# Matlab hw

% Example of sampling,quantization and zero order hold clear; clf; td=0.002; % original sampling rate 500 Hz t=[0:td:1.]; % time interval of 1 second xsig=sin(2*pi*t)-sin(6*pi*t); % 1Hz+3Hz sinusoids Lsig=length(xsig); ts=0.02; % new sampling rate=50 Hz Nfactor=ts/td; % send the signal through a 16-level uniform quantizer [s_out,sq_out,sqh_out,Delta,SQNR]=sampandquant(xsig,16,td,ts); % receive 3 signals % 1. sampled signal s_out % 2. sampled and quantized signal s_out % 3. sampled, quantized, and zero-order hold signal sqh_out %%%%%%%%%% Calculate the fourier transform %%%%%%%%%%%% Lfft=2^ceil(log2(Lsig)+1); Fmax=1/(2*td); Faxis=linspace(-Fmax,Fmax,Lfft); Xsig=fftshift(fft(xsig,Lfft)); S_out=fftshift(fft(s_out,Lfft)); % Examples of sampling and reconstruction using % a)ideal impulse train through LPF % b)flat top pulse reconstruction through LPF % plot the original signal and the sample signals in time and frequency % domain figure(1); subplot(311); sfigla=plot(t,xsig,'k'); hold on; sfig1b=plot(t,s_out(1:Lsig),'b'); hold off; set(sfigla,'Linewidth',2); set(sfig1b,'Linewidth',2.); xlabel('time (sec)'); title('Signal g(t) and its uniform samples'); subplot(312); sfig1c=plot(Faxis,abs(Xsig)); xlabel('freqency (Hz)'); axis([-150 150 0 300]); set(sfig1c,'Linewidth',1); title('Spectrum of g(t)') subplot(313); sfig1d=plot(Faxis,abs(S_out)); xlabel('freqency (Hz)'); axis([-150 150 0 300/Nfactor]); set(sfig1c,'Linewidth',1); title('Spectrum of gT(t)') % Calculate the reconstructed signal from ideal sampling and ideal LPF % Maximum LPF bandwith equals to BW=floor((Lfft/Nfactor)/2); BW=10; % Bandwith is no larger than 10 Hz. H_lpf=zeros(1,Lfft); H_lpf(Lfft/2-BW:Lfft/2+BW-1)=1; % ideala LPF S_recv=Nfactor*S_out.*H_lpf; % ideal filtering s_recv=real(ifft(fftshift(S_recv))); % reconstructed f domain s_recv=s_recv(1:Lsig); % plot the ideally reconstructed signal in time % and frequency domain figure(2); subplot(211); sfig2a=plot(Faxis,abs(S_recv)); xlabel('freqency (Hz)'); axis([-150 150 0 300]); title('spectrum of ideal filtering (reconstruction)'); subplot(212); sfig2b=plot(t,xsig,'k-.',t,s_recv(1:Lsig),'b'); legend('original signal','reconstructed signal'); xlabel('time (sec)'); title('original signal versus ideally reconstructed signal'); set(sfig2b,'Linewidth',2); % nonideal reconstruction ZOH=ones(1,Nfactor); s_ni=kron(downsample(s_out,Nfactor),ZOH); S_ni=fftshift(fft(s_ni,Lfft)); S_recv2=S_ni.*H_lpf; % ideal filtering s_recv2=real(ifft(fftshift(S_recv2))); % reconstructed f- domain s_recv2=s_recv2(1:Lsig); % reconstructed f- domain % plot the ideally reconstructed signal in time and frequency domain figure(3); subplot(211); sfig3a=plot(t,xsig,'b',t,s_ni(1:Lsig),'b'); xlabel('time (sec)'); title('original signal versus flat-top reconstruction'); subplot(212); sfig3b=plot(t,xsig,'b',t,s_recv2(1:Lsig),'b--'); legend('original signal','LPF reconstruction'); xlabel('time (sec)'); set(sfig3a,'Linewidth',2); set(sfig3b,'Linewidth',2); title('original and flat-top reconstruction after LPF');