diff options
Diffstat (limited to 'numpy/fft/fftpack.py')
| -rw-r--r-- | numpy/fft/fftpack.py | 61 |
1 files changed, 33 insertions, 28 deletions
diff --git a/numpy/fft/fftpack.py b/numpy/fft/fftpack.py index 8dc3eccbc..7486ff51e 100644 --- a/numpy/fft/fftpack.py +++ b/numpy/fft/fftpack.py @@ -467,34 +467,36 @@ def irfft(a, n=None, axis=-1, norm=None): def hfft(a, n=None, axis=-1, norm=None): """ - Compute the FFT of a signal which has Hermitian symmetry (real spectrum). + 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 necessary. If the - input is longer than this, it is cropped. If it is shorter than this, - it is padded with zeros. If `n` is not given, it is determined from - the length of the input along the axis specified by `axis`. + Length of the transformed axis of the output. For `n` output + points, ``n//2 + 1`` input points are necessary. If the input is + longer than this, it is cropped. If it is shorter than this, it is + padded with zeros. If `n` is not given, it is determined from the + length of the input along the axis specified by `axis`. axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used. norm : {None, "ortho"}, optional - .. versionadded:: 1.10.0 - Normalization mode (see `numpy.fft`). Default is None. + .. versionadded:: 1.10.0 + Returns ------- out : ndarray The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. The length of the transformed axis is `n`, or, if `n` is not given, - ``2*(m-1)`` where ``m`` is the length of the transformed axis of the - input. To get an odd number of output points, `n` must be specified. + ``2*m - 2`` where ``m`` is the length of the transformed axis of + the input. To get an odd number of output points, `n` must be + specified, for instance as ``2*m - 1`` in the typical case, Raises ------ @@ -509,10 +511,12 @@ def hfft(a, n=None, axis=-1, norm=None): Notes ----- `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the - opposite case: here the signal has Hermitian symmetry in the time domain - and is real in the frequency domain. So here it's `hfft` for which - you must supply the length of the result if it is to be odd: - ``ihfft(hfft(a), len(a)) == a``, within numerical accuracy. + opposite case: here the signal has Hermitian symmetry in the time + domain and is real in the frequency domain. So here it's `hfft` for + which you must supply the length of the result if it is to be odd. + + * even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error, + * odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error. Examples -------- @@ -545,33 +549,32 @@ def hfft(a, n=None, axis=-1, norm=None): def ihfft(a, n=None, axis=-1, norm=None): """ - Compute the inverse FFT of a signal which has Hermitian symmetry. + Compute the inverse FFT of a signal that has Hermitian symmetry. Parameters ---------- a : array_like Input array. n : int, optional - Length of the inverse FFT. - Number of points along transformation axis in the input to use. - If `n` is smaller than the length of the input, the input is cropped. - If it is larger, the input is padded with zeros. If `n` is not given, - the length of the input along the axis specified by `axis` is used. + Length of the inverse FFT, the number of points along + transformation axis in the input to use. If `n` is smaller than + the length of the input, the input is cropped. If it is larger, + the input is padded with zeros. If `n` is not given, the length of + the input along the axis specified by `axis` is used. axis : int, optional Axis over which to compute the inverse FFT. If not given, the last axis is used. norm : {None, "ortho"}, optional - .. versionadded:: 1.10.0 - Normalization mode (see `numpy.fft`). Default is None. + .. versionadded:: 1.10.0 + Returns ------- out : complex ndarray The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. - If `n` is even, the length of the transformed axis is ``(n/2)+1``. - If `n` is odd, the length is ``(n+1)/2``. + The length of the transformed axis is ``n//2 + 1``. See also -------- @@ -580,10 +583,12 @@ def ihfft(a, n=None, axis=-1, norm=None): Notes ----- `hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the - opposite case: here the signal has Hermitian symmetry in the time domain - and is real in the frequency domain. So here it's `hfft` for which - you must supply the length of the result if it is to be odd: - ``ihfft(hfft(a), len(a)) == a``, within numerical accuracy. + opposite case: here the signal has Hermitian symmetry in the time + domain and is real in the frequency domain. So here it's `hfft` for + which you must supply the length of the result if it is to be odd: + + * even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error, + * odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error. Examples -------- |