function m = mod(n,N)

%computes m = mod(n mod N)

%___________________

%m = mod(n,N)

m = rem(n,N);

m = m+N;

m = rem(m,N);

function y = cirshiftt(x,m,N)

%circular shift of  m samples wrt size N in sequnce x:

%-----------------------------------------------------

%[y] = cirshiftt(x,m,N)

%y = output sequence containing the circular shift

%;x = input sequence of length <= N

% m = simple shift

% N = size of circular buffer

% method: y(n)=x((n-m) mod N)

% check for length of x

if length (x)> N

        error('N must be >= the length of X')

end

x = [x ,zeros(1,N - length(x))];

n = [0:1:N-1];

n = mod(n-m,N);

y = x(n+1);

n = 0:10 ;

x = 10*(0.8).^n;

y = cirshiftt(x,6,15);

n = 0: 14;

x = [x,zeros(1,4)];

subplot(2,1,1);

stem(n,x);

title('oringnal signal');

subplot(2,1,2);

stem(n,y);

title('x((n-m) mod 15)');