Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum. Parameters ---------- a : array_like The input array. n : int, optional Length of the transformed axis of the output. For `n` output points, ``n//2 + 1`` input points are
(a, n=None, axis=-1, norm=None)
| 516 | |
| 517 | @array_function_dispatch(_fft_dispatcher) |
| 518 | def hfft(a, n=None, axis=-1, norm=None): |
| 519 | """ |
| 520 | Compute the FFT of a signal that has Hermitian symmetry, i.e., a real |
| 521 | spectrum. |
| 522 | |
| 523 | Parameters |
| 524 | ---------- |
| 525 | a : array_like |
| 526 | The input array. |
| 527 | n : int, optional |
| 528 | Length of the transformed axis of the output. For `n` output |
| 529 | points, ``n//2 + 1`` input points are necessary. If the input is |
| 530 | longer than this, it is cropped. If it is shorter than this, it is |
| 531 | padded with zeros. If `n` is not given, it is taken to be ``2*(m-1)`` |
| 532 | where ``m`` is the length of the input along the axis specified by |
| 533 | `axis`. |
| 534 | axis : int, optional |
| 535 | Axis over which to compute the FFT. If not given, the last |
| 536 | axis is used. |
| 537 | norm : {"backward", "ortho", "forward"}, optional |
| 538 | .. versionadded:: 1.10.0 |
| 539 | |
| 540 | Normalization mode (see `numpy.fft`). Default is "backward". |
| 541 | Indicates which direction of the forward/backward pair of transforms |
| 542 | is scaled and with what normalization factor. |
| 543 | |
| 544 | .. versionadded:: 1.20.0 |
| 545 | |
| 546 | The "backward", "forward" values were added. |
| 547 | |
| 548 | Returns |
| 549 | ------- |
| 550 | out : ndarray |
| 551 | The truncated or zero-padded input, transformed along the axis |
| 552 | indicated by `axis`, or the last one if `axis` is not specified. |
| 553 | The length of the transformed axis is `n`, or, if `n` is not given, |
| 554 | ``2*m - 2`` where ``m`` is the length of the transformed axis of |
| 555 | the input. To get an odd number of output points, `n` must be |
| 556 | specified, for instance as ``2*m - 1`` in the typical case, |
| 557 | |
| 558 | Raises |
| 559 | ------ |
| 560 | IndexError |
| 561 | If `axis` is not a valid axis of `a`. |
| 562 | |
| 563 | See also |
| 564 | -------- |
| 565 | rfft : Compute the one-dimensional FFT for real input. |
| 566 | ihfft : The inverse of `hfft`. |
| 567 | |
| 568 | Notes |
| 569 | ----- |
| 570 | `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the |
| 571 | opposite case: here the signal has Hermitian symmetry in the time |
| 572 | domain and is real in the frequency domain. So here it's `hfft` for |
| 573 | which you must supply the length of the result if it is to be odd. |
| 574 | |
| 575 | * even: ``ihfft(hfft(a, 2*len(a) - 2)) == a``, within roundoff error, |
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