The following Matlab function filterfir performs the FIR fil

The following Matlab function, filterfir, performs the FIR filtering as given in (1). function y = filterfir(h, x) % FILTERFIR Finite impulse response (FIR) filtering function % % Y=FILTERFIR(H, X) returns the FIR filter result of X by the LTI system % whose impulse response is H. It is assumed that both H and X represent % signals that start at time zero. If X is a row vector, then Y will be % a row vector. If X is a column vector, Y will be column vector. % % EXAMPLE: % h=[0 2]; % x=[2 4 1]; % y=filterfir(h, x) lenh=length(h); lenx=length(x); leny=lenh+lenx-1; % Make an empty Y vector in the same direction as X if size(x, 1)==lenx y=zeros(leny, 1); else y=zeros(1, leny); end % Do the filtering operation for k=1: lenh y(k:k+lenx-1)=y(k:k+lenx-1)+h(k)*x; end return; % End of the function Exercise 1. Explain in your own words how filterfir works.

Solution

Example:

h=[0 2];

x=[2 4 1];

first it calculates the lenths fo the h, x and y. as shown below

lenh=length(h)

lenh =

     2

lenx=length(x)

lenx =

     3

leny=lenh+lenx-1

leny =

     4

Making zeros to y based on the condition

Here, size(x,1) is not equal to lenx

size(x,1)

ans =

     1

then it starts filtering by using of

y(k:k+lenx-1)=y(k:k+lenx-1)+h(k)*x