This example uses a Gaussian signal to calculate the amplitude spectrum, phase spectrum, two-sided power spectrum, two-sided power spectral density, one-sided power spectrum, and one-sided power spectral density.The full width at half maximum (FWHM) of the Gaussian signal is 50 ps, with the center point located at 2.5 ns.
MATLAB Code:
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%Author:yoyoba
%Email: [email protected]
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clc;
clear;
FWHM=50e-12;
% FWHM width of Gaussian signal is 50 ps
time_window=100*FWHM;
% Sampling window width of Gaussian signal, this value determines the frequency resolution after Fourier transform
Ns=2048;
% Number of sampling points
dt=time_window/(Ns-1);
% Sampling time interval
t=0:dt:time_window;
% Sampling time
gauss_time=exp(-0.5*(2*sqrt(2*log(2))*(t-2.5e-9)/FWHM).^2);
% Gaussian pulse, centered at 2.5 ns.
plot(t*1e+9,gauss_time,’linewidth’,2.5);
xlabel(‘Time/ns’);
ylabel(‘Amplitude/V’);
title(‘Gauss pulse’);
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% Below calculates two-sided spectrum, two-sided power spectrum, two-sided power spectral density
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gauss_spec=fftshift(fft(ifftshift(gauss_time)));
% Fourier transform and perform fftshift operation.
gauss_spec=gauss_spec/Ns;
% Calculate the actual amplitude value;
df=1/time_window;
% Frequency resolution
k=floor(-(Ns-1)/2:(Ns-1)/2),
double_f=k*df;
% Frequency points corresponding to two-sided spectrum
figure;% Amplitude spectrum
plot(double_f*1e-9,abs(gauss_spec),’linewidth’,2.5);
xlabel(‘Frequency/GHz’);
ylabel(‘Amplitude/V’);
title(‘double Amplitude spectrum’);
figure;% Phase spectrum
plot(double_f*1e-9,angle(gauss_spec),’linewidth’,2.5);
xlabel(‘Frequency/GHz’);
ylabel(‘Phase/rad’);
title(‘double Phase spectrum’);
figure;% Power spectrum
double_power_spec_W=abs(gauss_spec).^2;
% Two-sided power spectrum, unit W;
double_power_spec_mW=double_power_spec_W*1e+3;
% Two-sided power spectrum, unit mW;
double_power_spec_dBm=10*log10(double_power_spec_mW);
% Two-sided power spectrum, unit dBm;
plot(double_f*1e-9,double_power_spec_dBm,’linewidth’,2.5);
xlabel(‘Frequency/GHz’);
ylabel(‘Power/dBm’);
title(‘double Power spectrum’);
figure;% Power spectral density
double_power_specD_W=abs(gauss_spec).^2/(df);
% Two-sided power spectral density, unit W/Hz
double_power_specD_mW=double_power_specD_W*1e+3;
% Two-sided power spectral density, unit mW/Hz
double_power_specD_dBm=10*log10(double_power_specD_mW);
% Two-sided power spectral density, unit 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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% Below calculates one-sided spectrum, one-sided power spectrum, and one-sided power spectral density
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gauss_spec=fft(ifftshift(gauss_time));
% One-sided spectrum calculation does not require fftshift
gauss_spec=gauss_spec/Ns;
% Calculate the real amplitude value
single_gauss_spec=gauss_spec(1:floor(Ns/2));
single_f=(0:floor(Ns/2)-1)*df;
figure;% Amplitude spectrum
plot(single_f*1e-9,abs(single_gauss_spec),’linewidth’,2.5);
xlabel(‘Frequency/GHz’);
ylabel(‘Amplitude/V’);
title(‘single Amplitude spectrum’);
figure;% Phase spectrum
plot(single_f*1e-9,angle(single_gauss_spec),’linewidth’,2.5);
xlabel(‘Frequency/GHz’);
ylabel(‘Phase/rad’);
title(‘single Phase spectrum’);
figure;% Power spectrum
double_power_spec_W=abs(gauss_spec).^2;
single_power_spec_W=2*double_power_spec_W(1:floor(Ns/2));
% One-sided power spectrum, unit W
single_power_spec_mW=single_power_spec_W*1e+3;
% One-sided power spectrum, unit mW;
single_power_spec_dBm=10*log10(single_power_spec_mW);
% One-sided power spectrum, unit dBm;
plot(single_f*1e-9,single_power_spec_dBm,’linewidth’,2.5);
xlabel(‘Frequency/GHz’);
ylabel(‘Power/dBm’);
title(‘single Power spectrum’);
figure;% Power spectral density
double_power_specD_W=abs(gauss_spec).^2/(df);
single_power_specD_W=2*double_power_specD_W(1:floor(Ns/2));
% One-sided power spectral density, unit W/Hz
single_power_specD_mW=single_power_specD_W*1e+3;
% One-sided power spectral density, unit mW/Hz
single_power_specD_dBm=10*log10(single_power_specD_mW);
% One-sided power spectral density, unit 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’);
Results:
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