Matlab实例：频谱、功率谱和功率谱密度计算

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　　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：

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%作者：yoyoba

%Email：stuyou@126.com

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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');

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%以下计算双边谱、双边功率谱、双边功率谱密度

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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/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');

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%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');

　　运行结果：

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