convolution
[y]=convol(h,x)
[y,e1]=convol(h,x,e0)
:h a vector, first input sequence (“short” one) : :x a vector, second input sequence ( “long” one) : :e0 a vector,old tail to overlap add (not used in first call) : :y a vector, the convolution. : :e1 new tail to overlap add (not used in last call) :
Calculates the convolution y= h*x of two discrete sequences by using the fft. The convolution is defined as follow:
Overlap add method can be used.
USE OF OVERLAP ADD METHOD: For x=[x1,x2,...,xNm1,xN] First call is [y1,e1]=convol(h,x1); Subsequent calls : [yk,ek]=convol(h,xk,ekm1); Final call : [yN]=convol(h,xN,eNm1); Finally y=[y1,y2,...,yNm1,yN].
The algorithm based on the convolution definition is implemented for polynomial product: y=convol(h,x) is equivalent to y=coeff(poly(h,’z’,’c’)*poly(x,’z’,’c’) but much more efficient if x is a “long” array.
x=1:3;
h1=[1,0,0,0,0];h2=[0,1,0,0,0];h3=[0,0,1,0,0];
x1=convol(h1,x),x2=convol(h2,x),x3=convol(h3,x),
convol(h1+h2+h3,x)
p1=`poly`_(x,'x','coeff')
p2=`poly`_(h1+h2+h3,'x','coeff')
p1*p2