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signal.py
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1418 lines (1020 loc) · 37.9 KB
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#######################################################
# Copyright (c) 2015, ArrayFire
# All rights reserved.
#
# This file is distributed under 3-clause BSD license.
# The complete license agreement can be obtained at:
# http://arrayfire.com/licenses/BSD-3-Clause
########################################################
"""
Signal processing functions (fft, convolve, etc).
"""
from .library import *
from .array import *
from .bcast import broadcast
@broadcast
def _scale_pos_axis0(x_curr, x_orig):
x0 = x_orig[0, 0, 0, 0]
dx = x_orig[1, 0, 0, 0] - x0
return((x_curr - x0) / dx)
@broadcast
def _scale_pos_axis1(y_curr, y_orig):
y0 = y_orig[0, 0, 0, 0]
dy = y_orig[0, 1, 0, 0] - y0
return((y_curr - y0) / dy)
def approx1(signal, x, method=INTERP.LINEAR, off_grid=0.0, xp = None):
"""
Interpolate along a single dimension.Interpolation is performed along axis 0
of the input array.
Parameters
----------
signal: af.Array
Input signal array (signal = f(x))
x: af.Array
The x-coordinates of the interpolation points. The interpolation
function is queried at these set of points.
method: optional: af.INTERP. default: af.INTERP.LINEAR.
Interpolation method.
off_grid: optional: scalar. default: 0.0.
The value used for positions outside the range.
xp : af.Array
The x-coordinates of the input data points
Returns
-------
output: af.Array
Values calculated at interpolation points.
Note
-----
This holds applicable when x_input isn't provided:
The initial measurements are assumed to have taken place at equal steps between [0, N - 1],
where N is the length of the first dimension of `signal`.
"""
output = Array()
if(xp is not None):
pos0 = _scale_pos_axis0(x, xp)
else:
pos0 = x
safe_call(backend.get().af_approx1(c_pointer(output.arr), signal.arr, pos0.arr,
method.value, c_float_t(off_grid)))
return output
def approx2(signal, x, y,
method=INTERP.LINEAR, off_grid=0.0, xp = None, yp = None
):
"""
Interpolate along a two dimension.Interpolation is performed along axes 0 and 1
of the input array.
Parameters
----------
signal: af.Array
Input signal array (signal = f(x, y))
x : af.Array
The x-coordinates of the interpolation points. The interpolation
function is queried at these set of points.
y : af.Array
The y-coordinates of the interpolation points. The interpolation
function is queried at these set of points.
method: optional: af.INTERP. default: af.INTERP.LINEAR.
Interpolation method.
off_grid: optional: scalar. default: 0.0.
The value used for positions outside the range.
xp : af.Array
The x-coordinates of the input data points. The convention followed is that
the x-coordinates vary along axis 0
yp : af.Array
The y-coordinates of the input data points. The convention followed is that
the y-coordinates vary along axis 1
Returns
-------
output: af.Array
Values calculated at interpolation points.
Note
-----
This holds applicable when x_input/y_input isn't provided:
The initial measurements are assumed to have taken place at equal steps between [(0,0) - [M - 1, N - 1]]
where M is the length of the first dimension of `signal`,
and N is the length of the second dimension of `signal`.
"""
output = Array()
if(xp is not None):
pos0 = _scale_pos_axis0(x, xp)
else:
pos0 = x
if(yp is not None):
pos1 = _scale_pos_axis1(y, yp)
else:
pos1 = y
safe_call(backend.get().af_approx2(c_pointer(output.arr), signal.arr,
pos0.arr, pos1.arr, method.value, c_float_t(off_grid)))
return output
def fft(signal, dim0 = None , scale = None):
"""
Fast Fourier Transform: 1D
Parameters
----------
signal: af.Array
A 1 dimensional signal or a batch of 1 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
Returns
-------
output: af.Array
A complex af.Array containing the full output of the fft.
"""
if dim0 is None:
dim0 = 0
if scale is None:
scale = 1.0
output = Array()
safe_call(backend.get().af_fft(c_pointer(output.arr), signal.arr, c_double_t(scale), c_dim_t(dim0)))
return output
def fft2(signal, dim0 = None, dim1 = None , scale = None):
"""
Fast Fourier Transform: 2D
Parameters
----------
signal: af.Array
A 2 dimensional signal or a batch of 2 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
dim1: optional: int. default: None.
- Specifies the size of the output.
- If None, dim1 is calculated to be the second dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
Returns
-------
output: af.Array
A complex af.Array containing the full output of the fft.
