7/26/2019 Nonstationary Time Frequency

1/17

Non Stationary Time Frequency Signal Processing

Techniques

Presentation Prepared by:

Jatin Kumar

Biswajit Sahoo

Soumaa Samanta

!run Kumar

7/26/2019 Nonstationary Time Frequency

2/17

"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.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time

Amplitude

Stationary Signal

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time

Amplitude

Non-Stationary Signal

7/26/2019 Nonstationary Time Frequency

3/17

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

7/26/2019 Nonstationary Time Frequency

4/17

7/26/2019 Nonstationary Time Frequency

5/17

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.

7/26/2019 Nonstationary Time Frequency

6/17

7/26/2019 Nonstationary Time Frequency

7/17

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time

A

m

p

litu

d

e

Windowed signal from 0 to 3 seconds

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time

A

m

p

litu

d

e

Windowed signal from 3 to 6 seconds

0 1 2 3 4 5 6 7 8 9 10-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time

A

m

p

litu

d

e

Windowed signal from 6th to 9th second

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time

A

m

p

litu

d

e

Initial signal

7/26/2019 Nonstationary Time Frequency

8/17

7/26/2019 Nonstationary Time Frequency

9/17

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10

Time

Frequency(H

z)

0.2

0.4

0.6

0.8

1

1.2

1.4

The S!ectrogram

7/26/2019 Nonstationary Time Frequency

10/17

0 2 4 6 8 10

0

1

2

3

4

5

6

7

8

9

10

Time

Frequency(H

z)

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

uest For 'act Time nformation//

7/26/2019 Nonstationary Time Frequency

11/17

"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.

7/26/2019 Nonstationary Time Frequency

12/17

+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)

7/26/2019 Nonstationary Time Frequency

13/17

,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.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Scaling (2ecreasing Scaling Factor) Shifting

7/26/2019 Nonstationary Time Frequency

14/17

+aelet ,oe##icients Not Frequencies

Original

Signal

Mother

Wavelet

Continuo

us

Wavelet

Coefcien

ts

7/26/2019 Nonstationary Time Frequency

15/17

"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.

S

a1

a2 d

2

d

1

$nd so on till no. of sam!les e'hausts

7/26/2019 Nonstationary Time Frequency

16/17

!pplication in Signal "enoising

(Si' Stage 2enoising)

7/26/2019 Nonstationary Time Frequency

17/17

Than' -ou.

!ny queries&