%==========================================================================
%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(stuyou@126.com)
%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\');