数字信号处理(英文版)课后习题问题详解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=2

π

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

F

s

=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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where

( or

Consider only the region where

therefore

where

END

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2.3

For

each

where

sampling frequence

(b)

is given for each case.

Hz

shown,

determine

is the sampled sequence. The

(d)

Hz

theory: the relationship between DTFT and FT is

where

or

b. ans:

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