Write MATLAB Codes to answer the following Consider the syst

Write MATLAB Codes to answer the following:

Consider the system described by y[n] = x^2[n]. Find: The impulse response of the system h[n]. The response of the system if x[n] = [1 2 3 4], 0 lessthanorequalto n lessthanorequalto 3 by directly substituting x[n] into the system equation. Compute the output using the \'cony\' command. Compute the response of the system using DTFT. Comparing the results of (b), (c), and (d), what do you conclude? Explain

Solution

a)Impulse response:

y[n]=x²[n]

y[n]/x[n]=x[n]

h[n]=x[n]

b)

n=0;x[0]=1,y[0]=1²=1;

n=1;x[1]=2,y[1]=2²=4;

n=2;x[2]=3,y[2]=3²=9;

n=3;x[3]=4,y[0]=4²=16;

y[n]=[1 4 9 16]

c)

x=[1 2 3 4];
h=[1 2 3 4];
y=conv(x,h)

y =

1 4 10 20 25 24 16