### XE31CZS Exercise - Periodicity in Short-Time DFT Spectrum

• Simulated and Real Periodicity in DFT
• Load one period of voiced speech signal vm0-per.bin.
(The signal is binary, to load it into MATLAB use attached function loadbin.m ) and find shortime DFT of these signal. Lenght of the DFT should be same as the signal (period) length.
• Observe the changes in the spectrum when the given signal is extended by zeros into 2, 3, 4 -times higher length.
• Observe the changes in the spectrum when the length of the signal is changed by repetition of the same period. Realize it again for 2, 3, 4 -times repetition of the period.
• Observe the changes in the spectrum when the signal with 4 times repeated period is analyzed by DFT of the length
a) 479, 481
b) 470, 490
c) 256, 512
• Observe the periodicity in real signal (voiced sound of speech) vm0.bin, evaluate it for lengths 128, 256, 512, 1024.
• Estimate fundamental period (and fundamental frequency) of sounds vf5.bin and vm5.bin from their short-time DFT spectra.
• Observe short-time DFT spectra for unvoiced sound of speech uf5.bin and um5.bin

• Weigthing and the Periodicity in ST-DFT
• Observe periodograms (short-time DFT spectrum) of above available signals for widow lengths 128, 256, 512, 1024.
• Observe and explain the changes in achieved results when different weighting windows are used (rectangular, Hamming, Blackman).

• Evaluation of convolution by DFT
• Create input traingular sequence x1[n] of length 200
• Create input rectangular sequence x2[n] of length 200
• Evaluate convolution of these two sequences using DFT for N = 200, 400, 256, 500 samples

• NOTE. Compare linear and logaritmic scale of y-axis for observation of short-time magnitude spectra (i.e. 'plot(f,abs(S))' or 'semilogy(f,abs(S))' respectively).