1 / 72

Chapter 2 Discrete-time signals and systems

Chapter 2 Discrete-time signals and systems. 2.1 Discrete-time signals:sequences. 2.2 Discrete-time system. 2.3 Frequency-domain representation of discrete-time signal and system. 2.1 Discrete-time signals:sequences. 2.1.1 Definition.

corinthia
Download Presentation

Chapter 2 Discrete-time signals and systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 2 Discrete-time signals and systems 2.1 Discrete-time signals:sequences 2.2 Discrete-time system 2.3 Frequency-domain representation of discrete-time signal and system

  2. 2.1 Discrete-time signals:sequences 2.1.1 Definition 2.1.2 Classification of sequence 2.1.3 Basic sequences 2.1.4 Period of sequence 2.1.5 Symmetry of sequence 2.1.6 Energy of sequence 2.1.7 The basic operations of sequences

  3. Enumerative representation Function representation 2.1.1 Definition EXAMPLE

  4. 0.5 2 1 0 0 -1 -0.5 -2 -1 -3 0 5 10 -2 0 2 4 6 Graphical representation

  5. Generate and plot the sequence in MATLAB n=-1:5 x=[1,2,1.2,0,-1,-2,-2.5] stem(n,x, '.') n=0:9 y=0.9.^n.*cos(0.2*pi*n+pi/2) stem(n,y,'.')

  6. EXAMPLE Sampling the analog waveform Figure 2.2

  7. Display the wav speech signal in ULTRAEDIT

  8. local Blowup Display the wav speech signal in COOLEDIT The whole waveform Display the wav speech signal in

  9. 2.1.2 Classification of sequence Right-side Left-side Two-side Finite-length Causal Noncausal

  10. 2.1.3 Basic sequences 1. Unit sample sequence 2.The unit step sequence 3.The rectangular sequence

  11.  4.  Exponential sequence

  12. 5. Sinusoidal sequence

  13. For convenience, sinusoidal signals are usually expressed by exponential sequences. The relationship between ω and Ω:

  14. 2.1.4 Period of sequence

  15. Three kinds of period of sequence

  16. 2.1.5 Symmetry of sequence Conjugate-symmetric sequence Conjugate-antisymmetric sequence

  17. EXAMPLE n=[-5:5]; x=[0,0,0,0,0,1,2,3,4,5,6]; xe=(x+fliplr(x))/2 ; xo=(x-fliplr(x))/2; subplot(3,1,1) stem(n,x) subplot(3,1,2) stem(n,xe) subplot(3,1,3) stem(n,xo) Real sequences can be decomposed into two symmetrical sequences.

  18. EXAMPLE Complex sequences can be decomposed into two symmetrical sequences. n=[-5:5]; x=zeros(1,11); x((n>=0)&(n<=5))=(1+j).^[0:5] xe=(x+conj(fliplr(x)))/2; xo=(x-conj(fliplr(x)))/2 subplot(3,2,1); stem(n,real(x)) subplot(3,2,2); stem(n,imag(x)) subplot(3,2,3); stem(n,real(xe)) subplot(3,2,4); stem(n,imag(xe)) subplot(3,2,5); stem(n,real(xo)) subplot(3,2,6); stem(n,imag(xo))

  19. 2.1.6 Energy of sequence

  20. 2.1.7 The basic operations of sequences

  21. Basic operations of sequences

  22. Original speech sequences Original music sequence sequences after scalar multiplication sequences after vector addition sequences after vector multiplication echo

  23. The matlab codes on the addition of two sequences EXAMPLE

  24. n=[-4:2] ; x=[1,-2,4,6,-5,8,10] ; %x1[n]=x[n+2] n1=n-2; x1=x; %x2[n]=x[n-4] n2=n+4; x2=x; %y[n] m=[min(min(n1),min(n2)): max(max(n1),max(n2))] ; y1=zeros(1,length(m)) ; y2=y1; y1((m>=min(n1))&(m<=max(n1)))=x1;y2((m>=min(n2))&(m<=max(n2)))=x2; y=3*y1+y2; stem(m,y) Output:y =3 -6 12 18 -15 24 31 -2 4 6 -5 8 10

  25. 7.convolution sum: steps:turnover, shift, vector multiplication, addition

  26. EXAMPLE nx=0:10; x=0.5.^nx; nh=-1:4; h=ones(1,length(nh)) y=conv(x,h); stem([min(nx)+min(nh):max(nx)+max(nh)],y)

  27. 8.crosscorrelation: aotocorrelation:

  28. example:correlation detection in digital audio watermark

  29. 2.1 summary • 2.1.1 Definition • 2.1.2 Classification of sequence • 2.1.3 Basic sequences • 2.1.4 Period of sequence • 2.1.5 Symmetry of sequence • 2.1.6 Energy of sequence • 2.1.7 The basic operations of sequences

  30. requirements:judge the period of sequence ; • calculate convolution with graphical • and analytical evaluation . • key: convolution

  31. 2.2 Discrete-time system 2.2.1 Definition:input-output description of systems 2.2.2 Classification of discrete-time system 2.2.3 Linear time-invariant system(LTI) 2.2.4 Linear constant-coefficient difference equation 2.2.5. Direct implementation of discrete-time system

  32. 2.2.1 definition:input-output description of systems the impulse response

  33. EXAMPLE

  34. 2.2.2 classification of discrete-time system 1.Memoryless (static) system the output depends only on the current input. 2.Linear system 3.Time-invariant system: 4.Causal system: the output does not depend on the latter input. 5.Stable system:

  35. 2.2.3 linear time-invariant system(LTI) How to get h[n] from the input and output:

  36. the impulse response in LTI EXAMPLE

  37. h[n] Properties of LTI Figure 2.12

  38. classification of linear time-invariant system IIR: h[n]’s length is infinite the latter input the former input FIR must be stable。

  39. 2.2.4 linear constant-coefficient difference equation 1.relation with input-output description and convolution For IIR,the latter two are consistent. EXAMPLE input-output description convolution description infinite items,unrealizable difference equation description Finite items, realizable

  40. EXAMPLE For FIR,the followings are consistent input-output description and difference equation description (non-recursion) Convolution description Another difference equation description,recursion,lower rank For FIR and IIR,difference equations are not exclusive.

  41. 2.Recursive computation of difference equations: For IIR, there needs N initial conditions , then ,the solution is unique. For FIR, there needs no initial conditions. With initial-rest conditions (linear, time invariant, and causal), the solution is unique. EXAMPLE

  42. 3.computation of difference equations with homogeneous and particular solution

  43. 2.2.5. Direct implementation of discrete-time system EXAMPLE

  44. EXAMPLE

  45. EXAMPLE The matlab codes on the direct realization of LTI B=1; A=[1,-1] n=[0:100]; x=[n>=0]; y=filter(B,A,x); stem(n,y); axis([0,20,0,20])

More Related