CHAPTER 10
Applications of Digital Signal
Processing
Wang Weilian
wlwang@ynu.edu.cn
School of Information Science and Technology
Yunnan University
Outline
• Speech Signals Processing
• Dual-Tone Multifrequency Signal Detection
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis
– parameterize the speech signal
• To reduce the bandwidth
• To characterize the speech signal with only a few features
– Speech Signal Processing is one of the kernel
technologies in those fields as follows: Information
Superhighway, Multimedia, OAS (office automation
system), Modern Communications System, Intelligent
System and so on.
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — time-domain
– data windowing:
sw (n) 


s(m) w(n  m)
m
Windowing Calculation
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — time-domain
– Energy:
En 
En 




[ x(m) w(n  m)] 
2
m
m

[ x(m) w(n  m)]2
mn
[ x (m) w (n  m)] 
2
n N 1
2


[ x 2 (m)h(n  m)]  x 2 (n)  h(n)
m
h ( n )  w2 ( n )
• Selecting 10ms ~ 30ms as the length of the window in general
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — time-domain
– The zero crossing rate ( ZCR ):


Zn 
| sgn[ x(n)]  sgn[ x(n  1)] | w(n  m)
m
 |sgn[x(n)]  sgn[x(n  1)]|w(n)
• where
1
sgn[ x]  
0
( x  0)
( x  0)
1/ 2 N
w(n)  
0
(0  n  N  1)
other
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — time-domain
– Energy and ZCR:
Energy and ZCR
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — time-domain
– The Autocorrelation function:
Rn (k ) 

 [ x(m)  w(n  m)  x(m  k )  w(n  (m  k ))]
m
Rn (k )  Rn (k ) 
• If

 [ x(m)  w(n  m)  x(m  k )  w(n  (m  k ))]
m
hk (n)  w(n) w(n  k ) , then:
Rn (k ) 

 [ x(m)  x(m  k )]hk (n  m)  [ x(n) x(n  k )]  hk (n)
m
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — time-domain
– The Autocorrelation function:
The block diagram of the autocorrelation function
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — frequency-domain
– Fourier Transform and Spectrogram
j
X n (e ) 


x(m) w(n  m)e jm
m
The filter-explanation of the FT
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — frequency-domain
– The spectrogram:
The spectrogram
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — frequency-domain
– Spectra analysis
• The power spectra ( energy density function ):
Sn (e j )  X n (e j ) X n (e j ) | X n (e j ) |2
• Complex Ceptrum:

x(n)  Z 1[ln[ Z [ x(n)]]]
• Quefrency:

c ( n) 
云南大学滇池学院课程：数字信号处理

[ x(n)  x( n)]
2
Applications of Digital Signal Processing
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Speech Signals Processing
•
Speech Analysis — frequency-domain
– Linear Predictive:
•
The model of signal generation
Autoregressive Moving Average Model
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — frequency-domain
– Linear Predictive:
q
1  bj z j
H ( z)  G 
j 1
p

1   ai z i
S ( z)
U ( z)
i 1
• G is the gain factor.
• U(z) / S(z) is the Z-Transform of input / output sequence
p
q
i 1
j 0
s(n)   ai s(n  i )  G   b j u (n  j ) ， (b0  1)
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Analysis — frequency-domain
Linear Predictive ( autocorrelation method )
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Synthesis
– Formant Synthesis: the transfer function of formants
can be simulated by using a 2th-order digital filter
generally.
y(n)  Ax(n)  By(n  1)  Cy(n  2)
C   exp(2 BwT ),
B  2 exp( BwT ) cos(2 FT ),
A  1 B  C
F is the formant frequency, and Bw is the bandwidth .
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Speech Signals Processing
• Speech Recognition
Communication via Spoken Language
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Dual-Tone Multifrequency Signal Detection
• A DTMF signal consist of a sum of two tones with
frequencies taken from two mutually exclusive groups of
preassigned frequencies.
• Each pair of such tones represents a unique number or a
symbol.
云南大学滇池学院课程：数字信号处理
Applications of Digital Signal Processing
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Dual-Tone Multifrequency Signal Detection
• Decoding of a DTMF signal thus involves identifying the
two tones in that signal and determining their
corresponding number or symbol.
• The DTMF decoder computes the DFT samples closest in
frequency to the eight DTMF fundamental tones and their
respective second harmonics.
• The DFT length N determines the frequency spacing
between the locations of the DFT samples and the time it
takes to compute the DFT sample. The frequency
corresponding to the DFT index ( bin number ) k is:
f k  kFT N ,
云南大学滇池学院课程：数字信号处理
k  0,1,
, N 1
Applications of Digital Signal Processing
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