Return the Kaiser window. The Kaiser window is a taper formed by using a Bessel function. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. beta : float Shape parameter for window.
(M, beta)
| 3491 | |
| 3492 | @set_module('numpy') |
| 3493 | def kaiser(M, beta): |
| 3494 | """ |
| 3495 | Return the Kaiser window. |
| 3496 | |
| 3497 | The Kaiser window is a taper formed by using a Bessel function. |
| 3498 | |
| 3499 | Parameters |
| 3500 | ---------- |
| 3501 | M : int |
| 3502 | Number of points in the output window. If zero or less, an |
| 3503 | empty array is returned. |
| 3504 | beta : float |
| 3505 | Shape parameter for window. |
| 3506 | |
| 3507 | Returns |
| 3508 | ------- |
| 3509 | out : array |
| 3510 | The window, with the maximum value normalized to one (the value |
| 3511 | one appears only if the number of samples is odd). |
| 3512 | |
| 3513 | See Also |
| 3514 | -------- |
| 3515 | bartlett, blackman, hamming, hanning |
| 3516 | |
| 3517 | Notes |
| 3518 | ----- |
| 3519 | The Kaiser window is defined as |
| 3520 | |
| 3521 | .. math:: w(n) = I_0\\left( \\beta \\sqrt{1-\\frac{4n^2}{(M-1)^2}} |
| 3522 | \\right)/I_0(\\beta) |
| 3523 | |
| 3524 | with |
| 3525 | |
| 3526 | .. math:: \\quad -\\frac{M-1}{2} \\leq n \\leq \\frac{M-1}{2}, |
| 3527 | |
| 3528 | where :math:`I_0` is the modified zeroth-order Bessel function. |
| 3529 | |
| 3530 | The Kaiser was named for Jim Kaiser, who discovered a simple |
| 3531 | approximation to the DPSS window based on Bessel functions. The Kaiser |
| 3532 | window is a very good approximation to the Digital Prolate Spheroidal |
| 3533 | Sequence, or Slepian window, which is the transform which maximizes the |
| 3534 | energy in the main lobe of the window relative to total energy. |
| 3535 | |
| 3536 | The Kaiser can approximate many other windows by varying the beta |
| 3537 | parameter. |
| 3538 | |
| 3539 | ==== ======================= |
| 3540 | beta Window shape |
| 3541 | ==== ======================= |
| 3542 | 0 Rectangular |
| 3543 | 5 Similar to a Hamming |
| 3544 | 6 Similar to a Hanning |
| 3545 | 8.6 Similar to a Blackman |
| 3546 | ==== ======================= |
| 3547 | |
| 3548 | A beta value of 14 is probably a good starting point. Note that as beta |
| 3549 | gets large, the window narrows, and so the number of samples needs to be |
| 3550 | large enough to sample the increasingly narrow spike, otherwise NaNs will |