conv
Convolution and polynomial multiplication
Description
w = conv(
returns
the convolution of
vectors u,v
)u
and v
. If u
and v
are
vectors of polynomial coefficients, convolving them is equivalent
to multiplying the two polynomials.
Examples
Polynomial Multiplication via Convolution
Create vectors u
and v
containing the coefficients of the polynomials and .
u = [1 0 1]; v = [2 7];
Use convolution to multiply the polynomials.
w = conv(u,v)
w = 1×4
2 7 2 7
w
contains the polynomial coefficients for .
Vector Convolution
Create two vectors and convolve them.
u = [1 1 1]; v = [1 1 0 0 0 1 1]; w = conv(u,v)
w = 1×9
1 2 2 1 0 1 2 2 1
The length of w
is length(u)+length(v)-1
, which in this example is 9
.
Central Part of Convolution
Create two vectors. Find the central part of the convolution of u
and v
that is the same size as u
.
u = [-1 2 3 -2 0 1 2];
v = [2 4 -1 1];
w = conv(u,v,'same')
w = 1×7
15 5 -9 7 6 7 -1
w
has a length of 7
. The full convolution would be of length length(u)+length(v)-1
, which in this example would be 10.
Input Arguments
u,v
— Input vectors
vectors
Input vectors, specified as either row or column vectors. The
vectors u
and v
can be different
lengths or data types.
When u
or v
are of type single
,
then the output is of type single
. Otherwise, conv
converts
inputs to type double
and returns type double
.
Data Types: double
| single
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
| logical
Complex Number Support: Yes
shape
— Subsection of convolution
'full'
(default) | 'same'
| 'valid'
Subsection of the convolution, specified as 'full'
, 'same'
,
or 'valid'
.
'full' | Full convolution (default). |
'same' | Central part of the convolution of the same size as |
'valid' | Only those parts of the convolution that are computed
without the zero-padded edges. Using this option, |
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
k
th element is
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)
Using this definition, conv
calculates the direct convolution of two
vectors, rather than the FFT-based convolution.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
The
conv
function supports tall arrays with the following usage
notes and limitations:
The inputs
u
andv
must be column vectors.If
shape
is'full'
(default), then only one ofu
orv
can be a tall array.If
shape
is'same'
or'valid'
, thenv
cannot be a tall array.
For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
For information about C/C++ code generation limitations, see Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).
GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
The conv
function
fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray
(Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced before R2006a
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