### AE2M99CZS Exercise - Correlation Analysis and Applications

• Basic Properties of Autocorrelation Function (ACF)
• 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.
• 1st checked result:
Display ACF estimation for s1 + b1 when SNR=0, 10, -10 dB.

• Detection of the periodicity in signal using autocorrelation
• Estimate fundamental period of voiced sounds in speech signal on the basis of second principal maximum of autocorrelation function.
• Work with the following signals vf3.bin and vm3.bin, which were sampled by fs = 16000 Hz ( format of these signals is binary, to read them into MATLAB environment use the following attached function loadbin.m).
• 2nd checked result:
For both above mentioned signals:
• draw time waveform of whole available record,
• draw the short-time frame with the length of 512 samples from the beginning of the record,
• draw biased ACF estimation of above mentioned short-time frame with the length of 512 samples,
• estimated fundamental period and voice pitch from computed ACF estimation.
• Repeat also for vf0.bin, vm0.bin, vf1.bin, vm1.bin, vf2.bin, vm2.bin, vf4.bin, vm4.bin, vf5.bin, vm5.bin, vf6.bin, vm6.bin, vf7.bin, vm7.bin, vf8.bin, vm8.bin, vf9.bin, vm9.bin, and discuss the problems of this approach.

• Determine the pitch of a tone for particular musical instruments from the following records
cembalo_d_dur_2.wav, fletna_d_dur_6.wav, housle_d_dur_5.wav, kytara_d_dur_1.wav, piano_d_dur_4.wav, varhany1_d_dur_3.wav, varhany2_d_dur_8.wav
NOTE. WAV-files can be loaded into MATLAB environment using the function audioread. The information about sampling frequency which is save in the header of WAV-formated sound file can be obtained as the second output parameter of the function audioread.
• Within the first step, use the short-time frame with the length of 10 ms. (ATTENTION. Do not work with the 1st short-time frame from the beginning of a record, because it does not containt the required tone usually.)
• 3rd checked result:
For the signal housle_d_dur_5.wav make particular steps analogous to the previous estimation of speech pitch, i.e.
• draw whole waveform of available record,
• draw selected short-time frame for the analysis (do not forget that the sampling frequency of these records is different),
• draw ACF estimation of analyzed short-time frame,
• estimated interactively the fundamental period from ACF estimation and determine the tone pitch in Hz.
• Repeat the procedure also for other records and try to observe the influence of varoius short-time frame length to the precision of tone pitch estimation.

• Estimation of delay in GPS signal
• Try to estimate the delay between signals for following two-channel signals using Cross-Correlation Function. Estimated time delay should be both in samples (for discrete-time sequence of the signal samples) and in seconds (for real-time signal representation).
• In records sigX.gps (viz signaly_ML_odhad_zpozdeni) the samples of measured GPS signal with additive white gaussian noise are available.
• Used Pseudo-Random Sequence (PRN) is saved in the file prn1.txt.
• Chip rate of PRN sequence is fc = 1.023 * 10^6 chip/s (fs = 1.023 MHz).
• Measured signal was sampled by fsa = 65 MHz.
• The length of the signal within particular files sigX.gps is related to just one period of PRN sequence.
• 4th checked result:
For measured signal sig5.gps determine the delay and measured distance in the following steps
• draw generated PRN sequence prn1.txt,
• draw resampled replica of PRN sequence with the length same as for measured signal (i.e. transmitted signal),
• draw measured (received) signal sig5.gps,
• draw CCF estimation between measured (received) signal and (transmitted) PRN signal,
• On the basis of CCF estimate interactively a position of the maximum and then the delay of received signal.