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skills/neurokit2/references/signal_processing.md
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skills/neurokit2/references/signal_processing.md
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# General Signal Processing
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## Overview
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NeuroKit2 provides comprehensive signal processing utilities applicable to any time series data. These functions support filtering, transformation, peak detection, decomposition, and analysis operations that work across all signal types.
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## Preprocessing Functions
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### signal_filter()
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Apply frequency-domain filtering to remove noise or isolate frequency bands.
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```python
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filtered = nk.signal_filter(signal, sampling_rate=1000, lowcut=None, highcut=None,
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method='butterworth', order=5)
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```
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**Filter types (via lowcut/highcut combinations):**
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**Lowpass** (highcut only):
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```python
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lowpass = nk.signal_filter(signal, sampling_rate=1000, highcut=50)
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```
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- Removes frequencies above highcut
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- Smooths signal, removes high-frequency noise
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**Highpass** (lowcut only):
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```python
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highpass = nk.signal_filter(signal, sampling_rate=1000, lowcut=0.5)
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```
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- Removes frequencies below lowcut
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- Removes baseline drift, DC offset
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**Bandpass** (both lowcut and highcut):
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```python
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bandpass = nk.signal_filter(signal, sampling_rate=1000, lowcut=0.5, highcut=50)
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```
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- Retains frequencies between lowcut and highcut
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- Isolates specific frequency band
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**Bandstop/Notch** (powerline removal):
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```python
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notch = nk.signal_filter(signal, sampling_rate=1000, method='powerline', powerline=50)
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```
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- Removes 50 or 60 Hz powerline noise
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- Narrow notch filter
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**Methods:**
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- `'butterworth'` (default): Smooth frequency response, flat passband
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- `'bessel'`: Linear phase, minimal ringing
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- `'chebyshev1'`: Steeper rolloff, ripple in passband
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- `'chebyshev2'`: Steeper rolloff, ripple in stopband
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- `'elliptic'`: Steepest rolloff, ripple in both bands
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- `'powerline'`: Notch filter for 50/60 Hz
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**Order parameter:**
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- Higher order: Steeper transition, more ringing
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- Lower order: Gentler transition, less ringing
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- Typical: 2-5 for physiological signals
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### signal_sanitize()
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Remove invalid values (NaN, inf) and optionally interpolate.
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```python
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clean_signal = nk.signal_sanitize(signal, interpolate=True)
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```
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**Use cases:**
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- Handle missing data points
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- Remove artifacts marked as NaN
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- Prepare signal for algorithms requiring continuous data
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### signal_resample()
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Change sampling rate of signal (upsample or downsample).
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```python
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resampled = nk.signal_resample(signal, sampling_rate=1000, desired_sampling_rate=500,
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method='interpolation')
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```
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**Methods:**
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- `'interpolation'`: Cubic spline interpolation
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- `'FFT'`: Frequency-domain resampling
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- `'poly'`: Polyphase filtering (best for downsampling)
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**Use cases:**
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- Match sampling rates across multi-modal recordings
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- Reduce data size (downsample)
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- Increase temporal resolution (upsample)
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### signal_fillmissing()
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Interpolate missing or invalid data points.
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```python
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filled = nk.signal_fillmissing(signal, method='linear')
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```
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**Methods:**
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- `'linear'`: Linear interpolation
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- `'nearest'`: Nearest neighbor
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- `'pad'`: Forward/backward fill
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- `'cubic'`: Cubic spline
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- `'polynomial'`: Polynomial fitting
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## Transformation Functions
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### signal_detrend()
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Remove slow trends from signal.
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```python
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detrended = nk.signal_detrend(signal, method='polynomial', order=1)
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```
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**Methods:**
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- `'polynomial'`: Fit and subtract polynomial (order 1 = linear)
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- `'loess'`: Locally weighted regression
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- `'tarvainen2002'`: Smoothness priors detrending
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**Use cases:**
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- Remove baseline drift
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- Stabilize mean before analysis
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- Prepare for stationarity-assuming algorithms
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### signal_decompose()
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Decompose signal into constituent components.
