### XE31CZS Exercise - DFT and their Basic Properties

• Short-time DFT - frequency resolution and spectral leakage
• Generate sinosoidal with parameters f=500Hz, fs=8000Hz, to=0.1s (duration).
• Evaluate short-time DFT for given sequence (fcn fft) for N = 240, 242, 245, 256 samples
• Repeat poit above for sinosoidal with parameters f=487Hz, fs=8000Hz, to=0.1s (duration).
• Describe correctly scale on frequency axis in Hertz.
• Explain observed results.
• Evaluate short-time DFT for same sequences with application of Hamming weighting window (fcn hamming) of proper length.
• Observe same results with application of other weighting windows - fcn hanning, blackman (triang, kaiser).

• Spectral resolution of two sinusoidal signals
• Generate two sinusoidals with parameters: f1=500Hz, A1=1, f2=550Hz, A2=0.8, fs=8000Hz, delka trvani 1s and create their mixture by simple addition.
• What is the minimal length of the analyzed signal frame for safe resolution of these two harmonic components in short-time DFT ? (Take into account lengths as power of 2, i.e. ..., 64, 128, 256, ...)
a) Evaluate it theoretically
b) Realize it empirically in MATLAB
• Analyze the resolution of two harmonic signals when other weigthing windows are used within DFT evaluation.

• Short-time DFT analysis of speech signal samples
• Load a part of voiced speech signal vm0.bin.
Note1: The signal is in binary form. To load it into MATLAB environment use attached function loadbin.m, this function is not standard function of MATLAB toolboxes! You should place it into your working directory!
Note2: Sampling frequency of the signal is fs = 16 kHz .
• Evaluate short-time DFT of this signal, length of analyzed part of the signal should be in the range 50 - 2000 (i.e. typically 64, 128, 256, 1024, 2048 samples for possible ussing of FFT).
• Describe always correctly the frequency axis in short-time spectrum.
• Compare obtained results with rectangular window (i.e. without weighting) and using Hamming window (weighting minimizing spektral leakage).
• Repeat illustrativelly also for other signals vf5.bin, vm5.bin (parts of voiced speech) and uf5.bin, um5.bin (parts of unvoiced speech).