Convolution and polynomial multiplication of fi objects
c = conv(a,b)
c = conv(a,b,'shape')
c = conv(a,b) outputs the convolution of input vectors a and b, at least one of which must be a fi object.
c = conv(a,b,'shape') returns a subsection of the convolution, as specified by the shape parameter:
full — Returns the full convolution. This option is the default shape.
same — Returns the central part of the convolution that is the same size as input vector a.
valid — Returns only those parts of the convolution that the function computes without zero-padded edges. In this case, the length of output vector c is max(length(a)-max(0,length(b)-1), 0).
The fimath properties associated with the inputs determine the numerictype properties of output fi object c:
If either a or b has a local fimath object, conv uses that fimath object to compute intermediate quantities and determine the numerictype properties of c.
If neither a nor b have an attached fimath, conv uses the default fimath to compute intermediate quantities and determine the numerictype properties of c.
If either input is a built-in data type, conv casts it into a fi object using best-precision rules before the performing the convolution operation.
The output fi object c always uses the default fimath.
Refer to the MATLAB® conv reference page for more information on the convolution algorithm.
The following example illustrates the convolution of a 22-sample sequence with a 16-tap FIR filter.
x is a 22-sample sequence of signed values with a word length of 16 bits and a fraction length of 15 bits.
h is the 16 tap FIR filter.
u = (pi/4)*[1 1 1 -1 -1 -1 1 -1 -1 1 -1]; x = fi(kron(u,[1 1])); h = firls(15, [0 .1 .2 .5]*2, [1 1 0 0]);
Because x is a fi object, you do not need to cast h into a fi object before performing the convolution operation. The conv function does so using best-precision scaling.
Finally, use the conv function to convolve the two vectors:
y = conv(x,h);
The operation results in a signed fi object y with a word length of 36 bits and a fraction length of 31 bits. The default fimath properties associated with the inputs determine the numerictype of the output. The output does not have a local fimath.