dpnp.sinc

dpnp.sinc = <DPNPUnaryFunc 'sinc'>

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, making sinc not only everywhere continuous but also infinitely differentiable.

For full documentation refer to numpy.sinc.

Parameters:

x{dpnp.ndarray, usm_ndarray}

Input array, expected to have a floating-point data type.

out{None, dpnp.ndarray, usm_ndarray, tuple of ndarray}, optional

Output array to populate. Array must have the correct shape and the expected data type. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

Default: None.

order{None, "C", "F", "A", "K"}, optional

Memory layout of the newly output array, if parameter out is None.

Default: "K".

Returns:

outdpnp.ndarray

An array containing the element-wise result of the sinc(x) function. The data type of the returned array is determined by the Type Promotion Rules.

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.

Examples

>>> import dpnp as np
>>> x = np.linspace(-4, 4, 41, dtype=np.float64)
>>> np.sinc(x) # result may vary
    array([ 0.        , -0.04923628, -0.08409186, -0.08903844, -0.05846808,
            0.        ,  0.06682066,  0.11643488,  0.12613779,  0.08504448,
            0.        , -0.10394325, -0.18920668, -0.21623621, -0.15591488,
            0.        ,  0.23387232,  0.50455115,  0.75682673,  0.93548928,
            1.        ,  0.93548928,  0.75682673,  0.50455115,  0.23387232,
            0.        , -0.15591488, -0.21623621, -0.18920668, -0.10394325,
            0.        ,  0.08504448,  0.12613779,  0.11643488,  0.06682066,
            0.        , -0.05846808, -0.08903844, -0.08409186, -0.04923628,
            0.        ])