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A. Fourier Transform properties (a) If x ( t ) is real and even, show that its Fourier transform is real for all ω (i.e., its imaginary part is  identically 0).(b) If x ( t ) is real and odd, show that its Fourier transform is imaginary for all ω (i.e., its real part is identically 0)B.Discrete-time Fourier Transform (DTFT) B. Compute the DTFT of the following signals: (a) a [ n ] = δ [ n − 2] + δ [ n + 2] (b) b [ n ] = u [ n ] − u [ n − 4](c) c [ n ] = ( sin (( π/ 4) n )/ πn ) ^2

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Digital Signals Problems

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Subject: Engineering
Due on: 12/30/2016
Posted On: 12/28/2016 02:51 AM

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A. Fourier Transform properties

(a) If x ( t ) is real and even, show that its Fourier transform is real for all ? (i.e., its imaginary part is identically 0).

(b) If x ( t ) is real and odd, show that its Fourier transform is imaginary for all ? (i.e., its real part is identically 0)

B.Discrete-time Fourier Transform (DTFT)

B. Compute the DTFT of the following signals:

(a) a [ n ] = ? [ n ? 2] + ? [ n + 2]

(b) b [ n ] = u [ n ] ? u [ n ? 4]

(c) c [ n ] = ( sin (( ?/ 4) n )/ ?n ) ^2

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Tags problems signals digital real fourier transform dtft compute thefollowing fouriertransform signals imaginary andeven propertiesa imaginarypart identically isidentically oddshow 0bdiscretetime

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