MATLAB code is given below in bold letters.
clc;
clear all;
close all;
% Question a
N = 16;
n = 0:N-1;
x = 1./(2.^abs(n));
% 1000 points for frequency axis
k = 1:1000;
w = 2*pi*(k-1)/1000;clear k;
% initialize DTFTy
DTFTy = zeros(size(w));
for k = 1:length(w)
DTFTy(k) = sum(x.*exp(-1j*w(k)*n));
end
figure;plot(w/(pi),DTFTy,'linewidth',2);grid;xlabel('w/pi');ylabel('Amplitude');
title('Spectrum of x[n]=1/2^|^n^|');
% Question b
N = 16;
n = 0:N-1;
x = 1./(2.^n);
% 1000 points for frequency axis
k = 1:1000;
w = 2*pi*(k-1)/1000;clear k;
% initialize DTFTy
DTFTy2 = zeros(size(w));
for k = 1:length(w)
DTFTy2(k) = sum(x.*exp(-1j*w(k)*n));
end
figure;plot(w/(pi),DTFTy2,'linewidth',2);grid;xlabel('w/pi');ylabel('Amplitude');
title('Spectrum of x[n]=1/2^n');
% Question c
N = 16;
n = 0:N-1;
x = (n+1).*(n<=6) + (13-n).*(n>=7).*(n<=13);
% 1000 points for frequency axis
k = 1:1000;
w = 2*pi*(k-1)/1000;clear k;
% initialize DTFTy
DTFTy3 = zeros(size(w));
for k = 1:length(w)
DTFTy3(k) = sum(x.*exp(-1j*w(k)*n));
end
figure;plot(w/(pi),DTFTy3,'linewidth',2);grid;xlabel('w/pi');ylabel('Amplitude');
title('Spectrum of x_3[n]');
% Question d
N = 8;
n = 0:N-1;
x = (n+1).*(n<=6) + (13-n).*(n>=7).*(n<=13);
% 1000 points for frequency axis
k = 1:1000;
w = 2*pi*(k-1)/1000;clear k;
% initialize DTFTy
DTFTy4 = zeros(size(w));
for k = 1:length(w)
DTFTy4(k) = sum(x.*exp(-1j*w(k)*n));
end
figure;plot(w/(pi),DTFTy4,'linewidth',2);grid;xlabel('w/pi');ylabel('Amplitude');
title('Spectrum of x_4[n]');
1. For each of the following choices of r(n) and N, you will perform the five tasks stated below ...
I will upvote if u will solve What u need? DFT can also be obtained using matrix multiplication. Let X[r] show the transformed values and x[n] show the original signal. Using the analysis equation: Using matrix multiplication, this operation can be written as x[O X[1 1 e(2m/N) e-K4n/N) x12] [N-1]] e-j(2(N-1)T/N)e-j(4(N-1)m/N) Instead of huilt-in EFT function use matrix multinlication to solve 3th auestion [ 1 e-/(2(N-1)(N-1)T/N)]Le[N-1] DFT is an extension of DTFT in which frequency is discretized to a finite...
Please can you solve it using MATLAB. (1) Generate random signals [n] and hn, each of length N, and measure the time it takes to compute the linear convolution of r[n using the linear convolution definition and using the FFT method . Plot a graph of the results for N 104 to 10 in steps of 10. (2) Consider the signal x[n]-cos(0.3n),。£11S 100. Generate a plot of: ·The magnitude and phase of the DTFT of x[n] for 0 2π The...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
Lab #2 Discrete-time Fourier Transform (DTFT) OBJECTIVES: • Explore the DTFT, its meanings and concepts. • Get acquainted with Matlab/Octave 1) Start MATLAB and change the “Current Directory” in the top of the window (or type) >> cd '' (example: >> cd 'C:\NIU\lab2') Alternatively, if you don't want to use MATLAB, you can open a web-browser and go to “octave-online.net”. 2) Download and execute LAB2forStudent_A.M with >> lab2forStudent_A and observe that it produces a Discrete-Time (DT) signal xVec. 3) TO...
this is signal ....please answer clearly thank you For each problem below, convolve x[n) and h[n] by hand, and then compare the DTFT magnitude plots of X(12), H(12), and Y(12). In each case, does h[n) represent a low or high pass filter? Does the signal x[n) pass through the filter or get rejected? Why? (8) x[n] - [1 1 1] , h[n] - [1 -1] (9) x[n] - [1 0 -1 0], [n] - [11] (10) x[n] - [1 0...
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
I Need Help with 4,6,8,10,15,18 Problems 123 If f(n) is a periodic sequence with period N, it is also periodic with period 2N. Tet 8(k) denote the DFS coefficients of X(n) considered as a periodic sequence with period N and X,(k) denote the DFS coefficients of x(n) considered as a periodic sequence with period 2N. X,(k) is, of course, periodic with period N and X2(k) is periodic with period 2N. Determine 8(k) in terms of X (k). 5. Consider two...
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] = { 1, 2,-2, 1, 0, 0, 0, 0). The sequence x2In] is known as a zero-padded version of x,[n]. When answering the questions below, please use Table 1, provided on Page 3. a. [3 pts] Compute X1(eo), the Discrete-Time Fourier Transform (DTFT) of x1 [n], and evaluate it for the following values of normalized frequency: a-63 笎哮,쯤뀨 write the values in the table b....
please write code in MATLAB as well 5. (12 points) Create the following signal in Matlab: x[n] = u(n) - u[n-6] a. Mathematically compute yi[n] = x[n] * x[n] where * means convolution. Now use the conv command to perform the convolution. Graph x[n) and the resulting y(n), both over the interval Osns 20. How many non-zero terms does y(n) have? Does your computational result agree with the Matlab result? b. Repeat a. but this time with yz[n] = x[n]*h[n)...
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...