hw 1
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School
New York University *
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Course
6183
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
5
Uploaded by MagistrateProton12881
MATLAB HW #1
1.1)
1)
Code
% 1)
n = -10 : 10;
f = (n == 0);
figure(1)
stem (n,f)
Output
2)
Code
% 1)
n = -10 : 10;
f = (n == 0);
figure(1)
stem (n,f)
Output
3.
Code
% 3a-e)
% 3a
n = -5 : 5;
f=1-(1.*(n>=5));
subplot(3,2,1)
figure(3)
stem(n,f);
xlabel(
'n'
);
ylabel(
'f'
);
title(
'f(n)'
);
%3b
g=n-(2.*(n-5).*(n>=5))-((n-10).*(n>=10));
subplot(3,2,2)
stem(n,g);
xlabel(
'n'
);
ylabel(
'g'
);
title(
'g(n)'
);
%3c
x=1.*(n==0)-2.*(n==4);
subplot(3,2,3)
stem(n,x);
xlabel(
'n'
);
ylabel(
'x'
);
title(
'x(n)'
);
%3d
y=((0.9).^n).*(1-1.*(n>=20));
subplot(3,2,4)
stem(n,y);
xlabel(
'n'
);
ylabel(
'y'
);
title(
'y(n)'
);
%3e
v=cos(2*pi*n);
subplot(3,2,5)
stem(n,v);
xlabel(
'n'
);
ylabel(
'v'
);
title(
'v(n)'
);
Output
1.2
code
% 1.2
% a
f=[1 1 1 1 1];
g=[0 1 2 3 4 -5 -6 -7 -8 -9];
a=conv(f,f);
figure(4)
subplot(3,2,1)
stem(a)
xlabel(
'n'
)
ylabel(
'f*f'
)
title(
'convolution of f and f'
)
% b
f=[1 1 1 1 1];
g=[0 1 2 3 4 -5 -6 -7 -8 -9];
b=conv(f,conv(f,f));
subplot(3,2,2)
stem(b)
xlabel(
'n'
)
ylabel(
'f*f*f'
)
title(
'convolution of three f'
)
% c
f=[1 1 1 1 1];
g=[0 1 2 3 4 -5 -6 -7 -8 -9];
c=conv(f,g);
subplot(3,2,3)
stem(c)
xlabel(
'n'
)
ylabel(
'f*g'
)
title(
'convolution of f and g'
)
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% d
g=[0 1 2 3 4 -5 -6 -7 -8 -9];
delta=[1];
d=conv(g,delta);
subplot(3,2,4)
stem(d)
xlabel(
'n'
)
ylabel(
'g*delta'
)
title(
'convolution of g and delta'
)
% e
g=[0 1 2 3 4 -5 -6 -7 -8 -9];
e=conv(g,g);
subplot(3,2,5)
stem(e)
xlabel(
'n'
)
ylabel(
'g*g'
)
title(
'convolution of g and g'
)
Output
Questions
Do you see any relationship between
?
(
?
)
∗
?
(
?
) and
?
(
?
) ?
There is no relationship, they are not the same.
Compare
?
(
?
) with
?
(
?
)
∗
?
(
?
) and with
?
(
?
)
∗
?
(
?
)
∗
?
(
?
).
They are similar. The convolution of the three f is smaller.
What happens as you repeatedly convolve this signal with itself?
It provides triangular functions of different sizes.
3
Code
%3
function
[y]=myconv (x,h)
lx=length(x);
lh=length(h);
y = zeros(1,lx+lh-1);
for
i = 1:lx
for
j = 1:lh
y(j) = h(j)*x(i);
end
end
end
Output