Answered! I need MATLAB code for this problem Let a = 5, b = 1…

I need MATLAB code for this problem

Let a = 5, b = 1

PROBLEM STATEMENT The nature of convolutions is that they tend to smooth out signals. Convolved repeatedly, many signals end up looking like a Gaussian bell-shaped curve. We explore this characteristic of repeated convolutions in this problem. Let ab denote the leftmost two digits of your student ID number (a is the leftmost digi Su z (t) a--1) (1-t)--(b--1)(14-t Cult 1) w (t -1)) Throughout this assignment use a sampling time of 0.01 1. Plot r(t) and y2 (t) [r ac (t) on the same graph. 2. Plot ys (t) On the same graph e-B(t-a) where y is the max 3. A true Gaussian bell-shaped curve has the form y(t) ymax maximum value of ylt). Note that ln St2 8 t a 2 which implies that ln B t a 2. Taking square roots gives ln. y(t) VPlt al. Note that t al looks like ymax ln yi(t) the letter V, linear with slope 1 for t a and slope-1 for t a. Plot zi(t) max for i 4, 8, and 16 on a single graph. Hint: Use log (x) to compute a natural logarithm 4. Note that the derivative of a straight line is a constant, so di VBIt al equals VB if t a and -VB otherwise. Thus the absolute value l VBIt all equals VB everywhere. For a not very good approximation to the Gaussian curve, this may not be true. Plot l zi dt for i 4, 8, and 16 on a single graph. Note that the Gaussian approximation breaks down for t large

Expert Answer

 

copyable code:

clc

clear all

close all

a = 5;

b = 1;

t1 = -1;

t2 = 1;

t = t1:0.01:t2;

x = ((a+1)*(1-t)+(b+1)*(1+t)).*(heaviside(t+1)-heaviside(t-1))/(sqrt(2)*(a+b+2));

y2 = conv(x,x);

subplot(2,1,1)

plot(t,x)

title(‘x’)

subplot(2,1,2)

plot(t1*2:0.01:t2*2,y2)

title(‘y2’)

%% 2)

y4 = conv(y2,y2);

y8 = conv(y4,y4);

y16 = conv(y8,y8);

figure()

subplot(3,1,1)

plot(t1*4:0.01:t2*4,y4)

title(‘y4’)

subplot(3,1,2)

plot(t1*8:0.01:t2*8,y8)

title(‘y8’)

subplot(3,1,3)

plot(t1*16:0.01:t2*16,y16)

title(‘y16’)

%%3)

z4 = sqrt(-1*log(y4/max(y4)));

z8 = sqrt(-1*log(y8/max(y8)));

z16 = sqrt(-1*log(y16/max(y16)));

figure()

subplot(3,1,1)

plot(t1*4:0.01:t2*4,z4)

title(‘z4’)

subplot(3,1,2)

plot(t1*8:0.01:t2*8,z8)

title(‘z8’)

subplot(3,1,3)

plot(t1*16:0.01:t2*16,z16)

title(‘z16’)

%% 4)

diff1 = diff(z4);

diff2 = diff(z8);

diff3 = diff(z16);

figure()

subplot(3,1,1)

plot(t1*4:0.01:t2*4-0.01,diff1)

title(‘Z4’)

subplot(3,1,2)

plot(t1*8:0.01:t2*8-0.01,diff2)

title(‘Z8’)

subplot(3,1,3)

plot(t1*16:0.01:t2*16-0.01,diff3)

title(‘Z16’)

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