电子科技大学DSP课件

0
5
10
20


...
n
1
xd [ n] x[ nM ]
1
0


5
...
Fig 2.9
and 2.10
10
wk.baidu.com
n
1
Note: The Sampling Process If a continuous signal xa (t ) A cos(2f 0t ) A cos(0t ) ,the sampling frequency isFT 1 / T .The discrete signal is: x[n] xa (nT ) A cos( 0 nT ) (or x[n] A cos( 0 n ) ). Where 0 0T is digital angular frequency. If 0 / 2 f 0 / 2FT m / N ( 0 / 2 is not rational),X[n] is not periodic. 3.An arbitrary sequence can be represented as the sum of impulses :
1
n
0 N-1
4.The Exponential(Causal) sequence
a [n]
n
0
a [ n]
n
...
n
5.Sinusoidal and Exponential Sequence Sinusoidal: Exponential: x[ n]
n
x[n] A cos( 0 n ), n
x[n]
m
x[m] [n m] x[n] [n]

2.1.3 Sequence Generation Using MATLAB Program 2-1(read and excercise)
n=1:N; stem(n,real(x)); stem(n,imag(x));
Reference books: 1. A.V.Oppenheim and R.W.Schafer,Digital Signal Processing,1975 2. S.J.Orfanidis ,Introduction of Signal Processing,Prentice Hall,1998, 3. 彭启综等 ,《DSP 与实时数字信号处理》, 电子科大出版社,1995 4.程佩青,《数字信号处理教程》,清华大学 出版社,1997年 5.胡广书，《数字信号处理-理论、算法与 实现》，清华大学出版社,1997年 6.皇甫堪等，《现代数字信号处理》，电 子工业出版社，2003年
1
n
2.The Unit Step
1, n 0 δ [n] 0, n 0
1 0
0
[ n]
...
1, n 0 [n] 0, n 0
n
3.The Finite Gate sequence
RN [ n ]
1,0 n N 1 RN [n] 0, others
§2 Discrete-Time Signals And LTI Systems
In Time-Domain §2.1 Discrete-Time Signals
2.1.1 Sequences And Representation [ n] (Commonly used) 1.The Unit Impulse
2.1.2 The Basic Operations On Sequences 1. modulator(product or windowing) ,
adder(sum), shift , reversal
x[n] y[n]
w1[n] x[n] y[n]
x[n] y[n]
w2 [n] x[n] y[n]
must
be a rational number) .
example
1 f [n] cos n sin n 8 2 6

Its period is 48 which is the lease common mutiple of 16 and 12. Because
e
j0n
e
j (0 2 k ) n
modulator
x[n]
adder
w5 [n] x[n 1]
w3[n] Ax[n] x[n]
Z 1
x[n]
w5 [n] x[n 1]
Z
multipler
unit delay
unit advance
2. Scaling in time-domain(Sampling rate alteration) Up-sampling
• The impulse response is thus a finite-length
sequence of length 3:
1 h[n] [n] ( [n 1] [n 1]) 2
{h[n]} {0.5, 1 0.5}

3.
FIR And IIR System (recursive and nonrecursive)
x=K*exp(c*n);
Figure 2.16
§2.2 Discrete-Time Systems • • • • Linear System Shift-Invariant System Causal System Stable System
x[n]
y[n]
Discrete-time systme
x a (t )
S/H A/D
x[n] y[n]
Digital Processor Fig. 1.47
D/A LPF
ya (t )
x a (t )
ya (t )
y[n]
: analog signals :digital signals(binary)
x[n]
12 8 4
12 8 4
0 2
4 6 8 10 12 14 16 Time in sec (a)
N dk k 0
y[n k ]
M k 0
pk x[n k ]
(2.82)
Note: Up-sampling
x[n / L], n 0,1,2,... y[n] 0, otherwise
is a time-varying system,so does Down-sampling.
A , n
The Complex Exponential Sequence j0 n
e
cos 0 n j sin 0 n
0 / 2
It is periodic if 0 must be integer number (
2 m ,where N and m N
2. Time-Domain Characterization of LTI Discrete-Time System
Input-Output Relationship
Impulse and Step Responses
• The response of a discrete-time system to a unit sample sequence {[n]} is called the unit impulse response or simply, the impulse response, and is denoted by {h[n]} • The response of a discrete-time system to a unit step sequence {[n]} is called the unit step response or simply, the step response, and is denoted by {s[n]}
(FIR)
Example 2.3
y[n] 1x[n] 2 x[n 1] 3 x[n 2] 4 x[n 3]
Example 2.4 (IIR)
y[n] b0 x[n] b1 x[n 1] b2 x[n 2] a1 y[n 1] a2 y[n 2]
• Example - The impulse response {h[n]} of the factor-of-2 interpolator
y[n]
1 xu [n] ( xu [n 1] xu [n 1]) 2
is obtained by setting xu[n]=[n] and is given by
(k is integer ),the discrete sinusoidal signal has the highest angular frequency .
Note: some classification of sequences (a) Left-sided,right-sided,two-sided, finite-duration; (b) Even,odd; (c) Periodic,aperiodic(energy or power signal)
1. Linear Time-Invariant system
•---- A system satisfying both the linearity and the time-invariance property
Generally, The math model of a LTI system is a linear difference equation with constant coefficients,as following form:
Digital Signal Processing
The Textbook:Digital Signal Processing----A Computer- Based Approach, Sanjit K.Mitra,Second Edition,McGraw-Hill,2001
Website:
http://202.115.21.138/wlxt/listcourse.asp?courseid=0003
x[n / L], n 0L,1L,2L,... x u [n ] 0, otherwise
Down-sampling
xd [n] x[nM ]
1
x[n]
0

5

...
10
n
1
1
x[ n / L ], n 0,1,2,... xu [ n] 0, otherwise
0 2 4 6 8 10 12 14 16 Time in sec (f)
Fig 1.48:Typical waveforms of signals
A digital processor :Hardwares(VLSI) and Softwares.
2. Why DSP? Advantage to ASP: more reliable(less sensitive to tolerances such as temperature,noise),higher accurate,can be integrated on a single chip. Limit: A/D D/A rates are not enough available in some applications.
0 2 4 6 8 10 12 14 16 Time in sec (b)
0 2
4 6 8 10 12 14 16 Time in sec (c)
0 2 4 6 8 10 12 14 16 Time in sec (d) 12 8 4
12 8 4
0 2 4 6 8 10 12 14 16 Time in sec (e)
§1 Introduction 1.What’s DSP?How to DSP? DSP----Processing signals in digital form. The scheme for the digital processing of an analog signal (fig 1.47)