BE2M31DSP - seminar
Applications of coherence analysis
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Computation of coherence function for 2-channel signals
- Estimate according to the definition coherence function (MSC - Magnitude Square Coherence) for the following pairs of analyzed signals:
(All signals are binary,
16 bit PCM-files without a header, sampling frequency is 16 kHz, to load signals into MATLAB use loadbin.m)
- Simulation 1: signal in the channel No.1:
SA001S01.CS0 - signal in the second channel No.2
should be created by delaying of signal in channel No. 1 20 samples (IDEAL REFLECTION).
- Simulation 2: create the signal in the channel 2 by the filtering of the signal in channel 1 using wide-band FIR filter (exactly wide-band high-pass filter - cutoff frequency should be 0.05*fs/2, order 30). Add also small level white noise ot both channels
(standard deviation of generated white Gaussain noise should be approx. 0.1-0.01). Do not forget to generate two different (independent) realizations of white noise for both channels.
- Real signals I: channel 0 (CS0) -
SA001S01.CS0,
channel 1 (CS1) - SA001S01.CS1,
channel 2 (CS2) - SA001S01.CS2,
channel 3 (CS3) - SA001S01.CS3,
- Real signals II: channel 0 (CS0) -
SA176S01.CS0,
channel 1 (CS1) - SA176S01.CS1,
channel 2 (CS2) - SA176S01.CS2,
channel 3 (CS3) - SA176S01.CS3,
- Real signals III: channel 0 (CS0) -
SA005S01.CS0,
channel 1 (CS1) - SA005S01.CS1,
channel 2 (CS2) - SA005S01.CS2,
channel 3 (CS3) - SA005S01.CS3,
- Reálné řečové IV: s0001-l.bin a s0001-r.bin (fs = 8 kHz)
- Reálné signály V (nahrávané v hlučném prostředí): x0002-l.bin a x0002-r.bin.
(Všechny signály jsou binární:
16 bitové PCM-soubory bez hlavičky, vzorkovací kmitočet je 16 kHz, k načtení použijte následující
funkci loadbin.m)
- Coherence should be estimated (computed)using MATLAB function mscohere (or possibly according to the definitions from the estimationd of CPSD and PSDs using cpsd and pwelch).
- Observe the impact of the setup of analyzed frame length and number of DFT points to time dependancy of mean MSC of analyzed signals. Explain observed results. Take into account the importance of averaging during the computation of MSC.
- Prove theoretically that coherence function must not be computed just from one short-time frame without any averaging. Confirm this by a simulation of this situation in MATLAB.
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Result :
Observe computed coherence function in the following situations:
- from whole signals for Simulation 1 and
Simulation 2, frame length should be wlen = 512,
- from signals Simulation 2, but just for the selected vopiced part of the length of 2000 samples with the beginning at the sample 20000, same way also from unvoiced signal part of the length 2000 samples starting at the sample 38000, and finally also from the non-speech segment of the lengthof 2000 samples starting from the beginning at the sample 1. Length of the short-time frame for the computation of coherence should be equal to 512 samples.
- Repeat the previous point for shorter segments of the length of 512 samples (starting point should be the same ones), the length of short-time frame for MSC computation should be equal to a) 512, b) 128 samples.
- Repeat for abve mentioned real signals picked up in various channels
- Time dependancy of mean MSC
- Estimate cohergram of above mentioned signals and compare them with spectrograms of analyzes signals (in both channels).
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Result:
Observe cohergram and spectrograms in the case of signals from the
Simulation 2. Set the length of the first-level short-time frame (basic one)
equal to flen = 1024, the second-level short-time frame (the inner one) should be wlen = 256.
- Repeat for the choice flen/wlen: 2048/512
and 512/128.
- Compute the time dependancy of mean MSC for above mentioned signals (and variants of segmentation within MSC computations)
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Result:
Observe the resulting mean MSC computed with the setup of flen/wlen:
2048/512, 1024/256 and 512/128.
- Add a noise of varying level to the signals according to Simulation 2 and observe obtained results in particular steps as above for the case without the presence of noise.
- Repeat all above evaluations also for real signals and discuss obtained results.
- Impact of pre-filtering
- Take into the account possible improvement of obtained results using suitable pre-filtering (using the frequency selection of coherence in chosen band).
- Observe mainly a decrease of bottom threshold of mean MSC and improvement of dynamics of its time dependancy.
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