### XE31CZS Exercise - Multi-Band Signal Processing

• Signals for processing
• Sum of harmonic components
Generate the signal as sum of sinusoidals of different frequencies over full frequency band
Generation code:
fs=8000;
t=0:2*fs-1;
s=zeros(1,2*fs);
for f=100:100:fs/4-100,
s1=f*sin(2*pi*f*t/fs);
s2=f*sin(2*pi*(fs/4+f)*t/fs);
s=s+s1+s2;
end;
• Speech signal
sm1.bin - fs = 16 kHz (utterance "Mobilní hlasová shránka" - male - raining)
sf1.bin - fs = 16 kHz (utterance "Mobilní hlasová shránka" - female)
sm2.bin - fs = 16 kHz (utterance "1 0 6 4 7" - male)
sf2.bin - fs = 16 kHz (utterance "1 0 6 4 7" - female)

• Split the signal into two symetrical frequency bands:
• Design filter bank into following two frequency bands:
0 - fs/4 a fs/4 - fs/2.
• Filter analyzed signal.
• Observe spectral characteristics of the signals in particular bands.
Attention ! For sinusoidal observe short-time DFT spectrum, for Speech observe spectrgrams !
• Add separated signals and evaluate power of error signal (i.e. difference between original and output)

• Decimation
• Realize decimation 1:2 for original signal and also for signals in particular bands.
ATTENTION !!! It is not possible to use function decimate from Signal Processing Toolbox because it uses always low-pass filtering !!! You must realize it by direct removing of given signal samples.
• Observe spectral characteristics of all signals before and after decimation and explain results.

• Interpolation
• Insert zeros between samples of decimate signals and observe spectral characteristics of these signals.
• Realize the interpolation for both bands using suitable filtering. Observe again spectral characteristics of output signals.
• Add signals after interpolation and evaluate again the power of error signal and compare with previously evaluated results for the synthesis without decimation and interpolation.

• Try to realize splitting into 4 frequency bands, including decimation and interpolation. Take care about following problems:
• decimation order,
• changes of spectral characteristics in particular bands,
• changes in interpolation procedure.