array_api_extra.sinc¶
- array_api_extra.sinc(x, /, *, xp)¶
Return the normalized sinc function.
The sinc function is equal to \(\sin(\pi x)/(\pi x)\) for any argument \(x\ne 0\).
sinc(0)
takes the limit value 1, makingsinc
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. Usesinc(x / xp.pi)
to obtain the unnormalized sinc function \(\sin(x)/x\) 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) – The standard-compatible namespace for x.
- Returns:
res –
sinc(x)
calculated elementwise, which has the same shape as the input.- Return type:
array
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
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)