BE2M31DSP seminar
DFT and LPC cepstrum, cepstral distance
- Computation of DFT and LPC cepstrum in short-time frames
- Compute in short-time frames time dependancy of DFT and LPC
cepstrum of longer signal. Set the followign parameters of
short-time analysis and cepstrum computation:
- frame length of 32 ms, frame shoft of 16 ms, Hamming weighting window
- LPC order p=16,
- number of cepstral coefficients (excluding c[0]) cp=12,
- observe always coefficient c[0] - c[12] or c[1] - c[12] (i.e. without c[0])
Use available functions:
- real cepstrum computation - vrceps.m
- LPC cepstrum computation- vaceps.m, aceps.m, a2c.m, a2c0.m
- Signals for processing
- SA001S04.CS0 - raw data
without header, fs=16000 Hz.
- Result: for signal
SA001S04.CS0 display:
- coefficients c[0]-c[12] or c[1]-c[12] for DFT and LPC cepstrum,
- short-time DFT and LPC cepstrum for 105th short-time frame.
- Cepstral-distance-based evaluation of signal quality
- Create distorted signal from SA001S04.CS0 using FIR filter with the following parameters: low-pass, normalized cutoff frequency W_c = 0.9, use filter order M = 30-50.
- Compute time dependancy of short-time DFT and LPC cepstrum with the same setup as above also for the signal with modelled distortion.
- Compute Euclidan cepstral distance between the segments of original and distorted signal in the same time. Euclidan distance can be computed using function cde.m - compute the distance including coefficient c[0] and repeat it also for the case of distance without c[0].
- Result:
For above specified couple of original and distorted signal (SA001S04.CS0) observe:
- spectrograms of both signals,
- time dependancy of cepstral distance for DFT and LPC cepstrum,
- mean value of cepstral distance for all short-time frames,
- same results observe for the case of lower cutoff frequency of used low-pass filter, i.e. W_c = 0.8 or W_c = 0.6.
- Repeat for:
- Determination of segment boundaries based on DFT or LPC cepstrum
- Compute same way as in the first point above time dependancy of short-time DFT and LPC cepstrum for longer signals.
- Evaluate Euclidan cepstral distance (cd0.m
in variants with and without c[0]) between two successive short-time frames and observe its time dependancy. Try to find the maxima of cepstral distance in points of the change in spectral characteristics of analyzed signals.
- Signals for the analysis
- sinusovky.wav -
connected sinusoids of various frequencies (wav format),
- fletna_stupnice.wav
- scale of real tones played at a musical instrument (wav format),
- T10100P0.CS0 - sequence of Czech vowels (raw data without a header, fs=16000 Hz).
- Result:
Observe for above mentioned signals:
- time waveforms and spectrograms,
- time dependancy of DFT and LPC cepstra,
- tiem dependancy of cepstral distance between successive frames.
OPTIONAL PART for you work in free time or selfstudy at home
- Voice Activity Detection based on LPC cepstrum
- Compute time dependancy of LPC cepstrum with the same setup as in the first task for signals SA001S01.CS0 and SA001S01.CS1 and determine average cepstrum on the basis of the first 20 frames containing bacground only.
- Compute Euclidan cepstral distance cde.m for both signals between a cepstrum of each particular short-time frame and average cepstrum describing signal beckgroud. Use the variant without coefficient c[0]. Observe hager values (maxima) for the frames with the highest difference in spectral characteristics.
- Determine empiricaly a fixed threshold for detection of frames with voice activity.
- Repeat previous two step for Euclidan cepstral distance computed with the coefficient c[0] and compare achieved results.
- Compare achieved results with an approach based on time-dependancy of average coherence (MSC) computed between channels CS0 and CS1, see the task from seminar Coherence analysis and its applications.
- Result :
Observe always as 3 subplots in one figure window:
- spectrograms of signals in channels CS0 and CS1 and cohergram (MSC) between channels CS0-CS1,
- time dependancy of cepstral distance between current short-time frame and signal background for channels CS0 and CS1 aand time dependancy of average coherence (MSC) between channels CS0-CS1,
- cepstral distances and average coherece as well with empiricaly-defined thresholds and final voice activity detection.
- Repeat for signals from channels CS2 and CS3, i.e. SA001S01.CS2 and SA001S01.CS3 and compare achieved results.
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