**Tasks to do: **

**Basic computation of LPC-based spectrum and the comparison with DFT spectrum**- The first steps of LPC-spectrum computation should be realized
using the signal
vm0-600.bin of length
*N = 600 samples*. Signal should be weighted by Hamming window. - Using the function
*lpc*compute autoregressive coefficients of analyzed signal. Use the order of AR model*p=16*. - Observe frequency response of AR model of analyzed signal with
numerator of transfer function equal to 1 ( use fcn
*freqz*) and compare achieved result with DFT spectrum of signal. - 1st checked result (1 point):
- Display the waveform (weighted by Hamming window) of the signal vm0-600.bin same as its amplitude DFT spectrum in logarithmic scaling.
- Display frequency response of AR model with transfer function
*H(z) = 1 / A(z)*.

- Compare LPC spectrum (i.e. based on frequency response of signal AR model) and its power DFT-based spectrum (PSD). Draw both estimations into one figure by different colours !!
- Observe mainly the contribution of power of prediction
error
*Ep*to both estimations, same as the number of samples of particular estimations (spectra). - Observe also the changes of smoothed LPC spectrum for varying
order of AR model, i.e.
*p=16, 10, 6, 30, 80*. Explain !! - 2n checked result (1 point):
- LPC spectrum of the order 16 and DFT-based power spectrum in one figure.
- LPC spectrum of the order 6 and DFT-based power spectrum in one figure.
- LPC spectrum of the order 30 and DFT-based power spectrum in one figure.

- The first steps of LPC-spectrum computation should be realized
using the signal
vm0-600.bin of length
**DFT and LPC spectrum of harmonic signals.**- Generate the following signals:
**s1**- sinusoid with fs = 8000 Hz, f1= 878 Hz, A1=0,8, duration 0.5s ;**s2**- sinusoid fs = 8000 Hz, f1= 2321 Hz, A1=0,7, duration 0.5s ;**n1**- Gaussian white noise of the same length as**s1**and**s2**, zero mean value, power of generated noise should be*P_n = 0.25*;

- Observe DFT and LPC spectra of signals containing one or two
harmonic components. Work with the following combiantions:
**s1****s1+n1****s1+s2****s1+s2+n1**

- Observe especially the influence on order of LPC model, wotk with
the following orders
*p=2, 4, 6, 8, 10*. - 3rd checked result (1 point):
- DFT and LPC spectrum of signals
**s1**resp.**s1+n1**for AR-model orders 2, 4 a 8. - DFT and LPC spectrum of signals
**s1+s2**resp.**s1+s2+n1**for AR-model orders 2, 4 a 8.

- DFT and LPC spectrum of signals

*OPTIONAL HOMEWORK*- Generate the following signals:
**AR modelling of speech signal.**- use prepared demo m-file cv11_AR_to_complete.m- Work with the signal
vm0-600.bin of length
*N = 600 samples*.**Signál should not be weigthed !** - Use function
*lpc*and compute parameters of AR model, i.e. autoregressive coefficients**a**and power of prediction error**Ep**. In the first step, use the order*p=10*. - Observe analyzed signal and error signal obtained by the filtering of analyzed signal by FIR filter with transfer function A(z).
- Observe modelled signal in the followign situations:
- H(z) = 1 / A(z), excitation by obtained error signal,
- H(z) = 1 / A(z), excitation by unite pulses with period To=120 samples,
- H(z) = sqrt(Ep) / A(z), excitation by unite pulses with period To=120 samples and the power equal to 1,
- H(z) = sqrt(Ep) / A(z), excitation by unite pulses with varying period and the power equal to 1, use To=80, 150 samples.

- Observe the contribution of model order. Use
*p=10, 6, 16, 30*.

- Work with the signal
vm0-600.bin of length