convol

Arguments

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)

Description

Calculates the convolution y= h*x of two discrete sequences by using the fft. The convolution is defined as follows:

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.

Examples

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

See also

• corr — correlation, covariance
• fft — Transformée de Fourier discrète rapide.
• pspect — two sided cross-spectral estimate between 2 discrete time signals using the Welch's average periodogram method.