diff options
Diffstat (limited to 'numpy/dft/fftpack.py')
| -rw-r--r-- | numpy/dft/fftpack.py | 148 |
1 files changed, 64 insertions, 84 deletions
diff --git a/numpy/dft/fftpack.py b/numpy/dft/fftpack.py index 6310ca071..70e76085c 100644 --- a/numpy/dft/fftpack.py +++ b/numpy/dft/fftpack.py @@ -5,26 +5,22 @@ The underlying code for these functions is an f2c translated and modified version of the FFTPACK routines. fft(a, n=None, axis=-1) -inverse_fft(a, n=None, axis=-1) -real_fft(a, n=None, axis=-1) -inverse_real_fft(a, n=None, axis=-1) -hermite_fft(a, n=None, axis=-1) -inverse_hermite_fft(a, n=None, axis=-1) -fftnd(a, s=None, axes=None) -inverse_fftnd(a, s=None, axes=None) -real_fftnd(a, s=None, axes=None) -inverse_real_fftnd(a, s=None, axes=None) -fft2d(a, s=None, axes=(-2,-1)) -inverse_fft2d(a, s=None, axes=(-2, -1)) -real_fft2d(a, s=None, axes=(-2,-1)) -inverse_real_fft2d(a, s=None, axes=(-2, -1)) +ifft(a, n=None, axis=-1) +refft(a, n=None, axis=-1) +irefft(a, n=None, axis=-1) +hfft(a, n=None, axis=-1) +ihfft(a, n=None, axis=-1) +fftn(a, s=None, axes=None) +ifftn(a, s=None, axes=None) +refftn(a, s=None, axes=None) +irefftn(a, s=None, axes=None) +fft2(a, s=None, axes=(-2,-1)) +ifft2(a, s=None, axes=(-2, -1)) +refft2(a, s=None, axes=(-2,-1)) +irefft2(a, s=None, axes=(-2, -1)) """ -__all__ = ['fft','inverse_fft', 'ifft', 'real_fft', 'refft', - 'inverse_real_fft', 'irefft', 'hfft', 'ihfft', 'refftn', - 'irefftn', 'refft2', 'irefft2', 'fft2', 'ifft2', - 'hermite_fft','inverse_hermite_fft','fftnd','inverse_fftnd', - 'fft2d', 'inverse_fft2d', 'real_fftnd', 'real_fft2d', - 'inverse_real_fftnd', 'inverse_real_fft2d','fftn','ifftn'] +__all__ = ['fft','ifft', 'refft', 'irefft', 'hfft', 'ihfft', 'refftn', + 'irefftn', 'refft2', 'irefft2', 'fft2', 'ifft2', 'fftn', 'ifftn'] from numpy.core import asarray, zeros, swapaxes, shape, Complex, conjugate, \ Float, take @@ -90,8 +86,8 @@ def fft(a, n=None, axis=-1): return _raw_fft(a, n, axis, fftpack.cffti, fftpack.cfftf, _fft_cache) -def inverse_fft(a, n=None, axis=-1): - """inverse_fft(a, n=None, axis=-1) +def ifft(a, n=None, axis=-1): + """ifft(a, n=None, axis=-1) Will return the n point inverse discrete Fourier transform of a. n defaults to the length of a. If n is larger than a, then a will be @@ -101,7 +97,7 @@ def inverse_fft(a, n=None, axis=-1): The input array is expected to be packed the same way as the output of fft, as discussed in it's documentation. - This is the inverse of fft: inverse_fft(fft(a)) == a within numerical + This is the inverse of fft: ifft(fft(a)) == a within numerical accuracy. This is most efficient for n a power of two. This also stores a cache of @@ -115,8 +111,8 @@ def inverse_fft(a, n=None, axis=-1): return _raw_fft(a, n, axis, fftpack.cffti, fftpack.cfftb, _fft_cache) / n -def real_fft(a, n=None, axis=-1): - """real_fft(a, n=None, axis=-1) +def refft(a, n=None, axis=-1): + """refft(a, n=None, axis=-1) Will return the n point discrete Fourier transform of the real valued array a. n defaults to the length of a. n is the length of the input, not @@ -136,8 +132,8 @@ def real_fft(a, n=None, axis=-1): return _raw_fft(a, n, axis, fftpack.rffti, fftpack.rfftf, _real_fft_cache) -def