Aim : Write a Mat Lab Program for generation of Basic sequences like Unit Impulse, Unit Step, Unit Ramp, Exponential, Sine and Cosine.

%Program For Unit Impulse
n=-2:2
a=[zeros(1,2),ones(1,1),zeros(1,2)]
subplot(3,2,1)
stem(n,a)
xlabel('n->')
ylabel('Magnitude')
title('Unit Impulse')

%Program For Unit Step
n=-2:2
a=[zeros(1,2),ones(1,3)]
subplot(3,2,2)
stem(n,a)
xlabel('n->')
ylabel('Magnitude')
title('Unit Step')

%Program For Unit Ramp
n=-2:3
a=[zeros(1,2),0:3]
subplot(3,2,3)
stem(n,a)
xlabel('n->')
ylabel('Magnitude')
title('Unit Ramp')

%Program For Exponential
n=0:10
a=0.5
ans=a.^m
subplot(3,2,4)
stem(n,ans)
xlabel('n->')
ylabel('Magnitude')
title('Exponential')

%Program For Sin
n=-1:0.001:1
a=sin(2*pi*n)
subplot(3,2,5)
plot(n,a)
xlabel('n->')
ylabel('Magnitude')
title('Sine')

%Program For Cos
n=-1:0.001:1
a=cos(2*pi*n)
subplot(3,2,6)
plot(n,a)
xlabel('n->')
ylabel('mag')
title('Cosin')

Aim : Write a Mat Lab Program to find convolution of two finite length Sequences.
Program :

% Program for Convolution
u=input('Enter 1st Sequence : ');
v=input('Enter 2nd Sequence : ');
u1=length(u)
v1=length(v)
dpx=0:u1-1
dph=0:v1-1

subplot(2,2,1)
stem(dpx,u)
xlabel('n->')
ylabel('Magnitude')
title('1st Sequence')

subplot(2,2,2)
stem(dph,v)
xlabel('n->')
ylabel('Magnitude')
title('2nd Sequence')

y=conv(u,v)
dpy=0:(u1+v1-2)
subplot(2,2,[3,4])
stem(dpy,y)
xlabel('n->')
ylabel('Magnitude')
title('Convolution')

Aim : Write a Mat Lab Program to verify the properties of Z – Transform.
i.	Linearity
ii.	Scaling in Z Domain
iii.	Time Reversal
iv.	Differential in Z- Domain

Program :

% Program for Linearity
syms n
f= 2^n
ztrans(f)
g= 3^n
ztrans(g)
x=f+g
ztrans(x)

% Program for Scaling in Z Domain
syms a n w
x1=(a^n)*cos(w.*n)
ztrans(x1)

% Program for Time Reversal
syms a n
x2= (a^(-n))
ztrans(x2)

% Program for Differential in Z Domain
syms a n
x3=n.*(a^n)
ztrans(x3)


Aim: Write a MATLAB program to design a low pas FIR filter using rectangular window.

Program:
%Program to design a Low Pass FIR Filter using rectangular window
%Taking Input
rp =input('Enter Pass Band Ripple : ')
rs=input('Enter Stop Band Ripple : ')
fp=input('Enter Pass Band Frequency : ')
fs=input('Enter Stop Band Frequency : ')
f=input('Enter Sampling Frequency : ')

%Calculating Order
wp=(2*fp)/f
num= -20*log10(sqrt(rp*rs))
den=14.6*(fs-fp)/f
n=ceil(num/den)
n1=n+1

%Odd value
if(rem(n,2)~=0)
    n1=n
    n=n+1
end

%Low Pass FIR Filter
y=rectwin(n1)
b=fir1(n,wp,y)
[h,o]=freqz(b,1,256)
m=20*log10(abs(h))

%Plotting Values
plot(o/pi,m)
xlabel('Normalized Frequency')
ylabel('Gain in DB')