gauss_spec=gauss_spec(1:floor(Ns/2));
single_f=(0:floor(Ns/2)-1)*df;


figure; %幅度谱
plot(single_f*1e-9,abs(single_gauss_spec),'linewidth',2.5);
xlabel('Frequency/GHz');
ylabel('Amplitude/V');
title('single Amplitude spectrum');


figure; %相位谱
plot(single_f*1e-9,angle(single_gauss_spec),'linewidth',2.5);
xlabel('Frequency/GHz');
ylabel('Phase/rad');
title('single Phase spectrum');


figure;%功率谱
double_power_spec_W=abs(gauss_spec).^2;  
single_power_spec_W=2*double_power_spec_W(1:floor(Ns/2));   %单边功率谱，单位W
single_power_spec_mW=single_power_spec_W*1e+3;              %单边功率谱，单位mW；
single_power_spec_dBm=10*log10(single_power_spec_mW);       %双边功率谱，单位dBm；
plot(single_f*1e-9,single_power_spec_dBm,'linewidth',2.5);  
xlabel('Frequency/GHz');
ylabel('Power/dBm');
title('single Power spectrum');


figure;%功率谱密度
double_power_specD_W=abs(gauss_spec).^2/(df);
single_power_specD_W=2*double_power_specD_W(1:floor(Ns/2));         %单边功率谱密度，单位W/Hz
single_power_specD_mW=single_power_specD_W*1e+3;                    %单边功率谱密度，单位mW/Hz
single_power_specD_dBm=10*log10(single_power_specD_mW);             %单边功率谱密度，单位dBm/Hz
plot(single_f*1e-9,single_power_specD_mW,'linewidth',2.5);
xlabel('Frequency/GHz');
ylabel('Power/(dBm/Hz)');
title('single power spectrum density');

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运行结果：


spectrum_analysis.rar