inverse_real_fft(a, n=None, axis=-1): - """inverse_real_fft(a, n=None, axis=-1) +def irefft(a, n=None, axis=-1): + """irefft(a, n=None, axis=-1) Will return the real valued n point inverse discrete Fourier transform of a, where a contains the nonnegative frequency terms of a Hermite-symmetric @@ -148,10 +144,10 @@ def inverse_real_fft(a, n=None, axis=-1): If you specify an n such that a must be zero-padded or truncated, the extra/removed values will be added/removed at high frequencies. One can thus resample a series to m points via Fourier interpolation by: a_resamp - = inverse_real_fft(real_fft(a), m). + = irefft(refft(a), m). - This is the inverse of real_fft: - inverse_real_fft(real_fft(a), len(a)) == a + This is the inverse of refft: + irefft(refft(a), len(a)) == a within numerical accuracy.""" a = asarray(a).astype(complex) @@ -161,40 +157,40 @@ def inverse_real_fft(a, n=None, axis=-1): _real_fft_cache) / n -def hermite_fft(a, n=None, axis=-1): - """hermite_fft(a, n=None, axis=-1) - inverse_hermite_fft(a, n=None, axis=-1) +def hfft(a, n=None, axis=-1): + """hfft(a, n=None, axis=-1) + ihfft(a, n=None, axis=-1) - These are a pair analogous to real_fft/inverse_real_fft, but for the + These are a pair analogous to refft/irefft, but for the opposite case: here the signal is real in the frequency domain and has Hermite symmetry in the time domain. So here it's hermite_fft for which you must supply the length of the result if it is to be odd. - inverse_hermite_fft(hermite_fft(a), len(a)) == a + ihfft(hfft(a), len(a)) == a within numerical accuracy.""" a = asarray(a).astype(Complex) if n == None: n = (shape(a)[axis] - 1) * 2 - return inverse_real_fft(conjugate(a), n, axis) * n + return irefft(conjugate(a), n, axis) * n -def inverse_hermite_fft(a, n=None, axis=-1): - """hermite_fft(a, n=None, axis=-1) - inverse_hermite_fft(a, n=None, axis=-1) +def ihfft(a, n=None, axis=-1): + """hfft(a, n=None, axis=-1) + ihfft(a, n=None, axis=-1) - These are a pair analogous to real_fft/inverse_real_fft, but for the + These are a pair analogous to refft/irefft, but for the opposite case: here the signal is real in the frequency domain and has - Hermite symmetry in the time domain. So here it's hermite_fft for which + Hermite symmetry in the time domain. So here it's hfft for which you must supply the length of the result if it is to be odd. - inverse_hermite_fft(hermite_fft(a), len(a)) == a + ihfft(hfft(a), len(a)) == a within numerical accuracy.""" a = asarray(a).astype(Float) if n == None: n = shape(a)[axis] - return conjugate(real_fft(a, n, axis))/n + return conjugate(refft(a, n, axis))/n def _cook_nd_args(a, s=None, axes=None, invreal=0): @@ -226,8 +222,8 @@ def _raw_fftnd(a, s=None, axes=None, function=fft): return a -def fftnd(a, s=None, axes=None): - """fftnd(a, s=None, axes=None) +def fftn(a, s=None, axes=None): + """fftn(a, s=None, axes=None) The n-dimensional fft of a. s is a sequence giving the shape of the input an result along the transformed axes, as n for fft. Results are packed @@ -243,16 +239,16 @@ def fftnd(a, s=None, axes=None): return _raw_fftnd(a,s,axes,fft) -def inverse_fftnd(a, s=None, axes=None): - """inverse_fftnd(a, s=None, axes=None) +def ifftn(a, s=None, axes=None): + """ifftn(a, s=None, axes=None) - The