【轉載】時域信號的頻譜、功率譜和功率譜密度計算

原文地址：http://blog.chinaunix.net/uid-11829250-id-4992257.html

 

以高斯信號爲例，計算幅度譜、相位譜、雙邊功率譜、雙邊功率譜密度、單邊功率譜、單邊功率譜密度。（轉載請註明出處）

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MATLAB程序代碼：

%==========================================================================%Name:      spectrum_analysis.m%Desc:      以高斯信號爲例，求解其頻譜、雙邊功率譜、單邊功率譜、雙邊功率譜密度、%           單邊功率譜密度，這裏高斯信號的半波全寬FWHM=50ps，中心點位於2.5ns處。%Parameter: %Return:    %Author:    yoyoba(stuyou@126.com)%Date:      2015-4-28%Modify:    2015-4-29%=========================================================================clc;clear;FWHM=50e-12;            %高斯信號FWHM寬度，爲50pstime_window=100*FWHM;   %高斯信號的採樣窗口寬度，該值決定了傅里葉變換後的頻率分辨率Ns=2048;                %採樣點dt=time_window/(Ns-1);  %採樣時間間隔t=0:dt:time_window;     %採樣時間gauss_time=exp(-0.5*(2*sqrt(2*log(2))*(t-2.5e-9)/FWHM).^2); %高斯脈衝，中心位於2.5ns處。plot(t*1e+9,gauss_time,'linewidth',2.5);xlabel('Time/ns');ylabel('Amplitude/V');title('Gauss pulse');%===========如下計算雙邊譜、雙邊功率譜、雙邊功率譜密度=================gauss_spec=fftshift(fft(ifftshift(gauss_time)));    %傅里葉變換，而且進行fftshift移位操做。gauss_spec=gauss_spec/Ns;   %求實際的幅度值；df=1/time_window;               %頻率分辨率k=floor(-(Ns-1)/2:(Ns-1)/2);    % k=0:Ns-1;double_f=k*df;   %雙邊頻譜對應的頻點figure; %幅度譜plot(double_f*1e-9,abs(gauss_spec),'linewidth',2.5);xlabel('Frequency/GHz');ylabel('Amplitude/V');title('double Amplitude spectrum');figure; %相位譜plot(double_f*1e-9,angle(gauss_spec),'linewidth',2.5);xlabel('Frequency/GHz');ylabel('Phase/rad');title('double Phase spectrum');figure; %功率譜double_power_spec_W=abs(gauss_spec).^2;                 %雙邊功率譜，單位W；double_power_spec_mW=double_power_spec_W*1e+3;          %雙邊功率譜，單位mW；double_power_spec_dBm=10*log10(double_power_spec_mW);   %雙邊功率譜，單位dBm；plot(double_f*1e-9,double_power_spec_dBm,'linewidth',2.5);xlabel('Frequency/GHz');ylabel('Power/dBm');title('double Power spectrum');figure; %功率譜密度double_power_specD_W=abs(gauss_spec).^2/(df);       %雙邊功率譜密度,單位W/Hzdouble_power_specD_mW=double_power_specD_W*1e+3;    %雙邊功率譜密度,單位mW/Hzdouble_power_specD_dBm=10*log10(double_power_specD_mW);%雙邊功率譜密度,單位dBm/Hzplot(double_f*1e-9,double_power_specD_dBm,'linewidth',2.5);xlabel('Frequency/GHz');ylabel('Power/(dBm/Hz)');title('double power spectrum Density');%==========如下計算單邊譜、單邊功率譜及單邊功率譜密度=========gauss_spec=fft(ifftshift(gauss_time));  %計算單邊譜無需fftshiftgauss_spec=gauss_spec/Ns;       %計算真實的幅度值single_gauss_spec=gauss_spec(1:floor(Ns/2));single_f=(0:floor(Ns/2)-1)*df;figure; %幅度譜plot(single_f*1e-9,abs(single_gauss_spec),'linewidth',2.5);xlabel('Frequency/GHz');ylabel('Amplitude/V');title('single Amplitude spectrum');figure; %相位譜plot(single_f*1e-9,angle(single_gauss_spec),'linewidth',2.5);xlabel('Frequency/GHz');ylabel('Phase/rad');title('single Phase spectrum');figure;%功率譜double_power_spec_W=abs(gauss_spec).^2;  single_power_spec_W=2*double_power_spec_W(1:floor(Ns/2));   %單邊功率譜，單位Wsingle_power_spec_mW=single_power_spec_W*1e+3;              %單邊功率譜，單位mW；single_power_spec_dBm=10*log10(single_power_spec_mW);       %雙邊功率譜，單位dBm；plot(single_f*1e-9,single_power_spec_dBm,'linewidth',2.5);  xlabel('Frequency/GHz');ylabel('Power/dBm');title('single Power spectrum');figure;%功率譜密度double_power_specD_W=abs(gauss_spec).^2/(df);single_power_specD_W=2*double_power_specD_W(1:floor(Ns/2));         %單邊功率譜密度，單位W/Hzsingle_power_specD_mW=single_power_specD_W*1e+3;                    %單邊功率譜密度，單位mW/Hzsingle_power_specD_dBm=10*log10(single_power_specD_mW);             %單邊功率譜密度，單位dBm/Hzplot(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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運行結果：