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```python
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components = nk.signal_decompose(signal, sampling_rate=1000, method='emd')
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```
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**Methods:**
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**Empirical Mode Decomposition (EMD):**
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```python
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components = nk.signal_decompose(signal, sampling_rate=1000, method='emd')
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```
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- Data-adaptive decomposition into Intrinsic Mode Functions (IMFs)
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- Each IMF represents different frequency content (high to low)
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- No predefined basis functions
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**Singular Spectrum Analysis (SSA):**
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```python
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components = nk.signal_decompose(signal, method='ssa')
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```
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- Decomposes into trend, oscillations, and noise
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- Based on eigenvalue decomposition of trajectory matrix
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**Wavelet decomposition:**
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- Time-frequency representation
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- Localized in both time and frequency
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**Returns:**
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- Dictionary with component signals
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- Trend, oscillatory components, residual
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**Use cases:**
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- Isolate physiological rhythms
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- Separate signal from noise
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- Multi-scale analysis
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### signal_recompose()
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Reconstruct signal from decomposed components.
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```python
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reconstructed = nk.signal_recompose(components, indices=[1, 2, 3])
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```
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**Use case:**
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- Selective reconstruction after decomposition
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- Remove specific IMFs or components
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- Adaptive filtering
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### signal_binarize()
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Convert continuous signal to binary (0/1) based on threshold.
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```python
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binary = nk.signal_binarize(signal, method='threshold', threshold=0.5)
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```
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**Methods:**
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- `'threshold'`: Simple threshold
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- `'median'`: Median-based
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- `'mean'`: Mean-based
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- `'quantile'`: Percentile-based
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**Use case:**
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- Event detection from continuous signal
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- Trigger extraction
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- State classification
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### signal_distort()
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Add controlled noise or artifacts for testing.
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```python
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distorted = nk.signal_distort(signal, sampling_rate=1000, noise_amplitude=0.1,
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noise_frequency=50, artifacts_amplitude=0.5)
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```
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**Parameters:**
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- `noise_amplitude`: Gaussian noise level
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- `noise_frequency`: Sinusoidal interference (e.g., powerline)
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- `artifacts_amplitude`: Random spike artifacts
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- `artifacts_number`: Number of artifacts to add
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**Use cases:**
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- Algorithm robustness testing
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- Preprocessing method evaluation
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- Realistic data simulation
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### signal_interpolate()
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Interpolate signal at new time points or fill gaps.
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```python
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interpolated = nk.signal_interpolate(x_values, y_values, x_new=None, method='quadratic')
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```
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**Methods:**
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- `'linear'`, `'quadratic'`, `'cubic'`: Polynomial interpolation
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- `'nearest'`: Nearest neighbor
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- `'monotone_cubic'`: Preserves monotonicity
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**Use case:**
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- Convert irregular samples to regular grid
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- Upsample for visualization
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- Align signals with different time bases
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### signal_merge()
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Combine multiple signals with different sampling rates.
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```python
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merged = nk.signal_merge(signal1, signal2, time1=None, time2=None, sampling_rate=None)
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```
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**Use case:**
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- Multi-modal signal integration
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- Combine data from different devices
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- Synchronize based on timestamps
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### signal_flatline()
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Identify periods of constant signal (artifacts or sensor failure).
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```python
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flatline_mask = nk.signal_flatline(signal, duration=5.0, sampling_rate=1000)
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```
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**Returns:**
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- Binary mask where True indicates flatline periods
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- Duration threshold prevents false positives from normal stability
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### signal_noise()
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Add various types of noise to signal.
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```python
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noisy = nk.signal_noise(signal, sampling_rate=1000, noise_type='gaussian',
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amplitude=0.1)
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```
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**Noise types:**
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- `'gaussian'`: White noise
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- `'pink'`: 1/f noise (common in physiological signals)
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- `'brown'`: Brownian (random walk)
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- `'powerline'`: Sinusoidal interference (50/60 Hz)
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### signal_surrogate()
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Generate surrogate signals preserving certain properties.