"""
if dim0 is None:
dim0 = 0
if dim1 is None:
dim1 = 0
if scale is None:
scale = 1.0
output = Array()
safe_call(backend.get().af_fft2(c_pointer(output.arr), signal.arr, c_double_t(scale),
c_dim_t(dim0), c_dim_t(dim1)))
return output
def fft3(signal, dim0 = None, dim1 = None , dim2 = None, scale = None):
"""
Fast Fourier Transform: 3D
Parameters
----------
signal: af.Array
A 3 dimensional signal or a batch of 3 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
dim1: optional: int. default: None.
- Specifies the size of the output.
- If None, dim1 is calculated to be the second dimension of `signal`.
dim2: optional: int. default: None.
- Specifies the size of the output.
- If None, dim2 is calculated to be the third dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
Returns
-------
output: af.Array
A complex af.Array containing the full output of the fft.
"""
if dim0 is None:
dim0 = 0
if dim1 is None:
dim1 = 0
if dim2 is None:
dim2 = 0
if scale is None:
scale = 1.0
output = Array()
safe_call(backend.get().af_fft3(c_pointer(output.arr), signal.arr, c_double_t(scale),
c_dim_t(dim0), c_dim_t(dim1), c_dim_t(dim2)))
return output
def ifft(signal, dim0 = None , scale = None):
"""
Inverse Fast Fourier Transform: 1D
Parameters
----------
signal: af.Array
A 1 dimensional signal or a batch of 1 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.0 / (dim0)
Returns
-------
output: af.Array
A complex af.Array containing the full output of the inverse fft.
Note
----
The output is always complex.
"""
if dim0 is None:
dim0 = signal.dims()[0]
if scale is None:
scale = 1.0/float(dim0)
output = Array()
safe_call(backend.get().af_ifft(c_pointer(output.arr), signal.arr, c_double_t(scale), c_dim_t(dim0)))
return output
def ifft2(signal, dim0 = None, dim1 = None , scale = None):
"""
Inverse Fast Fourier Transform: 2D
Parameters
----------
signal: af.Array
A 2 dimensional signal or a batch of 2 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
dim1: optional: int. default: None.
- Specifies the size of the output.
- If None, dim1 is calculated to be the second dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.0 / (dim0 * dim1)
Returns
-------
output: af.Array
A complex af.Array containing the full output of the inverse fft.
Note
----
The output is always complex.
"""
dims = signal.dims()
if dim0 is None:
dim0 = dims[0]
if dim1 is None:
dim1 = dims[1]
if scale is None:
scale = 1.0/float(dim0 * dim1)
output = Array()
safe_call(backend.get().af_ifft2(c_pointer(output.arr), signal.arr, c_double_t(scale),
c_dim_t(dim0), c_dim_t(dim1)))
return output
def ifft3(signal, dim0 = None, dim1 = None , dim2 = None, scale = None):
"""
Inverse Fast Fourier Transform: 3D
Parameters
----------
signal: af.Array
A 3 dimensional signal or a batch of 3 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
dim1: optional: int. default: None.
- Specifies the size of the output.
- If None, dim1 is calculated to be the second dimension of `signal`.
dim2: optional: int. default: None.
- Specifies the size of the output.
- If None, dim2 is calculated to be the third dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.0 / (dim0 * dim1 * dim2).
Returns
-------
output: af.Array
A complex af.Array containing the full output of the inverse fft.
Note
----
The output is always complex.
