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Oct 2, 2025
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ENH: delegate sinc function #453

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3 changes: 1 addition & 2 deletions src/array_api_extra/__init__.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
"""Extra array functions built on top of the array API standard."""

from ._delegation import expand_dims, isclose, nan_to_num, one_hot, pad
from ._delegation import expand_dims, isclose, nan_to_num, one_hot, pad, sinc
from ._lib._at import at
from ._lib._funcs import (
apply_where,
Expand All @@ -12,7 +12,6 @@
kron,
nunique,
setdiff1d,
sinc,
)
from ._lib._lazy import lazy_apply

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96 changes: 95 additions & 1 deletion src/array_api_extra/_delegation.py
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Original file line number Diff line number Diff line change
Expand Up @@ -18,7 +18,7 @@
from ._lib._utils._helpers import asarrays
from ._lib._utils._typing import Array, DType

__all__ = ["expand_dims", "isclose", "nan_to_num", "one_hot", "pad"]
__all__ = ["expand_dims", "isclose", "nan_to_num", "one_hot", "pad", "sinc"]


def expand_dims(
Expand Down Expand Up @@ -414,3 +414,97 @@ def pad(
return xp.nn.functional.pad(x, tuple(pad_width), value=constant_values) # type: ignore[arg-type] # pyright: ignore[reportArgumentType]

return _funcs.pad(x, pad_width, constant_values=constant_values, xp=xp)


def sinc(x: Array, /, *, xp: ModuleType | None = None) -> Array:
r"""
Return the normalized sinc function.

The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument
:math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not
only everywhere continuous but also infinitely differentiable.

.. note::

Note the normalization factor of ``pi`` used in the definition.
This is the most commonly used definition in signal processing.
Use ``sinc(x / xp.pi)`` to obtain the unnormalized sinc function
:math:`\sin(x)/x` that is more common in mathematics.

Parameters
----------
x : array
Array (possibly multi-dimensional) of values for which to calculate
``sinc(x)``. Must have a real floating point dtype.
xp : array_namespace, optional
The standard-compatible namespace for `x`. Default: infer.

Returns
-------
array
``sinc(x)`` calculated elementwise, which has the same shape as the input.

Notes
-----
The name sinc is short for "sine cardinal" or "sinus cardinalis".

The sinc function is used in various signal processing applications,
including in anti-aliasing, in the construction of a Lanczos resampling
filter, and in interpolation.

For bandlimited interpolation of discrete-time signals, the ideal
interpolation kernel is proportional to the sinc function.

References
----------
#. Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
Resource. https://mathworld.wolfram.com/SincFunction.html
#. Wikipedia, "Sinc function",
https://en.wikipedia.org/wiki/Sinc_function

Examples
--------
>>> import array_api_strict as xp
>>> import array_api_extra as xpx
>>> x = xp.linspace(-4, 4, 41)
>>> xpx.sinc(x, xp=xp)
Array([-3.89817183e-17, -4.92362781e-02,
-8.40918587e-02, -8.90384387e-02,
-5.84680802e-02, 3.89817183e-17,
6.68206631e-02, 1.16434881e-01,
1.26137788e-01, 8.50444803e-02,
-3.89817183e-17, -1.03943254e-01,
-1.89206682e-01, -2.16236208e-01,
-1.55914881e-01, 3.89817183e-17,
2.33872321e-01, 5.04551152e-01,
7.56826729e-01, 9.35489284e-01,
1.00000000e+00, 9.35489284e-01,
7.56826729e-01, 5.04551152e-01,
2.33872321e-01, 3.89817183e-17,
-1.55914881e-01, -2.16236208e-01,
-1.89206682e-01, -1.03943254e-01,
-3.89817183e-17, 8.50444803e-02,
1.26137788e-01, 1.16434881e-01,
6.68206631e-02, 3.89817183e-17,
-5.84680802e-02, -8.90384387e-02,
-8.40918587e-02, -4.92362781e-02,
-3.89817183e-17], dtype=array_api_strict.float64)
"""

