Convolution Integral for one dimensional data. More...

Functions

AFAPI array convolve1 (const array &signal, const array &filter, const convMode mode=AF_CONV_DEFAULT, const convDomain domain=AF_CONV_AUTO)
 C++ Interface for convolution on one dimensional signals. More...
 
AFAPI array fftConvolve1 (const array &signal, const array &filter, const convMode mode=AF_CONV_DEFAULT)
 C++ Interface for convolution on 1D signals using FFT. More...
 
AFAPI af_err af_convolve1 (af_array *out, const af_array signal, const af_array filter, const af_conv_mode mode, af_conv_domain domain)
 C Interface for convolution on one dimensional signals. More...
 
AFAPI af_err af_fft_convolve1 (af_array *out, const af_array signal, const af_array filter, const af_conv_mode mode)
 C Interface for convolution on 1D signals using FFT. More...
 

Detailed Description

Convolution Integral for one dimensional data.

A convolution is a common operation between a source array, a, and a filter (or kernel) array b. The answer to the convolution is the same as computing the coefficients in polynomial multiplication, if a and b are the coefficients.

Another way to think about it is that the filter kernel is centered on each pixel in a, and the output for that pixel or data point is the sum of the products.

Depending on the size of the signal and the filter, any one of the following batch mode convolutions take place.

Note
All non-overlapping(interleaved) convolutions default to frequency domain AF_CONV_FREQ irrespective of the provided convolution mode argument.

For one dimensional signals (lets say m is size of 0th axis), below batch operations are possible.

Signal Size Filter Size Output Size Batch Mode Description
\( [m \ 1 \ 1 \ 1] \) \( [m \ 1 \ 1 \ 1] \) \( [m \ 1 \ 1 \ 1] \) No Batch Output will be a single convolved array
\( [m \ 1 \ 1 \ 1] \) \( [m \ n \ 1 \ 1] \) \( [m \ n \ 1 \ 1] \) Filter is Batched n filters applied to same input
\( [m \ n \ 1 \ 1] \) \( [m \ 1 \ 1 \ 1] \) \( [m \ n \ 1 \ 1] \) Signal is Batched 1 filter applied to n inputs
\( [m \ n \ p \ q] \) \( [m \ n \ p \ q] \) \( [m \ n \ p \ q] \) Identical Batches n*p*q filters applied to n*p*q inputs in one-to-one correspondence
\( [m \ n \ 1 \ 1] \) \( [m \ 1 \ p \ q] \) \( [m \ n \ p \ q] \) Non-overlapping batches p*q filters applied to n inputs to produce n x p x q results

There are various other permutations of signal and filter sizes that fall under the category of non-overlapping batch mode that are not listed in the above table. For any signal and filter size combination to fall under the non-overlapping batch mode, they should satisfy one of the following conditions.

Note
For the above tabular illustrations, we assumed af_conv_mode is AF_CONV_DEFAULT.

Function Documentation

◆ af_convolve1()

AFAPI af_err af_convolve1 ( af_array out,
const af_array  signal,
const af_array  filter,
const af_conv_mode  mode,
af_conv_domain  domain 
)

C Interface for convolution on one dimensional signals.

Parameters
[out]outis convolved array
[in]signalis the input signal
[in]filteris the signal that shall be flipped for the convolution operation
[in]modeindicates if the convolution should be expanded or not(where output size equals input)
[in]domainspecifies if the convolution should be performed in frequency os spatial domain
Returns
AF_SUCCESS if the convolution is successful, otherwise an appropriate error code is returned.
Note
The default parameter of domain, AF_CONV_AUTO, heuristically switches between frequency and spatial domain.

◆ af_fft_convolve1()

AFAPI af_err af_fft_convolve1 ( af_array out,
const af_array  signal,
const af_array  filter,
const af_conv_mode  mode 
)

C Interface for convolution on 1D signals using FFT.

Parameters
[out]outis convolved array
[in]signalis the input signal
[in]filteris the signal that shall be used for the convolution operation
[in]modeindicates if the convolution should be expanded or not(where output size equals input)
Returns
AF_SUCCESS if the convolution is successful, otherwise an appropriate error code is returned.

◆ convolve1()

AFAPI array af::convolve1 ( const array signal,
const array filter,
const convMode  mode = AF_CONV_DEFAULT,
const convDomain  domain = AF_CONV_AUTO 
)

C++ Interface for convolution on one dimensional signals.

// vector<dim4> numDims;
// vector<vector<float> > in;
array signal(numDims[0], &(in[0].front()));
// signal dims = [32 1 1 1]
array filter(numDims[1], &(in[1].front()));
// filter dims = [4 1 1 1]
array output = convolve1(signal, filter, AF_CONV_DEFAULT);
// output dims = [32 1 1 1] - same as input since expand(3rd argument is
// false) None of the dimensions > 1 has lenght > 1, so no batch mode is
// activated.
Parameters
[in]signalis the input signal
[in]filteris the signal that shall be flipped for the convolution operation
[in]modeindicates if the convolution should be expanded or not(where output size equals input)
[in]domainspecifies if the convolution should be performed in frequency os spatial domain
Returns
the convolved array
Note
The default parameter of domain, AF_CONV_AUTO, heuristically switches between frequency and spatial domain.

◆ fftConvolve1()

AFAPI array af::fftConvolve1 ( const array signal,
const array filter,
const convMode  mode = AF_CONV_DEFAULT 
)

C++ Interface for convolution on 1D signals using FFT.

Parameters
[in]signalis the input signal
[in]filteris the signal that shall be used for the convolution operation
[in]modeindicates if the convolution should be expanded or not(where output size equals input)
Returns
the convolved array
AF_CONV_DEFAULT
@ AF_CONV_DEFAULT
Output of the convolution is the same size as input.
Definition: defines.h:305
af::convolve1
AFAPI array convolve1(const array &signal, const array &filter, const convMode mode=AF_CONV_DEFAULT, const convDomain domain=AF_CONV_AUTO)
C++ Interface for convolution on one dimensional signals.
afcl::array
static af::array array(af::dim4 idims, cl_mem buf, af::dtype type, bool retain=false)
Create an af::array object from an OpenCL cl_mem buffer.
Definition: opencl.h:327
af::filter
AFAPI array filter(const array &image, const array &kernel)
Image Filtering.