"""
dims = signal.dims()
if dim0 is None:
dim0 = dims[0]
if dim1 is None:
dim1 = dims[1]
if dim2 is None:
dim2 = dims[2]
if scale is None:
scale = 1.0 / float(dim0 * dim1 * dim2)
output = Array()
safe_call(backend.get().af_ifft3(c_pointer(output.arr), signal.arr, c_double_t(scale),
c_dim_t(dim0), c_dim_t(dim1), c_dim_t(dim2)))
return output
def fft_inplace(signal, scale = None):
"""
In-place Fast Fourier Transform: 1D
Parameters
----------
signal: af.Array
A 1 dimensional signal or a batch of 1 dimensional signals.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
"""
if scale is None:
scale = 1.0
safe_call(backend.get().af_fft_inplace(signal.arr, c_double_t(scale)))
def fft2_inplace(signal, scale = None):
"""
In-place Fast Fourier Transform: 2D
Parameters
----------
signal: af.Array
A 2 dimensional signal or a batch of 2 dimensional signals.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
"""
if scale is None:
scale = 1.0
safe_call(backend.get().af_fft2_inplace(signal.arr, c_double_t(scale)))
def fft3_inplace(signal, scale = None):
"""
In-place Fast Fourier Transform: 3D
Parameters
----------
signal: af.Array
A 3 dimensional signal or a batch of 3 dimensional signals.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
"""
if scale is None:
scale = 1.0
output = Array()
safe_call(backend.get().af_fft3_inplace(signal.arr, c_double_t(scale)))
def ifft_inplace(signal, scale = None):
"""
Inverse In-place Fast Fourier Transform: 1D
Parameters
----------
signal: af.Array
A 1 dimensional signal or a batch of 1 dimensional signals.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.0 / (signal.dims()[0])
"""
if scale is None:
dim0 = signal.dims()[0]
scale = 1.0/float(dim0)
safe_call(backend.get().af_ifft_inplace(signal.arr, c_double_t(scale)))
def ifft2_inplace(signal, scale = None):
"""
Inverse In-place Fast Fourier Transform: 2D
Parameters
----------
signal: af.Array
A 2 dimensional signal or a batch of 2 dimensional signals.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.0 / (signal.dims()[0] * signal.dims()[1])
"""
dims = signal.dims()
if scale is None:
dim0 = dims[0]
dim1 = dims[1]
scale = 1.0/float(dim0 * dim1)
safe_call(backend.get().af_ifft2_inplace(signal.arr, c_double_t(scale)))
def ifft3_inplace(signal, scale = None):
"""
Inverse In-place Fast Fourier Transform: 3D
Parameters
----------
signal: af.Array
A 3 dimensional signal or a batch of 3 dimensional signals.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.0 / (signal.dims()[0] * signal.dims()[1] * signal.dims()[2]).
"""
dims = signal.dims()
if scale is None:
dim0 = dims[0]
dim1 = dims[1]
dim2 = dims[2]
scale = 1.0 / float(dim0 * dim1 * dim2)
safe_call(backend.get().af_ifft3_inplace(signal.arr, c_double_t(scale)))
def fft_r2c(signal, dim0 = None , scale = None):
"""
Real to Complex Fast Fourier Transform: 1D
Parameters
----------
signal: af.Array
A 1 dimensional signal or a batch of 1 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
Returns
-------
output: af.Array
A complex af.Array containing the non-redundant parts of the full FFT.
"""
if dim0 is None:
dim0 = 0
if scale is None:
scale = 1.0
output = Array()
safe_call(backend.get().af_fft_r2c(c_pointer(output.arr), signal.arr, c_double_t(scale), c_dim_t(dim0)))
return output
def fft2_r2c(signal, dim0 = None, dim1 = None , scale = None):
"""
Real to Complex Fast Fourier Transform: 2D
Parameters
----------
signal: af.Array
A 2 dimensional signal or a batch of 2 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
dim1: optional: int. default: None.
- Specifies the size of the output.
- If None, dim1 is calculated to be the second dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
Returns
-------
output: af.Array
A complex af.Array containing the non-redundant parts of the full FFT.
"""
if dim0 is None:
dim0 = 0
if dim1 is None:
dim1 = 0
if scale is None:
scale = 1.0
output = Array()
safe_call(backend.get().af_fft2_r2c(c_pointer(output.arr), signal.arr, c_double_t(scale),
c_dim_t(dim0), c_dim_t(dim1)))
return output
def fft3_r2c(signal, dim0 = None, dim1 = None , dim2 = None, scale = None):
"""
Real to Complex Fast Fourier Transform: 3D
Parameters
----------
signal: af.Array
A 3 dimensional signal or a batch of 3 dimensional signals.
dim0: optional: int. default: None.
- Specifies the size of the output.
- If None, dim0 is calculated to be the first dimension of `signal`.
dim1: optional: int. default: None.
- Specifies the size of the output.
- If None, dim1 is calculated to be the second dimension of `signal`.
dim2: optional: int. default: None.
- Specifies the size of the output.
- If None, dim2 is calculated to be the third dimension of `signal`.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1.
Returns
-------
output: af.Array
A complex af.Array containing the non-redundant parts of the full FFT.
