conv

Convolution and polynomial multiplication of fi objects

Syntax

c = conv(a,b)

c = conv(a,b,shape)

Description

c = conv(a,b) returns the convolution of 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 shape.

Examples

Convolution of 22-Sample Sequence with 16-Tap FIR Filter

Find 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 this automatically using best-precision scaling.

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.

Central Part of Convolution of Two fi Vectors

Create two fi vectors. Find the central part of the convolution of a and b that is the same size as a.

a = fi([-1 2 3 -2 0 1 2]);
b = fi([2 4 -1 1]);
c = conv(a,b,'same')

c = 

    15     5    -9     7     6     7    -1

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 34
        FractionLength: 25

c has a length of 7. The full convolution would be of length length(a)+length(b)-1, which in this example would be 10.

Input Arguments

a,b — Input vectors

vectors

Input vectors, specified as either row or column vectors. The vectors a and b can be different lengths or data types.

At least one input must be a fi object. If either input is a built-in data type, the conv function casts it into a fi object using best-precision rules before the performing the convolution operation.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

shape — Subset of convolution

'full' (default) | 'same' | 'valid'

Subset of convolution, specified as one of these values:

• 'full' — Full convolution. This option is the default shape.

• 'same' — Central part of the convolution of the same size as a.

• 'valid' — Only those parts of the convolution that are computed without zero-padded edges.

Data Types: char

Output Arguments

c — Convolved vector

vector

Convolved vector, returned as a row or column vector.

In R2026a: The orientation of the output does not depend on the length of the input. When shape is set to 'full', the output is a column vector if and only if both inputs are column vectors. The conv function returns a row vector otherwise.

More About

Convolution

The convolution of two vectors, u and v, represents the area of overlap under the points as v slides across u. Algebraically, convolution is the same operation as multiplying polynomials whose coefficients are the elements of u and v.

Let m = length(u) and n = length(v). Then w is the vector of length m+n-1 whose kth element is

$$w(k)={\displaystyle \sum _{j}u}(j)v(k-j+1).$$

The sum is over all the values of j that lead to legal subscripts for u(j) and v(k-j+1), specifically j = max(1,k+1-n):1:min(k,m). When m = n, this gives

w(1) = u(1)*v(1)
w(2) = u(1)*v(2)+u(2)*v(1)
w(3) = u(1)*v(3)+u(2)*v(2)+u(3)*v(1)
...
w(n) = u(1)*v(n)+u(2)*v(n-1)+ ... +u(n)*v(1)
...
w(2*n-1) = u(n)*v(n)

Algorithms

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• variable-size inputs are only supported when the SumMode property of the governing fimath is set to SpecifyPrecision or KeepLSB.

• For variable-size signals, you might see different results between generated code and MATLAB^®.

  • In the generated code, the output for variable-size signals is computed using the SumMode property of the governing fimath.

  • In MATLAB, the output for variable-size signals is computed using the SumMode property of the governing fimath when both inputs are nonscalar. However, if either input is a scalar, MATLAB computes the output using the ProductMode of the governing fimath.

Version History

Introduced in R2009b

R2026a: conv: Output orientation does not depend on length of input

The orientation of the output of the conv function does not depend on the length of the input. When shape is set to 'full', the output is a column vector if and only if both inputs are column vectors. The conv function returns a row vector otherwise.