BE2M31DSPA Exercise - Correlation Analysis and Applications
Tasks to do:
- 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,
6. mixture of s1 + b1 with given SNR,
- Discuss different properties of given estimations.
- Checked result:
Display ACF estimation for s1 + b1 when SNR=0, 10, -10 dB.
- Detection of the periodicity in signal using autocorrelation
- 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.)
- 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.
- Analyse also an impact of signal centering (i.e. removing of
non-zero mean value) to an estimation of ACF, especially in the case
of the following signal
kytara_d_dur_1.wav (guitar tone).
- 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).
- 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.
- Estimation of delay in GPS signal
- Measured GPS signals with additive white gaussian noise are available within files sigX.gps in the following directory
signaly_ML_odhad_zpozdeni commonly with transmitted pseudorandom PRN signal prn.gps.
- NOTE. Pseudo-Random Sequence (PRN) with chip rate fc = 1.023 * 10^6 chip/s (fs = 1.023 MHz) saved in the file prn1.txt was used for generation of transmitted signals sigX.gps sampled by fsa = 65 MHz.
The length of signals prn.gps and sigX.gps is related to just one period of pseudorandom sequence prn1.txt.
- Checked result:
For measured signal
sig5.gps determine the delay and measured distance in the
following steps
- draw transmitted PRN signal prn.gps,
- 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.