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1
1
Digital Speech Processing—
Lecture 2
Review of DSP
Fundamentals
2
What is DSP?
Analogto
Digital
Conversion
Computer
Input
Signal
Output
Signal
Digitalto
Analog
Conversion
Digital
• Method to represent a quantity, a phenomenon or an event
• Why digital?
Signal
• What is a signal?
– something (e.g., a sound, gesture, or object) that carries information
– a detectable physical quantity (e.g., a voltage, current, or magnetic field strength) by
which messages or information can be transmitted
• What are we interested in, particularly when the signal is speech?
Processing
• What kind of processing do we need and encounter almost
everyday?
• Special effects?
3
Common Forms of Computing
•
Text processing
– handling of text, tables, basic
arithmetic and logic operations (i.e., calculator
functions)
– Word processing
– Language processing
– Spreadsheet processing
– Presentation processing
•
Signal Processing
– a more general form of
information processing, including handling of speech,
audio, image, video, etc.
– Filtering/spectral analysis
– Analysis, recognition, synthesis and coding of real world signals
– Detection and estimation of signals in the presence of noise or
interference
4
Advantages of Digital Representations
•
Permanence and robustness of signal representations; zero
distortion reproduction may be achievable
•
Advanced IC technology works well for digital systems
•
Virtually infinite flexibility with digital systems
– Multifunctionality
– Multiinput/multioutput
•
Indispensable in telecommunications which is virtually all digital
at the present time
Signal
Processor
Input
Signal
Output
Signal
AtoD
Converter
DtoA
Converter
5
Digital Processing of Analog Signals
•
AtoD conversion:
bandwidth control, sampling and
quantization
•
Computational processing:
implemented on computers or
ASICs with finiteprecision arithmetic
–
basic numerical processing:
add, subtract, multiply
(scaling, amplification, attenuation), mute, …
–
algorithmic numerical processing:
convolution or linear
filtering, nonlinear filtering (e.g., median filtering), difference
equations, DFT, inverse filtering, MAX/MIN, …
•
DtoA conversion:
requantification* and filtering (or
interpolation) for reconstruction
x
c
(
t
)
x
[
n
]
y
[
n
]
y
c
(
t
)
AtoD
Computer
DtoA
6
DiscreteTime Signals
{[]
}
,
()
,
,
[]
( )
,
A sequence of numbers
Mathematical representation:
Sampled from an analog signal,
at time
is called the
and its recipr
a
a
xx
n
n
xt
t n
T
xn
x nT
n
T
=−
∞
<
<
∞
=
∞
<
<
∞
sampling period,
±
±
±
±
1/ ,
8000
1/ 8000
125
sec
10000
1/10000
100
sec
16000
1/16000
62.5
sec
20000
1/ 20000
50
sec
ocal,
is called the
Hz
Hz
Hz
Hz
S
S
S
S
S
FT
μ
=
=↔
=
=
=
=
=
=
=
=
sampling frequency
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Speech Waveform Display
7
plot(
);
stem(
);
8
Varying Sampling Rates
Fs=8000 Hz
Fs=6000 Hz
Fs=10000 Hz
Varying Sampling Rates
9
Fs=8000 Hz
Fs=6000 Hz
Fs=10000 Hz
Quantization
in
out
0.3
0.9
1.5
2.1
2.4
1.8
1.2
0.6
7
6
5
4
3
2
1
0
A 3bit uniform quantizer
Quantization:
• Transforming a continuously
valued input into a
representation that assumes
one out of a finite set of values
• The finite set of output values
is indexed; e.g., the value 1.8
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 Fall '08
 Rabiner,L

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