数字信号处理(英文版)课后习题答案4

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(Partial) Solutions to Assignment 4

pp.81-82

Discrete Fourier Series (DFS)

Discrete Fourier Transform (DFT)

, k=0,1,...N-1

, n=0,1,...N-1

Discrete Time Fourier Transform (DTFT)

is periodic with period=2π

Fourier Series (FS)

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Fourier Transform (FT)

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2.1 Consider a sinusoidal signal Q2.1 Consider a sinusoidal signal

that is sampled at a frequency Fs=2 kHz

a). Determine an expressoin for the sampled sequence determine its discrete time Fourier transform b) Determine

, and

c) Re-compute X(?) from X(F) and verify that you obtain the same expression as in (a)

a). ans:

=

where and

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. . . .

Using the formular:

b) ans:

where

c). ans:

Let

be the sample function.

The Fourier transform of is

Using the relationship

or

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