if xp is None:
xp = array_namespace(x)

if not xp.isdtype(x.dtype, "real floating"):
err_msg = "`x` must have a real floating data type."
raise ValueError(err_msg)

if (
is_numpy_namespace(xp)
or is_cupy_namespace(xp)
or is_jax_namespace(xp)
or is_torch_namespace(xp)
or is_dask_namespace(xp)
):
return xp.sinc(x)

return _funcs.sinc(x, xp=xp)
82 changes: 3 additions & 79 deletions src/array_api_extra/_lib/_funcs.py
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Original file line number Diff line number Diff line change
Expand Up @@ -864,86 +864,10 @@ def setdiff1d(
return x1_[_helpers.in1d(x1_, x2_, assume_unique=True, invert=True, xp=xp)]


def sinc(x: Array, /, *, xp: ModuleType | None = None) -> Array:
r"""
Return the normalized sinc function.

The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument
:math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not
only everywhere continuous but also infinitely differentiable.

.. note::

Note the normalization factor of ``pi`` used in the definition.
This is the most commonly used definition in signal processing.
Use ``sinc(x / xp.pi)`` to obtain the unnormalized sinc function
:math:`\sin(x)/x` that is more common in mathematics.

Parameters
----------
x : array
Array (possibly multi-dimensional) of values for which to calculate
``sinc(x)``. Must have a real floating point dtype.
xp : array_namespace, optional
The standard-compatible namespace for `x`. Default: infer.

Returns
-------
array
``sinc(x)`` calculated elementwise, which has the same shape as the input.

Notes
-----
The name sinc is short for "sine cardinal" or "sinus cardinalis".

The sinc function is used in various signal processing applications,
including in anti-aliasing, in the construction of a Lanczos resampling
filter, and in interpolation.

For bandlimited interpolation of discrete-time signals, the ideal
interpolation kernel is proportional to the sinc function.

References
----------
#. Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
Resource. https://mathworld.wolfram.com/SincFunction.html
#. Wikipedia, "Sinc function",
https://en.wikipedia.org/wiki/Sinc_function

Examples
--------
>>> import array_api_strict as xp
>>> import array_api_extra as xpx
>>> x = xp.linspace(-4, 4, 41)
>>> xpx.sinc(x, xp=xp)
Array([-3.89817183e-17, -4.92362781e-02,
-8.40918587e-02, -8.90384387e-02,
-5.84680802e-02, 3.89817183e-17,
6.68206631e-02, 1.16434881e-01,
1.26137788e-01, 8.50444803e-02,
-3.89817183e-17, -1.03943254e-01,
-1.89206682e-01, -2.16236208e-01,
-1.55914881e-01, 3.89817183e-17,
2.33872321e-01, 5.04551152e-01,
7.56826729e-01, 9.35489284e-01,
1.00000000e+00, 9.35489284e-01,
7.56826729e-01, 5.04551152e-01,
2.33872321e-01, 3.89817183e-17,
-1.55914881e-01, -2.16236208e-01,
-1.89206682e-01, -1.03943254e-01,
-3.89817183e-17, 8.50444803e-02,
1.26137788e-01, 1.16434881e-01,
6.68206631e-02, 3.89817183e-17,
-5.84680802e-02, -8.90384387e-02,
-8.40918587e-02, -4.92362781e-02,
-3.89817183e-17], dtype=array_api_strict.float64)
"""
if xp is None:
xp = array_namespace(x)
def sinc(x: Array, /, *, xp: ModuleType) -> Array:
# numpydoc ignore=PR01,RT01
"""See docstring in `array_api_extra._delegation.py`."""

if not xp.isdtype(x.dtype, "real floating"):
err_msg = "`x` must have a real floating data type."
raise ValueError(err_msg)
# no scalars in `where` - array-api#807
y = xp.pi * xp.where(
xp.astype(x, xp.bool),
Expand Down