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Non Stationary Time Frequency Signal Processing
Techniques
Presentation Prepared by:
Jatin Kumar
Biswajit Sahoo
Soumaa Samanta
!run Kumar
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"i##erence between Stationary and Non$Stationary Signals
Signals whose frequency content doesnt change with time are
stationary. On the other hand signals whose frequency content change with
time are non-stationary.
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Traditionally used signal Processing Technique
Fourier Transform or Fast Fourier Transform (FFT)
Can these methods e a!!lied to non-stationary signals"
#es
$re those effecti%e"
No
&ets see why in the ne't slide
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Fourier Transform is a gloal !henomenon. t re%eals frequencydomain information ut conceals time information.
*hereas frequency of non-stationary signals change with time
and time information as to when the frequency changed is
necessary.
+ut FT or FFT cant !ro%ide us the time information.
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Windowed signal from 0 to 3 seconds
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Windowed signal from 3 to 6 seconds
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Windowed signal from 6th to 9th second
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Initial signal
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The S!ectrogram
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uest For 'act Time nformation//
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"rawbac's o# STFT
0igher resolution in time domain results in !oor resolution in
frequency domain and %ice %ersa.
This is the famous %eisenberg(s )ncertainty Principle
*hich states that we can*tget e'act estimates of oth
time and frequency. f we want near e'act estimate of one
we ha%e to com!romise with the other.
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+aelet Trans#orm
t uses multiresolution technique to analy,e signals of differentfrequencies i.e. for low frequency signals1 it gi%es high
frequency resolution ut !oor tem!oral (time) resolution ut
for high frequency signals1 it gi%es high tem!oral resolution
ut !oor frequency resolution.
There are two ty!es of wa%elet transforms
Continuous wa%elet transform (C*T)
2iscrete wa%elet transform (2*T)
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,ontinuous +aelet Trans#orm
This method com!ares with the original wa%eform a mother wa%elet and
determines a set of coefficients de!ending u!on the similarity. The
mother wa%elet is stretched or com!ressed (scaled) and shifted to matchthe original wa%eform.
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Scaling (2ecreasing Scaling Factor) Shifting
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+aelet ,oe##icients Not Frequencies
Original
Signal
Mother
Wavelet
Continuo
us
Wavelet
Coefcien
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"iscrete +aelet Trans#orm
Continuous *a%elet Transform calculates too many coefficients of
which many are redundant. 2iscrete wa%elet transform rectifies
this !rolem y calculating the required coefficients.
This is done y suand coding.
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a1
a2 d
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$nd so on till no. of sam!les e'hausts
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!pplication in Signal "enoising
(Si' Stage 2enoising)
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Than' -ou.
!ny queries&