fourier transform of the shah function

21
1 Fourier Transform of the Shah Function j j wj i j wt i wt i j j j jw e dt e j t dt e j t j t FT j t 2 cos ) ( ) ( ) ( have We . ) ( be to defined is function shah The 2 2 2

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Fourier Transform of the Shah Function. The Sampling Theorem. Discrete Fourier Transform. Insight of Discrete Fourier Transform. Formula of Discrete Fourier Transform. Zero-Padding of DFT. Circular Convolution in the Discrete Case. Convolution Theorem in the Discrete Case. - PowerPoint PPT Presentation

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Page 1: Fourier Transform of the Shah Function

1

Fourier Transform of the Shah Function

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Page 2: Fourier Transform of the Shah Function

2

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Page 3: Fourier Transform of the Shah Function

3

domain.frequency in thefunction shah a is 2cos

rem,power theo by the ,Therefore

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Page 4: Fourier Transform of the Shah Function

4

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Page 5: Fourier Transform of the Shah Function

5

The Sampling Theorem

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Page 6: Fourier Transform of the Shah Function

6

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Page 7: Fourier Transform of the Shah Function

7

domain. ed transformin the numbers real

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Page 8: Fourier Transform of the Shah Function

8

Discrete Fourier Transform

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Page 9: Fourier Transform of the Shah Function

9

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Page 10: Fourier Transform of the Shah Function

10

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Page 11: Fourier Transform of the Shah Function

11

Insight of Discrete Fourier Transform

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Page 12: Fourier Transform of the Shah Function

12

Formula of Discrete Fourier Transform

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Page 13: Fourier Transform of the Shah Function
Page 14: Fourier Transform of the Shah Function
Page 15: Fourier Transform of the Shah Function

15

Zero-Padding of DFT

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have we theorem,sampling by the

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Page 16: Fourier Transform of the Shah Function
Page 17: Fourier Transform of the Shah Function

17

Circular Convolutionin the Discrete Case

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Page 18: Fourier Transform of the Shah Function

18

Convolution Theoremin the Discrete Case

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Page 19: Fourier Transform of the Shah Function

19

Implementation of the Linear Convolutionin the Discrete Case

.2for ,0 and

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Page 20: Fourier Transform of the Shah Function

20

Implementation of the Linear Convolutionin the Discrete Case

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Page 21: Fourier Transform of the Shah Function

21

Multi-Dimensional Discrete Fourier Transform

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