1. The problem statement, all variables and given/known data I have created four signals in Matlab and we need to play the sound of these signals. The four signals I've created are: n=[0:8191]; w0=2*pi*2000; T=1/8192; t=[0,1]; t=n*T; x=sin(w0*t); sound(x,1/T); ----------------- n=[0:8192]; w0=2*pi*2000; T=1/8192; t=[0,1]; t=n*T; x=sin(w0*t); [X,f]=ctfs(x,T); sound(X,1/T); ------------------------- n=[0:8191]; w0=2*pi*3000; T=1/8192; t=[0,1]; t=n*T; x=sin(w0*t); sound(x,1/T); -------------------- n=[0:8192]; w0=2*pi*3000; T=1/8192; t=[0,1]; t=n*T; x=sin(w0*t); stem(x(1:50)); --------------------- The function ctfs is defined as: function [X,f] = ctfts(x,T) % CTFTS calculates the continuous - time Fourier transform (CTFT) of a % periodic signal x(t) which is reconstructed from the samples in the % vector x using ideal band limited interpolation. The vector x % contains samples of x(t) over an integer number of periods, and T % contains the sampling period. % % The vector X contains the area of the impulses at the frequency % values stored in the vector f. % % This function m akes use of the relationship between the CTFT % of x(t) and the DTFT of its samples x[n], as well as the % relationship between the DTFT of the samples x[n] and the DTFS of x[n]. N = length(x); X = fftshift(fft(x,N))*(2*pi/N); f = linspace(-1,1-2/N,N)/(2*T); The w0 of the first two signals is 2*pi*2000 and the w0 of the last two signals is 2*pi*2000. Why the pitch of the signals increase as the w0 increase when we do not apply the ctfs function, while the pitches are the same when we apply the function? 2. Relevant equations 3. The attempt at a solution I tried to find out the reason why by deriving the Fourier series of the sampled signals. And the results are shown below: For w0=2*π*2000: The Fourier series is: x[n]=sin(2π*2000*n/8192) =sin(125πn/256) =1/2ej125πn/256-1/2e-j125πn/256 For w0=2*π*3000: The Fourier series is: x[n]=sin(2π*3000*n/8192) =sin(375πn/512) =1/2ej375πn/512-1/2e-j375πn/512 From these results, I found the magnitude spectra and I discovered that the distance between each magnitude components(?) getting longer as the w0 increase. Therefore, I think the pitch should be decrease with the increase of w0. On the other hand, I have no idea why the pitch does not change when we add the function ctfs? Thanks!