"""
if dim0 is None:
dim0 = 0
if dim1 is None:
dim1 = 0
if dim2 is None:
dim2 = 0
if scale is None:
scale = 1.0
output = Array()
safe_call(backend.get().af_fft3_r2c(c_pointer(output.arr), signal.arr, c_double_t(scale),
c_dim_t(dim0), c_dim_t(dim1), c_dim_t(dim2)))
return output
def _get_c2r_dim(dim, is_odd):
return 2 *(dim - 1) + int(is_odd)
def fft_c2r(signal, is_odd = False, scale = None):
"""
Real to Complex Fast Fourier Transform: 1D
Parameters
----------
signal: af.Array
A 1 dimensional signal or a batch of 1 dimensional signals.
is_odd: optional: Boolean. default: False.
- Specifies if the first dimension of output should be even or odd.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1 / (signal.dims()[0]).
Returns
-------
output: af.Array
A real af.Array containing the full output of the fft.
"""
if scale is None:
dim0 = _get_c2r_dim(signal.dims()[0], is_odd)
scale = 1.0/float(dim0)
output = Array()
safe_call(backend.get().af_fft_c2r(c_pointer(output.arr), signal.arr, c_double_t(scale), is_odd))
return output
def fft2_c2r(signal, is_odd = False, scale = None):
"""
Real to Complex Fast Fourier Transform: 2D
Parameters
----------
signal: af.Array
A 2 dimensional signal or a batch of 2 dimensional signals.
is_odd: optional: Boolean. default: False.
- Specifies if the first dimension of output should be even or odd.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1 / (signal.dims()[0] * signal.dims()[1]).
Returns
-------
output: af.Array
A real af.Array containing the full output of the fft.
"""
dims = signal.dims()
if scale is None:
dim0 = _get_c2r_dim(dims[0], is_odd)
dim1 = dims[1]
scale = 1.0/float(dim0 * dim1)
output = Array()
safe_call(backend.get().af_fft2_c2r(c_pointer(output.arr), signal.arr, c_double_t(scale), is_odd))
return output
def fft3_c2r(signal, is_odd = False, scale = None):
"""
Real to Complex Fast Fourier Transform: 3D
Parameters
----------
signal: af.Array
A 3 dimensional signal or a batch of 3 dimensional signals.
is_odd: optional: Boolean. default: False.
- Specifies if the first dimension of output should be even or odd.
scale: optional: scalar. default: None.
- Specifies the scaling factor.
- If None, scale is set to 1 / (signal.dims()[0] * signal.dims()[1] * signal.dims()[2]).
Returns
-------
output: af.Array
A real af.Array containing the full output of the fft.
"""
dims = signal.dims()
if scale is None:
dim0 = _get_c2r_dim(dims[0], is_odd)
dim1 = dims[1]
dim2 = dims[2]
scale = 1.0/float(dim0 * dim1 * dim2)
output = Array()
safe_call(backend.get().af_fft3_c2r(c_pointer(output.arr), signal.arr, c_double_t(scale), is_odd))
return output
def dft(signal, odims=(None, None, None, None), scale = None):
"""
Non batched Fourier transform.
This function performs n-dimensional fourier transform depending on the input dimensions.
Parameters
----------
signal: af.Array
- A multi dimensional arrayfire array.
odims: optional: tuple of ints. default: (None, None, None, None).
- If None, calculated to be `signal.dims()`
scale: optional: scalar. default: None.
- Scale factor for the fourier transform.
- If none, calculated to be 1.0.
Returns
-------
output: af.Array
- A complex array that is the ouput of n-dimensional fourier transform.
"""
odims4 = dim4_to_tuple(odims, default=None)
dims = signal.dims()
ndims = len(dims)
if (ndims == 1):
return fft(signal, dims[0], scale)
elif (ndims == 2):
return fft2(signal, dims[0], dims[1], scale)
else:
return fft3(signal, dims[0], dims[1], dims[2], scale)
def idft(signal, scale = None, odims=(None, None, None, None)):
"""
Non batched Inverse Fourier transform.
This function performs n-dimensional inverse fourier transform depending on the input dimensions.
Parameters
----------
signal: af.Array
- A multi dimensional arrayfire array.
odims: optional: tuple of ints. default: (None, None, None, None).
- If None, calculated to be `signal.dims()`
scale: optional: scalar. default: None.
- Scale factor for the fourier transform.
- If none, calculated to be 1.0 / signal.elements()
Returns
-------
output: af.Array
- A complex array that is the ouput of n-dimensional inverse fourier transform.
Note
----
the output is always complex.
