Time Domain Methods1 (1)

8/3/2019 Time Domain Methods1 (1)

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Time-Domain Methods forSpeech Processing

Introduction


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Speech Processing Methods

Time-Domain Method:

Involving the waveform of speech signal

directly.

Frequency-Domain Method:

Involving some form of spectrum

representation.


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Time-Domain Measurements

Averagezero-crossing rate, energy, and the

autocorrelation function.

Very simple to implement.

Provide a useful basis for estimating

important features of the speech signal, e.g., Voiced/unvoiced classification

Pitch estimation


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Time-Dependent

Processing of Speech


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Time Dependent Natural of Speech

This is a test.


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Time Dependent Natural of Speech


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Short-Time Behavior of Speech

Assumption

The properties of speech signal changeslowly with time.

Analysis Frames Short segment of speech signal.

Overlap one anotherusually.


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Time-Dependent Analyses

Analyzing each frame may produce eithera

single number, or a set of numbers, e.g., Energy (a single number)

Vocal tract parameters (a set of numbers)

This will produce a new time-dependentsequence.


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General Form

g

g!!

m

n mnwmxTQ )()]([

n: Frame index

x(m): Speech signal

T[]: A linear or nonlinear transformation.

w(m): A window function (finite of infinite).


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General Form

Qn is a sequence oflocal weightedaverage values of the sequence T[x(m)].

g

g!!

m

n mnwmxTQ )()]([


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Example

g

g!! m mxE )(2

Energy

2

1

( )n

n

m n N

E x m

!

! Short-Time

Energy


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Example

2

1

( )n

n

m n N

E x m

!

! Short-Time

Energy


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2

1

( )n

n

m n N

E x m

!

! Short-Time

Energy

)()]([ 2 mxmxT !

ee

!otherwise

Nmmw

0

101)(

g

g!

!m

n mnwmxTE )()]([

Example


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General Short-Time-Analysis Scheme

T[ ]Linear

Filter

Lowpass

Filter

Depending on the

choice of window


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Short-Time Energy and

Average Magnitude


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Applications

Silence Detection

Segmentation

Lip Sync


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Short-Time Energy

g

g!

!m

n mnwmxE2)]()([

g

g!

!m

mnwmx )()( 22

g

g!

!m

mnhmx )()(2

)(*)(2 mhmx!


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Block Diagram Representation

[ ]2x(n) x2

(n)

| |x(n) |x(n)|

h(n) En

w(n) Mn

)()( 2 mwnh !


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Block Diagram Representation

[ ]2x(n) x2

(n)

| |x(n) |x(n)|

h(n) En

w(n) Mn

)()( 2 mwnh !

What is the effect of windows?


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The Effects of Windows

Window length

Window function


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Rectangular Window

ee!

otherwiseNnnh

0101)(

)2/sin(

)2/sin()( 2/)1(

NeeH Njj !


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m[(

Mainlobe

width

Rectangular Window

)2/sin(

)2/sin()( 2/)1(

NeeH Njj !

Peak sidelobe

T T T2T 2

|)(|

j

eH

N

2

N

2

N=88


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Rectangular Window

)2/sin(

)2/sin()( 2/)1(

NeeH Njj !What is this?

Discuss the effect of window duration.

Discuss the effect of mainlobe width and sidelobe peak.

m[(

Mainlobe

width

Peak sidelobe

T T T2T 2

|)(|

j

eH

N

2

N

2

N=88


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Commonly Used Windows

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

R

ectangular

BlackmanHanning

Bartlett

Hamming


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0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Rectangular

Blackman

Hanning

Bartlett

Hamming

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Rectangular

Blackman

Hanning

Bartlett

Hamming


ee

!otherwise

Nnnw

0

101)(

e

ee

!

