How to Apply Signal Processing¶

This guide shows you how to smooth time series with digital filters, extract rate-of-change features, and use frequency-domain plots to choose filter parameters.

Prerequisites¶

• Familiarity with transformers (How to Use Preprocessing Transformers)
• Understanding of the fit/transform pattern (Getting Started)

Try it interactively¶

Smooth High-Frequency Noise¶

NumericalFilter applies standard digital IIR filters. A lowpass filter removes noise above a chosen cutoff frequency:

from yohou.preprocessing import NumericalFilter

smoother = NumericalFilter(
    design="butterworth",
    mode="lowpass",
    order=4,
    cutoff_frequency=0.2,
)
df_smooth = smoother.fit_transform(df)

The cutoff_frequency is normalized between 0 and 1, where 1 is the Nyquist frequency (half the sampling rate). Use plot_spectrum (below) to identify where noise begins and set the cutoff just below that point.

Start with design="butterworth" and order=4. If the filtered signal still contains unwanted frequencies, increase the order for a sharper rolloff. If you need an even steeper cutoff, switch to "chebyshev1" for passband ripple tolerance (sharper rolloff) or "chebyshev2" for stopband attenuation (cleaner rejection band). Use "elliptic" for the sharpest possible cutoff when both passband and stopband ripple are acceptable. Use "bessel" when preserving waveform shape matters more than a sharp cutoff.

Remove Low-Frequency Drift¶

Use a highpass filter to remove slow trends or baseline drift while preserving faster dynamics:

detrend = NumericalFilter(
    design="butterworth",
    mode="highpass",
    order=4,
    cutoff_frequency=0.05,
)
df_detrended = detrend.fit_transform(df)

Isolate a Frequency Band¶

For bandpass or bandstop filtering, pass a 2-tuple as the cutoff_frequency:

# Keep only frequencies between 0.1 and 0.4 of Nyquist
bandpass = NumericalFilter(
    mode="bandpass",
    cutoff_frequency=(0.1, 0.4),
)
df_band = bandpass.fit_transform(df)

Use mode="bandstop" instead to remove a specific frequency band (e.g., a known interference frequency).

Extract Rate of Change¶

NumericalDifferentiator computes numerical derivatives using central differences:

from yohou.preprocessing import NumericalDifferentiator

diff = NumericalDifferentiator(order=1)
df_rate = diff.fit_transform(df)

The order parameter controls boundary accuracy: 1 uses 2-point differences at boundaries, 2 uses 3-point second-order accurate differences.

To integrate a derivative back, use NumericalIntegrator:

from yohou.preprocessing import NumericalIntegrator

integrator = NumericalIntegrator(method="cumulative_trapezoid")
df_integrated = integrator.fit_transform(df)

The method parameter accepts "cumulative_trapezoid" (faster) or "cumulative_simpson" (more accurate).

Inspect the Frequency Spectrum¶

Use plot_spectrum to visualize the power spectral density before choosing a cutoff:

from yohou.plotting import plot_spectrum

fig = plot_spectrum(df, columns="value", show_peaks=True, n_peaks=3)
fig.show()

The show_peaks option annotates the dominant frequencies with their corresponding period in sample units, making it easier to identify the boundary between signal and noise.

Check Phase Alignment¶

Use plot_phase to inspect the phase angle of each frequency component via FFT:

from yohou.plotting import plot_phase

fig = plot_phase(df, columns="value")
fig.show()

Compare the phase plot before and after filtering to verify that the filter does not introduce unacceptable phase distortion at frequencies you care about.

See Also¶

• Preprocessing for the conceptual background on transformers
• Visualization for other plotting functions