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```python
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surrogate = nk.signal_surrogate(signal, method='IAAFT')
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```
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**Methods:**
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- `'IAAFT'`: Iterated Amplitude Adjusted Fourier Transform
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- Preserves amplitude distribution and power spectrum
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- `'random_shuffle'`: Random permutation (null hypothesis testing)
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**Use case:**
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- Nonlinearity testing
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- Null hypothesis generation for statistical tests
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## Peak Detection and Correction
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### signal_findpeaks()
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Detect local maxima (peaks) in signal.
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```python
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peaks_dict = nk.signal_findpeaks(signal, height_min=None, height_max=None,
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relative_height_min=None, relative_height_max=None)
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```
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**Key parameters:**
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- `height_min/max`: Absolute amplitude thresholds
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- `relative_height_min/max`: Relative to signal range (0-1)
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- `threshold`: Minimum prominence
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- `distance`: Minimum samples between peaks
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**Returns:**
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- Dictionary with:
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- `'Peaks'`: Peak indices
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- `'Height'`: Peak amplitudes
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- `'Distance'`: Inter-peak intervals
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**Use cases:**
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- Generic peak detection for any signal
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- R-peaks, respiratory peaks, pulse peaks
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- Event detection
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### signal_fixpeaks()
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Correct detected peaks for artifacts and anomalies.
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```python
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corrected = nk.signal_fixpeaks(peaks, sampling_rate=1000, iterative=True,
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method='Kubios', interval_min=None, interval_max=None)
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```
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**Methods:**
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- `'Kubios'`: Kubios HRV software method (default)
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- `'Malik1996'`: Task Force Standards (1996)
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- `'Kamath1993'`: Kamath's approach
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**Corrections:**
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- Remove physiologically implausible intervals
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- Interpolate missing peaks
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- Remove extra detected peaks (duplicates)
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**Use case:**
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- Artifact correction in R-R intervals
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- Improve HRV analysis quality
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- Respiratory or pulse peak correction
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## Analysis Functions
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### signal_rate()
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Compute instantaneous rate from event occurrences (peaks).
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```python
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rate = nk.signal_rate(peaks, sampling_rate=1000, desired_length=None)
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```
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**Method:**
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- Calculate inter-event intervals
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- Convert to events per minute
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- Interpolate to match desired length
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**Use case:**
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- Heart rate from R-peaks
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- Breathing rate from respiratory peaks
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- Any periodic event rate
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### signal_period()
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Find dominant period/frequency in signal.
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```python
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period = nk.signal_period(signal, sampling_rate=1000, method='autocorrelation',
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show=False)
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```
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**Methods:**
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- `'autocorrelation'`: Peak in autocorrelation function
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- `'powerspectraldensity'`: Peak in frequency spectrum
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**Returns:**
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- Period in samples or seconds
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- Frequency (1/period) in Hz
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**Use case:**
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- Detect dominant rhythm
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- Estimate fundamental frequency
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- Breathing rate, heart rate estimation
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### signal_phase()
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Compute instantaneous phase of signal.
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```python
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phase = nk.signal_phase(signal, method='hilbert')
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```
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**Methods:**
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- `'hilbert'`: Hilbert transform (analytic signal)
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- `'wavelet'`: Wavelet-based phase
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**Returns:**
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- Phase in radians (-π to π) or 0 to 1 (normalized)
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**Use cases:**
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- Phase-locked analysis
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- Synchronization measures
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- Phase-amplitude coupling
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### signal_psd()
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Compute Power Spectral Density.
