AE2M99CZS 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,
- 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
- Repeat also for
and discuss the problems of this approach.
- Determine the pitch of a tone for particular musical
instruments from the following records
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
particular steps analogous to the previous estimation of speech
- 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
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
- 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.