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Use scipy.signal.butter to design a low-pass, high-pass, band-pass, or band-stop Butterworth filter, then apply its coefficients with the filtering method that fits your data. For most designs, request second-order sections with output="sos"; set the cutoff in the right frequency units, and choose between causal filtering and forward-backward filtering based on whether phase and edge behavior matter.
Design a Butterworth filter with the right cutoff units
scipy.signal.butter designs digital or analog Butterworth filters and returns filter coefficients. A Butterworth critical frequency is the half-power point, corresponding to −3 dB; it is not necessarily the edge convention used by another filter family, such as an FIR design.
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The documented SciPy 1.18.0 signature is butter(N, Wn, btype='low', analog=False, output='ba', fs=None). Here, N is the filter order; btype selects low-pass, high-pass, band-pass, or band-stop; and analog selects analog rather than digital design.
- Digital, no
fs:Wnis normalized from 0 to 1, with 1 representing the Nyquist frequency. - Digital, with
fs: specifyWnin the same units as the sampling frequency. For example, iffsis in hertz,Wnis in hertz. - Analog:
Wnis angular frequency in radians per second. - Cutoff shape: use a scalar
Wnfor low-pass and high-pass filters, and a pair for band-pass and band-stop filters.
For example, this designs a digital high-pass filter with a 15 Hz critical frequency for data sampled at 1000 Hz:
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from scipy import signal
sos = signal.butter(10, 15, btype="highpass", fs=1000, output="sos")The values 15 and 1000 are in hertz because fs is supplied. Without fs, the same value 15 would instead be interpreted as a normalized frequency and would not mean 15 Hz. See the SciPy 1.18.0 butter reference for the function parameters and examples.
Use second-order sections for general-purpose filtering
Although butter defaults to output='ba', which returns numerator and denominator polynomial coefficients, SciPy recommends output='sos' for general use. A single high-degree polynomial can be numerically sensitive, particularly for high-order or narrowband designs. Second-order sections represent the filter as a cascade of lower-order sections and are the safer default for applying such filters.
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For a band-pass or band-stop design, the resulting SOS matrix represents order 2*N as N biquad sections. Do not confuse the number of sections with the order argument supplied to butter.
Choose ba only when a downstream interface requires numerator/denominator coefficients or compatibility makes that representation necessary. For sensitive designs, inspect the filter characteristics rather than assuming polynomial coefficients behave well. SciPy’s Butterworth reference and signal-processing tutorial describe the representation and numerical considerations.
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Choose between causal and zero-phase filtering
Use sosfilt for forward, causal processing
For a streaming pipeline or another workflow that processes samples in order, apply the designed SOS coefficients with signal.sosfilt(sos, x). This is a forward filter and can introduce phase delay. It is suitable when causal processing is required, but the output timing may shift relative to the input.
from scipy import signal
sos = signal.butter(10, 15, btype="highpass", fs=1000, output="sos")
y = signal.sosfilt(sos, x)Use sosfiltfilt for offline, zero-phase processing
When the full record is available and preserving phase is important, signal.sosfiltfilt(sos, x) filters forward and then backward. The two passes remove phase delay, but the effective order is doubled. The backward pass also means this is not a causal streaming method: the operation needs the data segment rather than only the current and past samples.
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from scipy import signal
sos = signal.butter(4, 0.125, output="sos")
y = signal.sosfiltfilt(sos, x)Here, 0.125 is normalized to Nyquist because fs is omitted. sosfiltfilt also handles endpoints using padding; the choice of padding and the record’s length can affect edge output and create transients. Pay particular attention when filtering short records. Consult the sosfiltfilt reference for its padding and endpoint behavior, and the filtfilt reference for the forward-backward method.
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Set filter order from passband and stopband requirements
If you know the passband edge, stopband edge, allowed passband loss, and required stopband attenuation, use signal.buttord instead of choosing an order by intuition. It returns the minimum Butterworth order and a natural frequency for those constraints. Pass both returned values to butter; when using a digital sampling frequency, supply fs consistently to both functions.
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from scipy import signal
N, Wn = signal.buttord(wp, ws, gpass, gstop, fs=fs)
sos = signal.butter(N, Wn, btype="lowpass", fs=fs, output="sos")In this pattern, wp and ws describe the passband and stopband edges, while gpass and gstop set the passband-loss and stopband-attenuation requirements in decibels. Use values and filter type that match the actual specification; the example’s "lowpass" is appropriate only for a low-pass design. See the buttord reference for parameter details and the documented analog example.
Check the design before relying on its output
- Confirm that digital frequency values use the intended convention: normalized-to-Nyquist when
fsis omitted, or the units offswhen it is supplied. - Confirm that analog designs use radians per second and that the selected filter type matches the desired passband.
- Prefer SOS for high-order or narrowband filters; be cautious about numerical behavior if a downstream requirement forces
ba. - Match the filtering method to the workflow:
sosfiltis forward and causal, whilesosfiltfiltis a two-pass, offline method with edge handling. - For explicit passband and stopband constraints, calculate the order with
buttordand pass its result tobutter.
These details reflect the SciPy 1.18.0 documentation. Check the reference for the SciPy version installed in your environment if its API or behavior differs.
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