""" Discrete Fourier Transforms - helper.py """ from __future__ import division, absolute_import, print_function from numpy.compat import integer_types from numpy.core import ( asarray, concatenate, arange, take, integer, empty ) # Created by Pearu Peterson, September 2002 __all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq'] integer_types = integer_types + (integer,) def fftshift(x, axes=None): """ Shift the zero-frequency component to the center of the spectrum. This function swaps half-spaces for all axes listed (defaults to all). Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even. Parameters ---------- x : array_like Input array. axes : int or shape tuple, optional Axes over which to shift. Default is None, which shifts all axes. Returns ------- y : ndarray The shifted array. See Also -------- ifftshift : The inverse of `fftshift`. Examples -------- >>> freqs = np.fft.fftfreq(10, 0.1) >>> freqs array([ 0., 1., 2., 3., 4., -5., -4., -3., -2., -1.]) >>> np.fft.fftshift(freqs) array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.]) Shift the zero-frequency component only along the second axis: >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) >>> freqs array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) >>> np.fft.fftshift(freqs, axes=(1,)) array([[ 2., 0., 1.], [-4., 3., 4.], [-1., -3., -2.]]) """ tmp = asarray(x) ndim = len(tmp.shape) if axes is None: axes = list(range(ndim)) elif isinstance(axes, integer_types): axes = (axes,) y = tmp for k in axes: n = tmp.shape[k] p2 = (n+1)//2 mylist = concatenate((arange(p2, n), arange(p2))) y = take(y, mylist, k) return y def ifftshift(x, axes=None): """ The inverse of `fftshift`. Although identical for even-length `x`, the functions differ by one sample for odd-length `x`. Parameters ---------- x : array_like Input array. axes : int or shape tuple, optional Axes over which to calculate. Defaults to None, which shifts all axes. Returns ------- y : ndarray The shifted array. See Also -------- fftshift : Shift zero-frequency component to the center of the spectrum. Examples -------- >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) >>> freqs array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) >>> np.fft.ifftshift(np.fft.fftshift(freqs)) array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) """ tmp = asarray(x) ndim = len(tmp.shape) if axes is None: axes = list(range(ndim)) elif isinstance(axes, integer_types): axes = (axes,) y = tmp for k in axes: n = tmp.shape[k] p2 = n-(n+1)//2 mylist = concatenate((arange(p2, n), arange(p2))) y = take(y, mylist, k) return y def fftfreq(n, d=1.0): """ Return the Discrete Fourier Transform sample frequencies. The returned float array `f` contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second. Given a window length `n` and a sample spacing `d`:: f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd Parameters ---------- n : int Window length. d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1. Returns ------- f : ndarray Array of length `n` containing the sample frequencies. Examples -------- >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float) >>> fourier = np.fft.fft(signal) >>> n = signal.size >>> timestep = 0.1 >>> freq = np.fft.fftfreq(n, d=timestep) >>> freq array([ 0. , 1.25, 2.5 , 3.75, -5. , -3.75, -2.5 , -1.25]) """ if not isinstance(n, integer_types): raise ValueError("n should be an integer") val = 1.0 / (n * d) results = empty(n, int) N = (n-1)//2 + 1 p1 = arange(0, N, dtype=int) results[:N] = p1 p2 = arange(-(n//2), 0, dtype=int) results[N:] = p2 return results * val #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d) def rfftfreq(n, d=1.0): """ Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). The returned float array `f` contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second. Given a window length `n` and a sample spacing `d`:: f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`) the Nyquist frequency component is considered to be positive. Parameters ---------- n : int Window length. d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1. Returns ------- f : ndarray Array of length ``n//2 + 1`` containing the sample frequencies. Examples -------- >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float) >>> fourier = np.fft.rfft(signal) >>> n = signal.size >>> sample_rate = 100 >>> freq = np.fft.fftfreq(n, d=1./sample_rate) >>> freq array([ 0., 10., 20., 30., 40., -50., -40., -30., -20., -10.]) >>> freq = np.fft.rfftfreq(n, d=1./sample_rate) >>> freq array([ 0., 10., 20., 30., 40., 50.]) """ if not isinstance(n, integer_types): raise ValueError("n should be an integer") val = 1.0/(n*d) N = n//2 + 1 results = arange(0, N, dtype=int) return results * val