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```python
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psd, freqs = nk.signal_psd(signal, sampling_rate=1000, method='welch',
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max_frequency=None, show=False)
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```
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**Methods:**
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- `'welch'`: Welch's periodogram (windowed FFT, default)
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- `'multitapers'`: Multitaper method (superior spectral estimation)
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- `'lomb'`: Lomb-Scargle (unevenly sampled data)
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- `'burg'`: Autoregressive (parametric)
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**Returns:**
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- `psd`: Power at each frequency (units²/Hz)
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- `freqs`: Frequency bins (Hz)
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**Use case:**
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- Frequency content analysis
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- HRV frequency domain
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- Spectral signatures
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### signal_power()
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Compute power in specific frequency bands.
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```python
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power_dict = nk.signal_power(signal, sampling_rate=1000, frequency_bands={
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'VLF': (0.003, 0.04),
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'LF': (0.04, 0.15),
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'HF': (0.15, 0.4)
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}, method='welch')
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```
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**Returns:**
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- Dictionary with absolute and relative power per band
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- Peak frequencies
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**Use case:**
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- HRV frequency analysis
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- EEG band power
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- Rhythm quantification
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### signal_autocor()
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Compute autocorrelation function.
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```python
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autocorr = nk.signal_autocor(signal, lag=1000, show=False)
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```
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**Interpretation:**
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- High autocorrelation at lag: signal repeats every lag samples
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- Periodic signals: peaks at multiples of period
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- Random signals: rapid decay to zero
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**Use cases:**
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- Detect periodicity
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- Assess temporal structure
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- Memory in signal
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### signal_zerocrossings()
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Count zero crossings (sign changes).
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```python
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n_crossings = nk.signal_zerocrossings(signal)
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```
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**Interpretation:**
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- More crossings: higher frequency content
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- Related to dominant frequency (rough estimate)
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**Use case:**
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- Simple frequency estimation
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- Signal regularity assessment
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### signal_changepoints()
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Detect abrupt changes in signal properties (mean, variance).
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```python
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changepoints = nk.signal_changepoints(signal, penalty=10, method='pelt', show=False)
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```
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**Methods:**
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- `'pelt'`: Pruned Exact Linear Time (fast, exact)
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- `'binseg'`: Binary segmentation (faster, approximate)
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**Parameters:**
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- `penalty`: Controls sensitivity (higher = fewer changepoints)
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**Returns:**
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- Indices of detected changepoints
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- Segments between changepoints
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**Use cases:**
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- Segment signal into states
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- Detect transitions (e.g., sleep stages, arousal states)
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- Automatic epoch definition
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### signal_synchrony()
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Assess synchronization between two signals.
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```python
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sync = nk.signal_synchrony(signal1, signal2, method='correlation')
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```
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**Methods:**
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- `'correlation'`: Pearson correlation
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- `'coherence'`: Frequency-domain coherence
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||||
- `'mutual_information'`: Information-theoretic measure
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||||
- `'phase'`: Phase locking value
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||||
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||||
**Use cases:**
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- Heart-brain coupling
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- Inter-brain synchrony
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- Multi-channel coordination
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||||
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### signal_smooth()
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Apply smoothing to reduce noise.
|
||||
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```python
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smoothed = nk.signal_smooth(signal, method='convolution', kernel='boxzen', size=10)
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||||
```
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||||
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||||
**Methods:**
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- `'convolution'`: Apply kernel (boxcar, Gaussian, etc.)
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||||
- `'median'`: Median filter (robust to outliers)
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||||
- `'savgol'`: Savitzky-Golay filter (preserves peaks)
|
||||
- `'loess'`: Locally weighted regression
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||||
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||||
**Kernel types (for convolution):**
|
||||
- `'boxcar'`: Simple moving average
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||||
- `'gaussian'`: Gaussian-weighted average
|
||||
- `'hann'`, `'hamming'`, `'blackman'`: Windowing functions
|
||||
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||||
**Use cases:**
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||||
- Noise reduction
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||||
- Trend extraction
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||||
- Visualization enhancement
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||||
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||||
### signal_timefrequency()
|
||||
|
||||
Time-frequency representation (spectrogram).
