Question
Link to .wav file:
https://files.fm/u/wjjjv669
I. Divide a speech signal or music signal into frames of size N = 64 2. Compute the N-point DFT of each frame. 3. Save only first L = 20 DFT coefficients. 4. Reconstruct the frame from these L coefficients. (Do not disturb the symmetry of * DFT during inverse DFT computation. Xk-X[N-k] for real signals, N 64 here. Pad zeros for missing DFT coefficients.) 5. Comment on the quality of reconstructed and the original speech signal 6. What is the effective data compression ratio? Note that DFT coefficients may be complex valued! 7. Repeat the above experiment for L 10 and L = 5. 8. Repeat all above with DCT instead of DFT. Hints 1. Pad zeros at the end of the original signal in order to get the number of total samples to have a multiple of N = 64 2. Effective Data Compression Rate (EDCR) can be calculated by: EDCR [(# of samples in the original signal) / (# of saved real coefficients + (2# of saved complex coefficients)] PS: You may use this formula for "per frame" or for the whole signal. These wil l give actually the same result. 3. You will save first L coefficients of DFT/DCT of original frame. And set the remaining coefficients to zero. Then, in reconstruction step of a frame, you should be careful about the conjugate symmetry of the DFT signal which is X[k]X [N-k] * PS: The first coefficient of DFT is always real, and X[0] = X[N-XIN by the above formula! 4. Using these L coefficients and corresponding (L-1) conjugate symmetric coefficients, (in between of these are all zeros), you take the IDFT of each frame. By the missing coefficients, the IDFT might be complex valued with the imaginary parts in the order of 1018 - 1020. You may ignore the imaginary parts and use the real parts of the reconstructed signal samples Please make comments and state any conclusions in your report. Plot the original signal and reconstructed signals to get some idea about the compression quality. Also listen to those signals and make comments about intelligibility. You may use soundsc(signal name,8000) command to listenthem in Matlab
Explanation / Answer
x=[your array of N samples]; n=round(length(x)/20); %find how many samples will each frame contain P=zeros(n,20); %preallocate the matrix for 20 colums of Nsamples/20 in each for k=0:19 P(:,k+1)=x(1+n*k:n*(k+1)); end
