BE2M31DSP - seminar 2
Idetification of AR model parameters, LPC-based spectral analysis
Particular tasks to do:
- Identification of unknown AR system, determination of parameters of unknown noise
- On the basis of available signals and using the function lpc, determine parameters of AR
system, which was used for generation of the 1st and 2nd order color noises. see the previous seminar.
Use signals generated at previous seminar or load them from the following files:
- nc1, AR-based LF color noise (nc1.bin, use the function loadbin.m to load the signal into MATLAB environment),
- nc2, AR-based HF color noise (nc2.bin)
- nc1ma and nc2ma, LF and HF color noises generated by MA systems,
- nc3, AR-based band color noise (nc3.bin)
- nc4.bin.
- Realize a spectral analysis in the case of unknown signal and determine
if it is LF, HF, or band noise and try to find suitable order p of LPC analysis (i.e. suitable order of AR
model).
- Result:
- Determine and compare mainly the following parameters of particular AR systems:
- autoregressive coefficients of original and identified system (compare results in exact values),
- draw into one figure zeros and poles of transfer function of original and identified system,
- Observe differences in compared values depending on the length of signal used for a system identification, i.e. full signal length (4000 samples) vs. shorter part (take 1000, 500, 100 samples).
- Observe an impact of the order of LPC analysis / AR model (use p = 1, 2, 4, 8) and explain what is the proper setup of the order.
- Estimation of PSD (smoothed) based on LPC, comparison with DFT-based power spectrum and PSD
- Use the signal
vm0-512.bin délky for the first computation of LPC and DFT spectra
(N = 512 samples, fs = 16
kHz, raw 16-bit PCM, use
loadbin.m yo load it into MATLAB). Weight the signal by Hamming window.
- Determine autoregressive coefficients using the function lpc. Use the order of AR model p=16.
- Observe frequency response of the filter representing AR model
(fcn freqz) of given signal and use 1 for the numerator of
transfer function. Compare observed freqeuncy response with
DFT-based spectrum.
- Result :
- Observe waveform and DFT-based power spectrum in dBs
(periodogram of the signal) for signal
vm0-512.bin weighted by Hamming
window.
- Observe frequency response of AR model of given signal. Take
into account transfer function in the form H(z) = 1 / A(z).
- Compare LPC spectrum (based on AR modelling) and power DFT-based spectrum in dBs within one figure!
- Create equivalent estimations of PSD based on DFT and LPC. Observe mainly impact of power of prediction error Ep to LPC spectrum and impact of number of samples in particular estimations.
- Observe the shape of LPC spectrum for various orders of AR model, use p=16, 10, 6, 30, 80 and explain !!
- Result:
- LPC spectrum of the order 16 a DFT-based periodogram in dBs in one figure.
- LPC spectrum of the order 6 a DFT-based periodogram in dBs in one figure.
- LPC spectrum of the order 30 a DFT-based periodogram in dBs in one figure.
Optional part for possible FREE TIME or for a HOMEWORK
DFT and LPC spectrum of harmonic signals.
- Analyze signals with the following parameters:
- s1 - sinusoid fs = 8000 Hz, f1= 878 Hz, A1=0,8, duration 0.5s ;
- s2 - sinusovka 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 meean value, power P_n1 = 0.25 ;
- Determine DFT and LPC spectra of signals containing one or two
harmonic components with various level of background noise,
i.e. work with the following combinations :
- s1
- s1+n1
- s1+s2
- s1+s2+n1
- Observe mainly the impact of AR model order, i,e, use
p=2, 4, 6, 8, 10.
- Result:
- DFT and LPC spectra of signals s1 resp. s1+n1 for orders 2, 4, and 8.
- DFT and LPC spectra of signals s1+s2 resp. s1+s2+n1
for orders 2, 4, and 8.
AR modeling of speech signal - use preliminary demo m-file
demo_02_AR_to_complete.m
- Work with the signal
vm0-512.bin of length N = 512
vzorků. Do not weight the signal !
- Determine the parameters of AR model using fcn lpc,
i.e. autoregressive coefficients a and power of the
prediction error Ep. Set the basic order of AR model to p=10.
- Observe analyzed signal and error signal obtained by the filtering
of analyzed signal using FIR filter with transfer function A(z).
- Observed modelled signal using AR model with the transfer function H(z)
and excitation signal in the following variants:
- H(z) = 1 / A(z), excitation by obtained error signal,
- H(z) = 1 / A(z), excitation by unit pulses with period To=120 samples,
- H(z) = sqrt(Ep) / A(z), excitation by pulses with power equal to 1
and period To=120 samples,
- H(z) = sqrt(Ep) / A(z), excitation by pulses with power equal to 1
and varying period To, use To=80 or 150 samples.
- Observe an impact of the order of AR model, i.e. use p=10, 6, 16, 30.
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