|
||||
|
||||
```python
|
||||
tf, time, freq = nk.signal_timefrequency(signal, sampling_rate=1000, method='stft',
|
||||
max_frequency=50, show=False)
|
||||
```
|
||||
|
||||
**Methods:**
|
||||
- `'stft'`: Short-Time Fourier Transform
|
||||
- `'cwt'`: Continuous Wavelet Transform
|
||||
|
||||
**Returns:**
|
||||
- `tf`: Time-frequency matrix (power at each time-frequency point)
|
||||
- `time`: Time bins
|
||||
- `freq`: Frequency bins
|
||||
|
||||
**Use cases:**
|
||||
- Non-stationary signal analysis
|
||||
- Time-varying frequency content
|
||||
- EEG/MEG time-frequency analysis
|
||||
|
||||
## Simulation
|
||||
|
||||
### signal_simulate()
|
||||
|
||||
Generate various synthetic signals for testing.
|
||||
|
||||
```python
|
||||
signal = nk.signal_simulate(duration=10, sampling_rate=1000, frequency=[5, 10],
|
||||
amplitude=[1.0, 0.5], noise=0.1)
|
||||
```
|
||||
|
||||
**Signal types:**
|
||||
- Sinusoidal oscillations (specify frequencies)
|
||||
- Multiple frequency components
|
||||
- Gaussian noise
|
||||
- Combinations
|
||||
|
||||
**Use cases:**
|
||||
- Algorithm testing
|
||||
- Method validation
|
||||
- Educational demonstrations
|
||||
|
||||
## Visualization
|
||||
|
||||
### signal_plot()
|
||||
|
||||
Visualize signal and optional markers.
|
||||
|
||||
```python
|
||||
nk.signal_plot(signal, sampling_rate=1000, peaks=None, show=True)
|
||||
```
|
||||
|
||||
**Features:**
|
||||
- Time axis in seconds
|
||||
- Peak markers
|
||||
- Multiple subplots for signal arrays
|
||||
|
||||
## Practical Tips
|
||||
|
||||
**Choosing filter parameters:**
|
||||
- **Lowcut**: Set below lowest frequency of interest
|
||||
- **Highcut**: Set above highest frequency of interest
|
||||
- **Order**: Start with 2-5, increase if transition too slow
|
||||
- **Method**: Butterworth is safe default
|
||||
|
||||
**Handling edge effects:**
|
||||
- Filtering introduces artifacts at signal edges
|
||||
- Pad signal before filtering, then trim
|
||||
- Or discard initial/final seconds
|
||||
|
||||
**Dealing with gaps:**
|
||||
- Small gaps: `signal_fillmissing()` with interpolation
|
||||
- Large gaps: Segment signal, analyze separately
|
||||
- Mark gaps as NaN, use interpolation carefully
|
||||
|
||||
**Combining operations:**
|
||||
```python
|
||||
# Typical preprocessing pipeline
|
||||
signal = nk.signal_sanitize(raw_signal) # Remove invalid values
|
||||
signal = nk.signal_filter(signal, sampling_rate=1000, lowcut=0.5, highcut=40) # Bandpass
|
||||
signal = nk.signal_detrend(signal, method='polynomial', order=1) # Remove linear trend
|
||||
```
|
||||
|
||||
**Performance considerations:**
|
||||
- Filtering: FFT-based methods faster for long signals
|
||||
- Resampling: Downsample early in pipeline to speed up
|
||||
- Large datasets: Process in chunks if memory-limited
|
||||
|
||||
## References
|
||||
|
||||
- Virtanen, P., et al. (2020). SciPy 1.0: fundamental algorithms for scientific computing in Python. Nature methods, 17(3), 261-272.
|
||||
- Tarvainen, M. P., Ranta-aho, P. O., & Karjalainen, P. A. (2002). An advanced detrending method with application to HRV analysis. IEEE Transactions on Biomedical Engineering, 49(2), 172-175.
|
||||
- Huang, N. E., et al. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London A, 454(1971), 903-995.
|
||||
Reference in New Issue
Block a user