分形维数计算的matlab_matlab_分形维数；差分盒维数；功率谱；结构函数_

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), 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 plot(single_f*1e-9,single_power_specD_mW,'linewidth',2.5); xlabel('Frequency/GHz'); ylabel('Power/(dBm/Hz)'); title('single power spectrum density');