Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Question
Chapter 30, Problem 3P
a.
Program Plan Intro
To show that d-dimensional DFT can be computed using 1-dimensional DFTs on each dimension in turn.
b.
Program Plan Intro
To represent a Toeplitz matrix so that you can add two n*n Toeplitz matrices in O(n) time.
c.
Program Plan Intro
To compute a 1-dimensional DFT using fast Fourier transform.
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Inverse Discret Fourier Transform AIM: To write a program
in MATLAB to perform Inverse Fourier Transform IFDT of a
sequence ALGORITHM: 1. Get the sequence x(k) of length
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signal: 4. x(n) = {N-1 X(K)ej2nk/N for n = 0, 1, 2, ..., N-1 ) N O
small x PROGRAM: X=[4,3,2,1,0,0,0,0]; N=8; y=ifft(x,N);
mag=abs(y); phase-angle(y); k=0:1:N-1; subplot(2,2,1);
stem(k,X); xlabel('k'); ylabel('X(k)'); title('input sequence');
subplot(2,2,2); stem(k,mag); xlabel('k'); ylabel('magnitude');
title('magnitude sequence'); subplot(2,2,3); stem(k,phase);
xlabel('k'); ylabel('angle'); title(phase sequence'); disp(y);
2. Find IDFT of each of the following sequences:i) X(k) = (1,
0, 1, 0] 1 ii) X(k) = (-4,5, 2, -3, 0, -2,3,4], 0
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take the inverse Fourier transform of this frequency domain representation and construct a graph with two
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write program for 2x2 matrix in 2d using for where users inputs any four integer
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