Signal Fundamentals
Understand what filtering and spectral estimation do to a signal well enough to choose parameters and predict their side effects.
You can now…
- Predict aliasing
- Read a spectrum
- Choose Welch parameters
- Explain leakage and zero-padding
- Design a filter and state its distortions
- Remove line noise without collateral damage
- Separate periodic peaks from the aperiodic background
Level 1 is the signal processing you need in order to choose parameters rather than accept defaults, and no more. It runs from sampling to spectral parameterization in seven lessons: what a sampling rate can and cannot represent; what a Fourier coefficient is and why resolution is one over the epoch length; how Welch’s method trades resolution for stability; what windows and zero-padding do and do not do; what a filter does to a trace, including the side effects that zero-phase filtering hides; how to remove mains interference without leaving a hole; and how to separate the peaks in a spectrum from the sloping background underneath them.
Every lesson runs on real recordings whose hardware fingerprints — sampling rates, online filters, mains frequency — are part of the material, and every technique is introduced together with what it looks like when misapplied. The capstone asks for a spectral fingerprint of a cohort: documented Welch settings, individual alpha frequency and aperiodic exponent per subject, and a methods paragraph that justifies every filter choice.
Lessons
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L1.1 Sampling, Nyquist and aliasing
The sampling theorem, alias frequencies, why decimation needs an anti-alias filter, and choosing a rate for a target analysis.
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L1.2 Time and frequency domains
Any signal as a sum of sinusoids; reading amplitude, phase and frequency; the DFT and its bins; resolution as 1/T; amplitude versus power versus dB.
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L1.3 Power spectral density
Why the periodogram is noisy, Welch's method and its parameters, correct units and scale, and averaging PSDs correctly.
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L1.4 Windowing, leakage and zero-padding
Spectral leakage, choosing a window, and what zero-padding does (interpolation) and does not do (resolution).
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L1.5 Filters: FIR, IIR, and what they do to your data
Choose a filter type, cutoff and transition band for a stated goal, and predict the distortions it will introduce.
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L1.6 Line noise
Detect 50/60 Hz and harmonics in a PSD, choose among notch, spectral-fit and spatial removal, and verify removal without collateral damage.
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L1.7 Aperiodic and periodic components
The 1/f-like background, separating peaks from slope with spectral parameterization, individual alpha frequency, and why band power conflates the two.