%==========================================================================

%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');