Computes the inverse of `rfft`. This function computes the inverse of the one-dimensional *n*-point discrete Fourier Transform of real input computed by `rfft`. In other words, ``irfft(rfft(a), len(a)) == a`` to within numerical accuracy. (See Notes below for why ``len(a)`` is
(a, n=None, axis=-1, norm=None)
| 412 | |
| 413 | @array_function_dispatch(_fft_dispatcher) |
| 414 | def irfft(a, n=None, axis=-1, norm=None): |
| 415 | """ |
| 416 | Computes the inverse of `rfft`. |
| 417 | |
| 418 | This function computes the inverse of the one-dimensional *n*-point |
| 419 | discrete Fourier Transform of real input computed by `rfft`. |
| 420 | In other words, ``irfft(rfft(a), len(a)) == a`` to within numerical |
| 421 | accuracy. (See Notes below for why ``len(a)`` is necessary here.) |
| 422 | |
| 423 | The input is expected to be in the form returned by `rfft`, i.e. the |
| 424 | real zero-frequency term followed by the complex positive frequency terms |
| 425 | in order of increasing frequency. Since the discrete Fourier Transform of |
| 426 | real input is Hermitian-symmetric, the negative frequency terms are taken |
| 427 | to be the complex conjugates of the corresponding positive frequency terms. |
| 428 | |
| 429 | Parameters |
| 430 | ---------- |
| 431 | a : array_like |
| 432 | The input array. |
| 433 | n : int, optional |
| 434 | Length of the transformed axis of the output. |
| 435 | For `n` output points, ``n//2+1`` input points are necessary. If the |
| 436 | input is longer than this, it is cropped. If it is shorter than this, |
| 437 | it is padded with zeros. If `n` is not given, it is taken to be |
| 438 | ``2*(m-1)`` where ``m`` is the length of the input along the axis |
| 439 | specified by `axis`. |
| 440 | axis : int, optional |
| 441 | Axis over which to compute the inverse FFT. If not given, the last |
| 442 | axis is used. |
| 443 | norm : {"backward", "ortho", "forward"}, optional |
| 444 | .. versionadded:: 1.10.0 |
| 445 | |
| 446 | Normalization mode (see `numpy.fft`). Default is "backward". |
| 447 | Indicates which direction of the forward/backward pair of transforms |
| 448 | is scaled and with what normalization factor. |
| 449 | |
| 450 | .. versionadded:: 1.20.0 |
| 451 | |
| 452 | The "backward", "forward" values were added. |
| 453 | |
| 454 | Returns |
| 455 | ------- |
| 456 | out : ndarray |
| 457 | The truncated or zero-padded input, transformed along the axis |
| 458 | indicated by `axis`, or the last one if `axis` is not specified. |
| 459 | The length of the transformed axis is `n`, or, if `n` is not given, |
| 460 | ``2*(m-1)`` where ``m`` is the length of the transformed axis of the |
| 461 | input. To get an odd number of output points, `n` must be specified. |
| 462 | |
| 463 | Raises |
| 464 | ------ |
| 465 | IndexError |
| 466 | If `axis` is not a valid axis of `a`. |
| 467 | |
| 468 | See Also |
| 469 | -------- |
| 470 | numpy.fft : For definition of the DFT and conventions used. |
| 471 | rfft : The one-dimensional FFT of real input, of which `irfft` is inverse. |
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