signal-processing

name	signal-processing
description	Performs signal processing tasks including spectral analysis (FFT), digital filtering, time-frequency decomposition, noise reduction, and modulation/demodulation; trigger when users discuss waveforms, frequency spectra, filters, or time series in engineering contexts.

When to Trigger

Activate this skill when the user mentions:

• FFT, DFT, spectral analysis, power spectral density
• Digital filters (FIR, IIR), Butterworth, Chebyshev
• Time-frequency analysis, STFT, wavelets, spectrograms
• Signal denoising, SNR, noise floor
• Sampling, Nyquist theorem, aliasing, ADC/DAC
• Modulation (AM, FM, QAM), demodulation, baseband
• Convolution, correlation, matched filtering

Step-by-Step Methodology

1. Signal characterization - Identify signal type (continuous/discrete, deterministic/stochastic, stationary/non-stationary). Determine sampling rate, duration, and bit depth. Check Nyquist criterion (fs > 2*fmax).
2. Preprocessing - Remove DC offset (mean subtraction). Apply windowing (Hann, Hamming, Blackman) to reduce spectral leakage. Handle missing data or outliers. Normalize amplitude if needed.
3. Spectral analysis - Compute FFT with appropriate zero-padding for frequency resolution. Estimate power spectral density (Welch's method for noise reduction, periodogram for snapshot). Identify dominant frequency components and harmonics.
4. Filtering - Design filter based on requirements: passband/stopband frequencies, ripple, attenuation. Choose type: FIR (linear phase, higher order) or IIR (lower order, nonlinear phase). Implement using appropriate method (Parks-McClellan for FIR, bilinear transform for IIR).
5. Time-frequency analysis - For non-stationary signals: compute STFT (spectrogram) with appropriate window size trade-off. Apply wavelet transform (CWT for analysis, DWT for decomposition/compression). Select mother wavelet (Morlet for frequency, Daubechies for transients).
6. Denoising - Estimate noise characteristics (white, colored, impulsive). Apply appropriate method: spectral subtraction, Wiener filter, wavelet thresholding (soft/hard), or adaptive filtering (LMS, RLS).
7. Validation - Verify filter response meets specifications (frequency response, phase response, group delay). Check for artifacts (ringing, Gibbs phenomenon). Compute output SNR improvement.

Key Databases and Tools

• SciPy signal - Python signal processing functions
• MATLAB Signal Processing Toolbox - Comprehensive DSP tools
• GNU Radio - Software-defined radio framework
• Librosa - Audio signal processing
• PyWavelets - Wavelet transform library

Output Format

• Frequency spectra with labeled axes (Hz or normalized frequency, dB or linear magnitude).
• Filter specifications: type, order, cutoff frequencies, passband ripple, stopband attenuation.
• Time-frequency plots (spectrograms) with time, frequency, and magnitude axes.
• SNR values in dB before and after processing.
• Transfer function coefficients (numerator b, denominator a for IIR; taps for FIR).

Quality Checklist

• Sampling rate and Nyquist criterion verified
• Windowing function specified and justified
• FFT length and frequency resolution stated
• Filter order and stability verified (all poles inside unit circle for IIR)
• Phase response considered (linear phase requirement?)
• Group delay acceptable for application
• SNR improvement quantified
• Edge effects and transient responses handled