# MATLAB EL6114

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1.1.7
f(n) = u(n)-n(n-4)

n = -5:5; f = (n >= 0); g = (n >= 4); stem (n,(f-g))

g(n)=r(n)-2r(n-5)+r(n-10)

n = -15:15; r = n.*(n >= 0); f = (n-5).*((n-5)>=0); h = (n-10).*((n-10)>=0); g = r - 2.*f + h; stem (n,g)

x(n) = δ(n) - 2δ(n-4)

n = -5:5; f = (n == 0); g = ((n-4)==0); x = f - 2.*g stem (n,x)

y(n) = (0.9)^n (u(n)-u(n-20))

n = -20:20; f = (n >= 0); g = ((n-20)>=0); y = 0.9.^n.*(f-g); stem (n,y)

v(n) = cos (0.12pi*n)u(n)

n = 0:40; f = cos(.12*pi*n) g = (n>=0); y = f.*g; stem (n,y)

1.3.8
The convmtx() function work like this:

For example, h =[1,3,-1,2]; convmtx(h',4) It use the basic principle of convolution. When this matrix multiple x’, every line of this matrix multiple x’ and finally add together.

1.3.9 f = (n>=0)-((n-5)>=0); g = n.*(n >= 0)-2.*(n-5).*(n >= 0)+(n-10).*((n-10) >= 0);

A f(n)*f(n)

B f(n)*f(n)*f(n)

C f(n)*g(n)

D g(n)*delta(n) Every signal convolve delta signal is it self.

E g(n) * g(n)

From the figure, we know that f(n)*f(n) is a shift of g(n).
The signal is amplified when the signal convolved to itself repeatedly.

1.3.10
Command:

n = -5:5 f = 3.*((n+2)==0)-((n-1)==0)+2.*((n-3)==0) g = ((n+4)>=0)-((n-3)>=0) y = conv(f,g) m = -10:10 stem (m,y); xlabel('n'); ylabel('y(n)')

14.1

1.5.1 b
Program: Plot:

n = -10:10; k = -20:20; h = -(n == 0)+2*(1/2).^n.*(n>= 0); inverse = -(n == 0)+2*(-1/2).^n.*(n>= 0); v = conv (h,inverse); stem (k,v)

1.5.2 c
Program: Plot:

n = -10:10; k = -20:20; h = (n ==0) + 3.5 * ((n-1)==0)+ 1.5 *((n-2) == 0); inverse = -0.2*(-1/2).^n.*(n>= 0) - 1.2 * (-3).^n .*((-n-1)>=0); v = conv (h,inverse); stem (k,v)

1.5.3 b

Program: Plot:

n = -10:10; k = -20:20 h = ((n+1) ==0) - 10/3 * (n==0)+ ((n-1) == 0)

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