Frequency-spectrum analysis
Analyze real sensor, audio, or sampled measurement data in the frequency domain.
SciPy · Function
fft.rfft
Computes the one-dimensional discrete Fourier transform of real-valued input using an efficient FFT algorithm. It returns the nonredundant complex spectrum along the selected axis.
How it works
rfft computes the one-dimensional, n-point discrete Fourier transform of real-valued input using an efficient FFT algorithm. It transforms the selected axis, optionally truncating or zero-padding it to n, and returns only the nonredundant frequency components.
Syntax
scipy.fft.rfft(x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None, *, plan=None)Parameters
| Name | Type | Description |
|---|---|---|
x | array_like | Input array. |
n | int, optional | Number of points along the transformation axis to use. If omitted, the axis length is used; smaller values crop and larger values zero-pad. |
axis | int, optional | Axis over which to compute the FFT. Defaults to the last axis. |
norm | {"backward", "ortho", "forward"}, optional | Normalization mode: "backward", "ortho", or "forward". Defaults to "backward". |
overwrite_x | bool, optional | Whether to allow overwriting the input array when possible. |
workers | int, optional | Maximum number of workers to use for parallel computation. |
plan | object, optional | Reserved for a future FFT plan argument; currently not used. |
Returns
complex ndarray: the transformed, truncated or zero-padded input along the selected axis; for even n its transformed-axis length is n/2 + 1, and for odd n it is (n + 1)/2.
Key points
- Use rfft to transform a real-valued one-dimensional signal into its frequency-domain representation.
- The implementation uses the Fast Fourier Transform for efficient computation.
- n determines how many samples along the transformation axis participate in the calculation.
- axis selects the dimension to transform, allowing multidimensional arrays to be processed along a chosen axis.
- When axis is omitted, the final array dimension is transformed.
- norm chooses the transform's normalization mode from backward, ortho, or forward.
- The result is a complex array representing the transformed input after any length adjustment.
Common mistakes
- Choosing n larger than the input length zero-pads the transformed axis; choosing a smaller n truncates it.
- The output length depends on n: it is n/2 + 1 for even n and (n + 1)/2 for odd n.
Example: Compute a real-input FFT
import numpy as np
from scipy.fft import rfft
samples = np.array([0.0, 1.0, 0.0, -1.0])
spectrum = rfft(samples)
print(spectrum)
print(spectrum.shape) # (3,)Transforms a real four-sample signal and prints its one-sided complex spectrum.
When to use it
Axis-specific transforms
Transform multidimensional real arrays along a selected dimension.
Length normalization
Control transform length for consistent FFT sizes or zero-padding.
Interview questions
QWhat does scipy.fft.rfft compute?
rfft computes the one-dimensional discrete Fourier transform for real-valued input with an FFT algorithm. It avoids returning the redundant negative-frequency half that is implied by a real input.
Follow-up: How does the output size change with n? For even n it is n/2 + 1; for odd n it is (n + 1)/2.
QWhat do n and axis control?
n specifies how many points along the chosen transformation axis are used. A smaller n crops the input, while a larger n pads it with zeros; if omitted, the axis length is used.
Follow-up: Which axis is transformed by default? The last axis, because axis defaults to -1.
QHow is normalization selected, and what is returned?
norm controls normalization and accepts backward, ortho, or forward. The default is backward, so callers should choose explicitly when interoperability requires a particular scaling convention.
Follow-up: What does the function return? A complex ndarray containing the transformed, possibly cropped or zero-padded input along the selected axis.
Related
scipy.fft.fftscipy.fft.irfftscipy.fft.rfftfreqscipy.fft.fftnscipy.fft.rfftn