Question

Consider a finite length DT sequence of length N -16 described below. 1, 0<n< 2 Use MATLAB built-in function dftmtx (N), and compute X[k] command and create stem plots for the following: DFT(X[k]. Use subplot (a) x n] vs n; (b) X[k] vs k; (c) angle (X [k) vs k. Label axes of these plots and include title for each of these plots

Answer 1

clear all;close all;clc;
N=8;
n=0:1:(N-1);
n1=0:1:((N/2)-1);
n2=(N/2):1:(N-1);
x1=ones(1,length(n1));
x2=zeros(1,length(n2));
x=[x1 x2];
X = x*dftmtx(N);
disp(X)
subplot(1,3,1)
stem(n,x);
xlabel('Discrete time (n)-->')
ylabel('Amplitude of x(n) -->')
title('Discrete time signal x(n)')
k=n;
subplot(1,3,2)
stem(k,abs(X));
xlabel('Discrete frequency (k) -->')
ylabel('Magnitude of X(k) -->')
title('Magnitude spectrum of X(k)')
subplot(1,3,3)
stem(k,angle(X));
xlabel('Discrete frequency (k) -->')
ylabel('Phase of X(k) -->')
title('Phase spectrum of X(k)')

x(n) = [1 1 1 1 0 0 0 0[
X(k) = [4 1 - 2.4142i 0 1 - 0.4142i 0 1 + 0.4142i 0 1 + 2.4142i]

Discrete time signal x(n) Magnitude spectrum of X(k) Phase spectrum of X(k) 1.5 0.9 3.5 0.8 0.7 0.5 2.5 0.6 0.5 0.4 1.5 0.3 0.2 0.5 1.5 Discrete time (n)-> Discrete frequency (k)-> Discrete frequency (k)>