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[Question 2]: Determine the periodic sequences given the following periodic DFS coefficients. First use the IDFS definition, and then verify your answers using MATLAB. 1. $X_1(k) = \{4, 3j, -3j\}$, $N = 3$ 2. $X_2(k) = \{j, 2j, 3j, 4j\}$, $N = 4$ 3. $X_3(k) = \{1, 2 + 3j, 4, 2 - 3j\}$, $N = 4$ Given this MATLAB example function [xn] = idfs (Xk, N) n = [0: 1: N-1]; % Row vector for n k = [0: 1: N-1]; WN = exp(-j2pi/N); nk = n' k; WNnk = WN.^ (-nk); xn = (Xk WNnk)/N; % Row vector for k % Wn factor % Creates an N by N matrix of nk values % IDFS matrix % Row vector for IDFS values

          [Question 2]:
Determine the periodic sequences given the following periodic DFS coefficients.
First use the IDFS definition, and then verify your answers using MATLAB.
1. $X_1(k) = \{4, 3j, -3j\}$, $N = 3$
2. $X_2(k) = \{j, 2j, 3j, 4j\}$, $N = 4$
3. $X_3(k) = \{1, 2 + 3j, 4, 2 - 3j\}$, $N = 4$
Given this MATLAB example
function [xn] = idfs (Xk, N)
n = [0: 1: N-1];
% Row vector for n
k = [0: 1: N-1];
WN = exp(-j*2*pi/N);
nk = n' *k;
WNnk = WN.^ (-nk);
xn = (Xk * WNnk)/N;
% Row vector for k
% Wn factor
% Creates an N by N matrix of nk values
% IDFS matrix
% Row vector for IDFS values

$[Question 2]: Determine the periodic sequences given the following periodic DFS coefficients. First use the IDFS definition, and then verify your answers using MATLAB. 1. X1(k) = {4, 3j, -3j}, N = 3 2. X2(k) = {j, 2j, 3j, 4j}, N = 4 3. X3(k) = {1, 2 + 3j, 4, 2 - 3j}, N = 4 Given this MATLAB example function [xn] = idfs (Xk, N) n = [0: 1: N-1]; % Row vector for n k = [0: 1: N-1]; WN = exp(-j*2*pi/N); nk = n' *k; WNnk = WN.^ (-nk); xn = (Xk * WNnk)/N; % Row vector for k % Wn factor % Creates an N by N matrix of nk values % IDFS matrix % Row vector for IDFS values$

Added by Jennifer R.

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