Label an FFT spectrum
Convert FFT array positions into physical frequency values for plotting or peak detection.
SciPy · Function
fft.fftfreq
Returns the discrete Fourier transform’s sample-frequency bins for a window of length n. Frequencies are scaled by the sample spacing, start at zero, and include negative-frequency bins.
How it works
Given a window length and sample spacing, fftfreq returns the frequency-bin centers associated with a discrete Fourier transform. Frequencies are expressed in cycles per unit of spacing, with zero first; negative-frequency bins follow the positive bins according to whether the length is even or odd.
Syntax
scipy.fft.fftfreq(n, d=1.0, *, xp=None, device=None)Parameters
| Name | Type | Description |
|---|---|---|
n | int | Window length. |
d | scalar, optional | Sample spacing (inverse of the sampling rate). Defaults to 1. |
xp | array_namespace, optional | The namespace for the return array. Default is None, where NumPy is used. |
device | device, optional | The device for the return array. Only valid when xp.fft.fftfreq implements the device parameter. |
Returns
f ndarray: Array of length n containing the sample frequencies.
Key points
- Use fftfreq to construct the frequency coordinates corresponding to DFT output bins.
- The result is a floating-point array whose entries represent bin centers rather than FFT coefficients.
- Frequency units follow the reciprocal of the unit used for d; seconds produce cycles per second.
- The first returned frequency is always the zero-frequency bin.
- d describes the interval between samples and therefore sets the frequency scale.
- xp lets callers choose the array namespace used to create the returned frequency array.
Common mistakes
- The device argument cannot be used unless the selected array namespace supports a device parameter for fftfreq.
Example: Get FFT sample frequencies
import numpy as np
from scipy.fft import fft, fftfreq
signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
frequencies = fftfreq(signal.size, d=0.1)
spectrum = fft(signal)
print(frequencies)
print(spectrum)Build the frequency-bin centers for an FFT sampled every 0.1 time units, then pair them with the transform output.
When to use it
Set frequency units
Translate a known sampling interval into cycles per unit of time or distance.
Work with alternate array backends
Create frequency coordinates using a compatible array namespace.
Interview questions
QWhat does scipy.fft.fftfreq return?
fftfreq returns an array of length n containing the FFT sample frequencies. The values are measured in cycles per unit of the sample spacing, and the first value is zero.
Follow-up: How does d affect the values? It scales the frequency grid by the inverse of the sample spacing, so increasing d decreases every frequency magnitude.
QHow are the frequency bins arranged for even and odd lengths?
For even n, the bins are formed from 0 through n/2−1, followed by −n/2 through −1, and all are divided by d·n. For odd n, the positive portion ends at (n−1)/2 and the negative portion begins at −(n−1)/2.
Follow-up: Which bin is the most negative for even n? It is −n/2 divided by d·n, giving the Nyquist-frequency bin at −1/(2d).
QWhat are the important parameters?
The n argument is the window length, while d is the sample spacing and defaults to 1. The optional xp argument selects the array namespace for the returned array; when omitted, NumPy is used.
Follow-up: What can device control? It specifies the return-array device, but only when the selected namespace's fftfreq implementation supports that parameter.
Related
scipy.fft.fftscipy.fft.rfftscipy.fft.rfftfreqscipy.fft.fftshift