inverse of fftnd.""" + The inverse of fftn.""" - return _raw_fftnd(a, s, axes, inverse_fft) + return _raw_fftnd(a, s, axes, ifft) -def fft2d(a, s=None, axes=(-2,-1)): - """fft2d(a, s=None, axes=(-2,-1)) +def fft2(a, s=None, axes=(-2,-1)): + """fft2(a, s=None, axes=(-2,-1)) The 2d fft of a. This is really just fftnd with different default behavior.""" @@ -260,17 +256,17 @@ def fft2d(a, s=None, axes=(-2,-1)): return _raw_fftnd(a,s,axes,fft) -def inverse_fft2d(a, s=None, axes=(-2,-1)): - """inverse_fft2d(a, s=None, axes=(-2, -1)) +def ifft2(a, s=None, axes=(-2,-1)): + """ifft2(a, s=None, axes=(-2, -1)) The inverse of fft2d. This is really just inverse_fftnd with different default behavior.""" - return _raw_fftnd(a, s, axes, inverse_fft) + return _raw_fftnd(a, s, axes, ifft) -def real_fftnd(a, s=None, axes=None): - """real_fftnd(a, s=None, axes=None) +def refftn(a, s=None, axes=None): + """refftn(a, s=None, axes=None) The n-dimensional discrete Fourier transform of a real array a. A real transform as real_fft is performed along the axis specified by the last @@ -279,24 +275,24 @@ def real_fftnd(a, s=None, axes=None): a = asarray(a).astype(Float) s, axes = _cook_nd_args(a, s, axes) - a = real_fft(a, s[-1], axes[-1]) + a = refft(a, s[-1], axes[-1]) for ii in range(len(axes)-1): a = fft(a, s[ii], axes[ii]) return a -def real_fft2d(a, s=None, axes=(-2,-1)): - """real_fft2d(a, s=None, axes=(-2,-1)) +def refft2(a, s=None, axes=(-2,-1)): + """refft2(a, s=None, axes=(-2,-1)) - The 2d fft of the real valued array a. This is really just real_fftnd with + The 2d fft of the real valued array a. This is really just refftn with different default behavior.""" return real_fftnd(a, s, axes) -def inverse_real_fftnd(a, s=None, axes=None): - """inverse_real_fftnd(a, s=None, axes=None) +def irefftn(a, s=None, axes=None): + """irefftn(a, s=None, axes=None) - The inverse of real_fftnd. The transform implemented in inverse_fft is + The inverse of refftn. The transform implemented in inverse_fft is applied along all axes but the last, then the transform implemented in inverse_real_fft is performed along the last axis. As with inverse_real_fft, the length of the result along that axis must be @@ -305,31 +301,15 @@ def inverse_real_fftnd(a, s=None, axes=None): a = asarray(a).astype(Complex) s, axes = _cook_nd_args(a, s, axes, invreal=1) for ii in range(len(axes)-1): - a = inverse_fft(a, s[ii], axes[ii]) - a = inverse_real_fft(a, s[-1], axes[-1]) + a = ifft(a, s[ii], axes[ii]) + a = irefft(a, s[-1], axes[-1]) return a +def irefft2(a, s=None, axes=(-2,-1)): + """irefft2(a, s=None, axes=(-2, -1)) -def inverse_real_fft2d(a, s=None, axes=(-2,-1)): - """inverse_real_fft2d(a, s=None, axes=(-2, -1)) - - The inverse of real_fft2d. This is really just inverse_real_fftnd with + The inverse of refft2. This is really just irefftn with different default behavior.""" - return inverse_real_fftnd(a, s, axes) - -ifft = inverse_fft -refft = real_fft -irefft = inverse_real_fft -hfft = hermite_fft -ihfft = inverse_hermite_fft - -fftn = fftnd -ifftn = inverse_fftnd -refftn = real_fftnd -irefftn = inverse_real_fftnd + return irefftn(a, s, axes) -fft2 = fft2d -ifft2 = inverse_fft2d -refft2 = real_fft2d -irefft2 = inverse_real_fft2d |