Python的绘图频率为fft.rfft

Question

这是我在stackoverflow上的第一个问题,我希望我不会犯大错.我正在分析一组采样率为1 Hz的时间序列.我需要绘制他们的傅立叶变换以研究他们的光谱.

这是我的一段代码:

from obspy.core import read
import numpy as np 
import matplotlib.pyplot as plt

st = read('../SC_noise/*HEC_109C*_s', format='SAC')
stp = st.copy()
stp.detrend('linear')
stp.taper('cosine')

for tr in stp:
  dataonly = tr.data
  spec = np.fft.rfft(dataonly)
  plt.plot(abs(spec))
  plt.show()

这很好用:情节与我使用SAC相同.但是xaxis没有显示频率.我徘徊了一下,发现了不同的想法:没有一个是有效的.例如,在fft(这里我使用rfft)的情况下,这应该做的工作

samp_rate=1
freq = np.fft.fftfreq(len(spec), d=1./samp_rate)

但如果我使用它会给我负频率.

有人有想法吗？非常感谢您提前获得所有帮助!

皮耶罗

Answer 1

如果您的 NumPy 版本足够新（1.8 或更高版本），请使用numpy.fft.rfftfreq。否则，这里是定义：

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,int) or isinstance(n, integer)):
        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