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Tut 8

The document is a tutorial sheet from the Malaviya National Institute of Technology, Jaipur, focusing on Digital Signal Processing (DSP). It includes various problems related to Discrete Time Fourier Transform (DTFT), normalized discrete frequency, Fourier Transform, and the analysis of discrete LTI systems. The exercises cover the computation of DTFT for given sequences, magnitude spectrum analysis, and system response determination.

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Yash Mathuria
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27 views1 page

Tut 8

The document is a tutorial sheet from the Malaviya National Institute of Technology, Jaipur, focusing on Digital Signal Processing (DSP). It includes various problems related to Discrete Time Fourier Transform (DTFT), normalized discrete frequency, Fourier Transform, and the analysis of discrete LTI systems. The exercises cover the computation of DTFT for given sequences, magnitude spectrum analysis, and system response determination.

Uploaded by

Yash Mathuria
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Malaviya National Institute of Technology, Jaipur-302017

Department of Electrical Engineering


Tutorial Sheet-08
Sub: Digital Signal Processing (DSP)

1. Find the the DTFT (Discrete Time Fourier Transform) of the finite sequence x[n] =
{1, 3, -2, 5}.

2. If the sampling frequency is 200 KHz, then for the frequency f = 25 KHz, What will
be the value of normalized discrete frequency (rad/sec).

𝜋
3. Find the DTFT of x[n] = {2,1,2} and compute its magnitude at 𝜔 = 0 𝑎𝑛𝑑 𝜔 = 2 .

4. If 𝑥[𝑛] = 𝑎|𝑛| ; 0<a<1. Find DTFT of x[n] and its magnitude spectrum.

5. Determine the Fourier Transform and plot the magnitude and phase spectrum of the
following signals
1, 0 ≤ 𝑛 ≤ 3
𝑥[𝑛] = {
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

6. Find 𝑋(𝑒 𝑗𝜔 ) = 2𝜋𝛿(𝜔), −𝜋 < 𝜔 < 𝜋, find x[n] and find x[n] if 𝑋(𝑒 𝑗𝜔 ) = 4𝑐𝑜𝑠 2 𝜔.

−𝑗𝜔

7. Given 𝑋(𝑒 𝑗𝜔
) = { 𝑒 2 , |𝜔| < 1 , Find x[n].
0, 1 < |𝜔| < 𝜋

8. A 5 point sequence x[n] is given as x[-3] =1, x[-2] = 1, x[0] = 5, x[1] = 1. Let 𝑋(𝑒 𝑗𝜔 )
𝜋
denotes the DTFT of x[n]. Find the value of ∫−𝜋 𝑥(𝑒 𝑗𝜔 )𝑑𝜔.

3
9. A causal discrete LTI system is described by difference equation 𝑦[𝑛] − 4 𝑦[𝑛 − 1] +
1
𝑦[𝑛 − 2] = 𝑥[𝑛]. Determine frequency response and inpulse response.
8

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