### XE31CZS Exercise - Correlation Analysis and Applications

• Basic Properties of Autocorrelation Function
• Evaluate autocorrelation coefficients of given signal (fcn 'xcorr').
• Try options 'biased, unbiased, coeff, none' and compare differences in results on following signals:
1. sinusoidal - s1 - f=15 Hz, fs=200 Hz, A=1, t=1 s ,
2. Gaussian white noise - b1 - power 0.7, mean value 0, fs=200 Hz, t=1 s,
3. Gaussian white noise - b2 - power 0.7, mean value 0, fs=200 Hz, t=10 s,
4. sinusoidal s1 + constant component 0.8,
5. noise b1 + constant component 0.8,
• Discuss different properties of given estimations.
• For signals defined in items 1., 2., 3. evaluate biased estimation of coefficients R[0] and R[12].
ATTENTION !!! To have comparable results, you must set always the seed of random generator of Gaussian noise to 0 by using command "randn('seed',0);" !!!

• Detection of the periodicity in signal using autocorrelation
• Estimate fundamental period of voiced sounds vf5.bin and vm5.bin on the basis of second main maximum of autocorrelation function
• Discuss the problems of this approach.

• Try to estimate the delay between signals from two different input channles using cross-correlation function. Sampling frequency of given signals is 8 kHz.
Clean speech signals: s0001-l.bin a s0001-r.bin
Speech with noisy background: x0002-l.bin a x0002-r.bin
• a) evaluate cross-correlation from whole signal
• a) evaluate cross-correlation from segmented signal; frame length wlen = 256, 512 samples without overlapping.