Matlab实例：频谱、功率谱和功率谱密度计算
本实例以高斯信号为例，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。高斯信号的半波全宽FWHM=50ps，中心点位于2.5ns处。MATLAB程序代码：
%================%作者：yoyoba%Email：stuyou@126.com%================clc;clear;FWHM=50e-12;%高斯信号FWHM宽度，为50pstime_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),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/Hzdouble_power_specD_mW=double_power_specD_W*1e+3;%双边功率谱密度，单位mW/Hzdouble_power_specD_dBm=10*log10(double_power_specD_mW);%双边功率谱密度，单位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');
%================%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fftshiftgauss_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Wsingle_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/Hzsingle_power_specD_mW=single_power_specD_W*1e+3;%单边功率谱密度，单位mW/Hzsingle_power_specD_dBm=10*log10(single_power_specD_mW);%单边功率谱密度，单位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');
运行结果：
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