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Digital Signal Processing

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Presentation on theme: "Digital Signal Processing"— Presentation transcript:

1 Digital Signal Processing
Electrical Engineering Department Iran University of Science & Tech. 2/17/2007 DSP Course-IUST-Spring Semester

2 Digital Signal Processing Topic 3: Fourier domain
4/24/2017 Digital Signal Processing Topic 3: Fourier domain 1. The Fourier domain 2. Discrete-Time Fourier Transform (DTFT) 3. Discrete Fourier Transform (DFT) 4. Convolution with the DFT 2/17/2007 DSP Course-IUST-Spring Semester DSP Course Spring Semester Dr. Rezai-Rad

3 DSP Course-IUST-Spring Semester
1. The Fourier Transform 2/17/2007 DSP Course-IUST-Spring Semester

4 DSP Course-IUST-Spring Semester
Fourier Series 2/17/2007 DSP Course-IUST-Spring Semester

5 DSP Course-IUST-Spring Semester
Fourier domain 2/17/2007 DSP Course-IUST-Spring Semester

6 DSP Course-IUST-Spring Semester
Fourier analysis 2/17/2007 DSP Course-IUST-Spring Semester

7 DSP Course-IUST-Spring Semester
Fourier analysis 2/17/2007 DSP Course-IUST-Spring Semester

8 DSP Course-IUST-Spring Semester
Fourier analysis 2/17/2007 DSP Course-IUST-Spring Semester

9 DSP Course-IUST-Spring Semester
sinc 2/17/2007 DSP Course-IUST-Spring Semester

10 DSP Course-IUST-Spring Semester
Fourier Analysis 2/17/2007 DSP Course-IUST-Spring Semester

11 DSP Course-IUST-Spring Semester
Fourier Transform 2/17/2007 DSP Course-IUST-Spring Semester

12 DSP Course-IUST-Spring Semester
Fourier Transform 2/17/2007 DSP Course-IUST-Spring Semester

13 Fourier Transform of a sine
2/17/2007 DSP Course-IUST-Spring Semester

14 DSP Course-IUST-Spring Semester
Fourier Transforms 2/17/2007 DSP Course-IUST-Spring Semester

15 2. Discrete Time FT (DTFT)
2/17/2007 DSP Course-IUST-Spring Semester

16 DSP Course-IUST-Spring Semester
DTFT 2/17/2007 DSP Course-IUST-Spring Semester

17 DSP Course-IUST-Spring Semester
Periodicity of DFT 2/17/2007 DSP Course-IUST-Spring Semester

18 DSP Course-IUST-Spring Semester
Inverse DTFT (IDTFT) 2/17/2007 DSP Course-IUST-Spring Semester

19 DSP Course-IUST-Spring Semester
IDTFT 2/17/2007 DSP Course-IUST-Spring Semester

20 DSP Course-IUST-Spring Semester
sinc again 2/17/2007 DSP Course-IUST-Spring Semester

21 DTFTs of simple sequences
2/17/2007 DSP Course-IUST-Spring Semester

22 DTFTs of simple sequences
2/17/2007 DSP Course-IUST-Spring Semester

23 DTFTs of simple sequences
2/17/2007 DSP Course-IUST-Spring Semester

24 DSP Course-IUST-Spring Semester
DTFT properties 2/17/2007 DSP Course-IUST-Spring Semester

25 DSP Course-IUST-Spring Semester
DTFT example 2/17/2007 DSP Course-IUST-Spring Semester

26 DSP Course-IUST-Spring Semester
DTFT symmetry 2/17/2007 DSP Course-IUST-Spring Semester

27 DSP Course-IUST-Spring Semester
DTFT of real x[n] 2/17/2007 DSP Course-IUST-Spring Semester

28 DSP Course-IUST-Spring Semester
DTFT and convolution 2/17/2007 DSP Course-IUST-Spring Semester

29 DSP Course-IUST-Spring Semester
Convolution with DTFT 2/17/2007 DSP Course-IUST-Spring Semester

30 DTFT convolution example
2/17/2007 DSP Course-IUST-Spring Semester

31 DSP Course-IUST-Spring Semester
DTFT modulation 2/17/2007 DSP Course-IUST-Spring Semester

32 DSP Course-IUST-Spring Semester
Parseval’s relation 2/17/2007 DSP Course-IUST-Spring Semester

33 Energy density spectrum
2/17/2007 DSP Course-IUST-Spring Semester

34 EDS and autocorrelation
2/17/2007 DSP Course-IUST-Spring Semester

35 DSP Course-IUST-Spring Semester
3. Discrete FT (DFT) 2/17/2007 DSP Course-IUST-Spring Semester

36 DSP Course-IUST-Spring Semester
DFT and IDFT 2/17/2007 DSP Course-IUST-Spring Semester

37 DSP Course-IUST-Spring Semester
IDFT 2/17/2007 DSP Course-IUST-Spring Semester

38 DSP Course-IUST-Spring Semester
DFT examples 2/17/2007 DSP Course-IUST-Spring Semester

39 DSP Course-IUST-Spring Semester
DFT: Matrix form 2/17/2007 DSP Course-IUST-Spring Semester

40 DSP Course-IUST-Spring Semester
Matrix IDFT 2/17/2007 DSP Course-IUST-Spring Semester

41 DSP Course-IUST-Spring Semester
DFT and DTFT 2/17/2007 DSP Course-IUST-Spring Semester

42 DSP Course-IUST-Spring Semester
DFT and MATLAB 2/17/2007 DSP Course-IUST-Spring Semester

43 DSP Course-IUST-Spring Semester
DTFT from DFT 2/17/2007 DSP Course-IUST-Spring Semester

44 DSP Course-IUST-Spring Semester
Periodic sinc 2/17/2007 DSP Course-IUST-Spring Semester

45 DSP Course-IUST-Spring Semester
Periodic sinc 2/17/2007 DSP Course-IUST-Spring Semester

46 DFT from overlength DTFT
2/17/2007 DSP Course-IUST-Spring Semester

47 DFT from overlength DTFT
2/17/2007 DSP Course-IUST-Spring Semester

48 DSP Course-IUST-Spring Semester
DFT from DTFT example 2/17/2007 DSP Course-IUST-Spring Semester

49 DSP Course-IUST-Spring Semester
DFT from DTFT example 2/17/2007 DSP Course-IUST-Spring Semester

50 Properties: Circular time shift
2/17/2007 DSP Course-IUST-Spring Semester

51 DSP Course-IUST-Spring Semester
Circular time shift 2/17/2007 DSP Course-IUST-Spring Semester

52 Circular time reversal
2/17/2007 DSP Course-IUST-Spring Semester

53 4. Convolution with the DFT
2/17/2007 DSP Course-IUST-Spring Semester

54 DSP Course-IUST-Spring Semester
Circular convolution 2/17/2007 DSP Course-IUST-Spring Semester

55 Circular convolution example
2/17/2007 DSP Course-IUST-Spring Semester

56 DSP Course-IUST-Spring Semester
Duality 2/17/2007 DSP Course-IUST-Spring Semester

57 DFT properties summary
2/17/2007 DSP Course-IUST-Spring Semester

58 Linear convolution w/ the DFT
2/17/2007 DSP Course-IUST-Spring Semester

59 Linear convolution w/ the DFT
2/17/2007 DSP Course-IUST-Spring Semester

60 Overlap-Add convolution
2/17/2007 DSP Course-IUST-Spring Semester

61 Overlap-Add convolution
2/17/2007 DSP Course-IUST-Spring Semester

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