"""
odims4 = dim4_to_tuple(odims, default=None)
dims = signal.dims()
ndims = len(dims)
if (ndims == 1):
return ifft(signal, scale, dims[0])
elif (ndims == 2):
return ifft2(signal, scale, dims[0], dims[1])
else:
return ifft3(signal, scale, dims[0], dims[1], dims[2])
def convolve1(signal, kernel, conv_mode = CONV_MODE.DEFAULT, conv_domain = CONV_DOMAIN.AUTO):
"""
Convolution: 1D
Parameters
-----------
signal: af.Array
- A 1 dimensional signal or batch of 1 dimensional signals.
kernel: af.Array
- A 1 dimensional kernel or batch of 1 dimensional kernels.
conv_mode: optional: af.CONV_MODE. default: af.CONV_MODE.DEFAULT.
- Specifies if the output does full convolution (af.CONV_MODE.EXPAND) or
maintains the same size as input (af.CONV_MODE.DEFAULT).
conv_domain: optional: af.CONV_DOMAIN. default: af.CONV_DOMAIN.AUTO.
- Specifies the domain in which convolution is performed.
- af.CONV_DOMAIN.SPATIAL: Performs convolution in spatial domain.
- af.CONV_DOMAIN.FREQ: Performs convolution in frequency domain.
- af.CONV_DOMAIN.AUTO: Switches between spatial and frequency based on input size.
Returns
--------
output: af.Array
- Output of 1D convolution.
Note
-----
Supported batch combinations:
| Signal | Kernel | output |
|:---------:|:---------:|:---------:|
| [m 1 1 1] | [m 1 1 1] | [m 1 1 1] |
| [m n 1 1] | [m n 1 1] | [m n 1 1] |
| [m n p 1] | [m n 1 1] | [m n p 1] |
| [m n p 1] | [m n p 1] | [m n p 1] |
| [m n p 1] | [m n 1 q] | [m n p q] |
| [m n 1 p] | [m n q 1] | [m n q p] |
"""
output = Array()
safe_call(backend.get().af_convolve1(c_pointer(output.arr), signal.arr, kernel.arr,
conv_mode.value, conv_domain.value))
return output
def convolve2(signal, kernel, conv_mode = CONV_MODE.DEFAULT, conv_domain = CONV_DOMAIN.AUTO):
"""
Convolution: 2D
Parameters
-----------
signal: af.Array
- A 2 dimensional signal or batch of 2 dimensional signals.
kernel: af.Array
- A 2 dimensional kernel or batch of 2 dimensional kernels.
conv_mode: optional: af.CONV_MODE. default: af.CONV_MODE.DEFAULT.
- Specifies if the output does full convolution (af.CONV_MODE.EXPAND) or
maintains the same size as input (af.CONV_MODE.DEFAULT).
conv_domain: optional: af.CONV_DOMAIN. default: af.CONV_DOMAIN.AUTO.
- Specifies the domain in which convolution is performed.
- af.CONV_DOMAIN.SPATIAL: Performs convolution in spatial domain.
- af.CONV_DOMAIN.FREQ: Performs convolution in frequency domain.
- af.CONV_DOMAIN.AUTO: Switches between spatial and frequency based on input size.
Returns
--------
output: af.Array
- Output of 2D convolution.
Note
-----
Supported batch combinations:
| Signal | Kernel | output |
|:---------:|:---------:|:---------:|
| [m n 1 1] | [m n 1 1] | [m n 1 1] |
| [m n p 1] | [m n 1 1] | [m n p 1] |
| [m n p 1] | [m n p 1] | [m n p 1] |
| [m n p 1] | [m n 1 q] | [m n p q] |
| [m n 1 p] | [m n q 1] | [m n q p] |
"""
output = Array()
safe_call(backend.get().af_convolve2(c_pointer(output.arr), signal.arr, kernel.arr,
conv_mode.value, conv_domain.value))
return output
def convolve2_separable(col_kernel, row_kernel, signal, conv_mode = CONV_MODE.DEFAULT):
"""
Convolution: 2D separable convolution
Parameters
-----------
col_kernel: af.Array
- A column vector to be applied along each column of `signal`
row_kernel: af.Array
- A row vector to be applied along each row of `signal`
signal: af.Array
- A 2 dimensional signal or batch of 2 dimensional signals.
conv_mode: optional: af.CONV_MODE. default: af.CONV_MODE.DEFAULT.
- Specifies if the output does full convolution (af.CONV_MODE.EXPAND) or
maintains the same size as input (af.CONV_MODE.DEFAULT).
Returns
--------
output: af.Array
- Output of 2D sepearable convolution.
"""
output = Array()