otherwise

NnNNn

NnNn

nw

0

12/)1()1/(22

2/)1(0)1/(2

)(

ee

! otherwise

NnNn

nw 0

10)]1/(2cos[5.05.0

)(

ee

!otherwise

NnNnnw

0

10)]1/(2cos[46.054.0)(

ee

! otherwise

NnNnNn

nw 0

10)]1/(4cos[8.0)]1/(2cos[5.042.0

)(

Rectangular

Bartlett

(Triangular)

Hanning

Hamming

Blackman


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Rectangular

Bartlett

Hanning

Hamming

Blackman

Least mainlobe width


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Examples: Short-Time Energy

RectangularWindow HammingWindow


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Examples: Average Magnitude

RectangularWindow HammingWindow


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The Effects of Window Length

Increasing the window lengthN, decreases

the bandwidth. IfNis too small, e.g., less than one pitch

period, En and Mn will fluctuate very rapidly.

IfNis too large, e.g., on the order of severalpitch periods, En and Mn will change very

slowly.


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The Choice of Window Length

No signal value ofNis entirely satisfactory.

This is because the duration of a pitch period

varies from about 2 ms for a high pitch

female or a child, up to 25 ms for a very lowpitch male.


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Sampling Rate Thebandwidth of both En and Mn is just that

of the lowpass filter. So, they need not be sampled as frequently as

speech signals.

For example Frame size =20ms

Sample period =10ms


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Main Applications ofEn and Mn

To provide the basis for distinguishing

voiced speech segments from unvoicedsegments.

Silence detection.


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Differences ofEn and Mn

g

g!!

m

n mnwmxE2

)]()([

g

g!

!m

n mnwmxM )(|)(|

Emphasizing large sample-to-

sample variations in x(n).

The dynamic range (max/min)

is approximately the square

root ofEn.

The differences in level between voiced and unvoiced

regions are not as pronounced as En.


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FIR and IIR

All the windows that we discussed

are FIRs.

Each of them is a lowpass filter.

It can also be an IIR.


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IIR Example

u

! 00

0

)( n

na

nh

n

11

1

)( ! azzH

Recursive formulas:

)(21 nxaEE nn !

|)(|1 nxaMM nn !

Short-Time Energy:

Short-Time

Average magnitude:


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Short-Time Average

Zero-Crossing Rate


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Voiced and Unvoiced Signals

Th/i/s

Thi/s/


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The Short-Time Average Zero-Crossing Rate

g

g!

!m

n mnwmxmxZ )(|)]1(sgn[)](sgn[|

x(n) FirstDifference

| |ZnLowpass

Filter

u!

0)(1

0)(1)](sgn[

mx

mxmx 10

2

1)( ee! Nm

Nmw


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Distribution of Zero-Crossings


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Example


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Block diagram of the voiced/unvoiced classification.


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Frame-byframe processing of speech signal.


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Zero-Crossings Rate

A zero crossing is said to occur if successive

samples have different algebraic signs.The rate at which zero crossings occur is a

simple measure of the frequency content of a

signal.Zero-crossing rate is a measure of number of

times in a given time interval/frame that the

amplitude of the speech signals passes through a

value of zero.


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Distribution of zero-crossings for unvoiced and voiced speech


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A definition for zero-crossings rate is:

Where

and


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Original speech signal for word four.


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Summary

Energy of a speech is a parameter for

classifying the voiced/unvoiced parts. The voiced part of the speech has high energy

because of its periodicity and the unvoiced part

of speech has low energy.


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Zero-crossing rate is an important parameter for voiced/

unvoiced classification.

used as a part of the front-end processing in automatic

speech recognition system.

Voiced speech is produced because of excitation of vocal

tract by the periodic flow of air at the glottis and usuallyshows a low zero-crossing count ,

The unvoiced speech is produced by the constriction of the

vocal tract narrow enough to cause turbulent airflow which

results in noise and shows high zero-crossing count.


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The results suggest that

zero crossing rates are low for voiced part andhigh for unvoiced part where as the energy is

high for voiced part and

low for unvoiced part.

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Time Domain Methods1 (1)