The following is a glossary of neuroscience and digital processing related terms that are used in NeuroDSP.

- periodic
- Properties or components of a signal that are rhythmic.
- aperiodic
- Properties or components of a signal that are arrhythmic, with no characteristic frequency.

For a general introduction to digital signal processing, we recommend Seeing Circles Sines and Signal by Jack Schaedler.

- time domain
- Signals that are represented as variations over time, and analyses of such signals.
- frequency domain
- Signals that are represented in terms of frequencies, and analyses of such signals.
- sampling rate
- The rate at which samples are taken.
- temporal resolution
- The precision of a measurement, in the time domain. This is set by the magnitude of time between successive measurements (e.g. 0.01 seconds between samples).
- frequency resolution
- The precision of a measurement, in the frequency domain. This is set by the magnitude of frequency between successive measurements (e.g. 0.5 Hz between measurements).

- Hertz (Hz)
- A unit of frequency, as the number of cycles per second.
- Decibels (dB)
- A unit of intensity, on a logarithmic scale.
- Volts (V)
- A unit of voltage, typically in the microvolt (uV) range for neural time series.

For a guide on filtering, specific to electrophysiological data, check out this paper from the journal of neuroscience methods.

For a more in depth tutorial, in code, check out the MNE Filtering Tutorial.

- Impulse Response
- The response of a filter when presented with an impulse; a single, brief input.
- FIR
- A Finite Impulse Response filter, meaning its impulse response settles to zero in finite time.
- IIR
- An Infinite Impulse Response filter, meaning the filter is recursive, and its impulse response continues infinitely.
- passband
- The range (band) of frequencies that are unattenuated by a filter.
- stopband
- The range (band) of frequencies that are attenuated (stopped) by a filter.
- passtype
The type of filter, defined in terms of what frequency bands or ranges it passes through, or filters out.

- bandpass: a filter whose passband is a specific frequency band, bound by a low and high frequency point.
- bandstop: a filter that passes through all frequencies except a band region that is attenuated.
- lowpass: a filter whose passband is all frequencies below a filter frequency (low frequencies pass through).
- highpass: a filter whose passband is all frequencies above a filter frequency (high frequencies pass through).

- transition band
- The range of frequencies that are in the transition region between the passband and the stopband.
- frequency response
- The response profile of a filter, specifying the gain and phase shift applied by the filter at each frequency.

- burst
- Periodic activity that lasts for a short or transient amount of time , as in a ‘burst of oscillatory activity’.

We currently have two general approaches to time frequency analyses:

- those based on the Hilbert transform
- There is a scholarpedia article on using the Hilbert Transform for Brain Waves
- See also this deep dive into Hilbert methods from VoytekLab member Richard Gao.

- wavelet based approaches.

- frequency
- The number of occurences over a unit of time, typically referred to as cycles per second, and measured in Hz.
- phase
- The position, at a point in time, on a waveform cycle.
- amplitude
- The magnitude of a signal, as the peak-to-trough.
- power
- The squared magnitude of a signal.
- period
- A single cycle of a rhythm, defined as the time between two consecutive troughs (or peaks).
- hilbert transform
- A mathematical transform that computes the ‘analytic signal’, a complex-valued representation of a time-series (signal) that can be used to find its analytic amplitude and phase.
- wavelet
- A wave-like signal, or ‘brief oscillation’, that starts at zero amplitude, increases in amplitude to some value, and then decays back to zero.

Many of the spectral methods available are based on the Fourier transform, for which there is an interactive guide by Better Explained and an explainer video by 3Blue1Brown.

- fourier transform
- A mathematical transformation to decompose a time series into its constituent frequencies.
- power spectrum
- A frequency domain representation, as an estimate of the power across frequencies in a signal.
- median filter
- A smoothing approach to replace each value in a signal with the median of the neighbouring entries.
- coefficient of variation
- A standardized measure of dispersion, as the ratio of the standard deviation to the mean.

For an overview of the aperiodic signals avaible in terms of their 1/f characteristics, check out this article from scholarpedia.

- noise signal
- Formally, a noise signal is a signal produced by a stochastic (random) process. The aperiodic signals that are simulated in NeuroDSP are noise signals.
- powerlaw
- A relationship between two quantities, whereby one quantity varies as a power of another. One-over-f relationships are powerlaw, as the spectral power varies by a power of the frequency.
- 1/f signal
- A signal for which the power spectrum can be described by a 1/f^chi powerlaw, where chi refers to the exponent of the powerlaw.
- coloured noise
The ‘colour’ of noise refers to the 1/f exponent of the power spectrum of a noise signal.

- white noise: a signal with a flat power spectrum, with equal power at all frequencies. White noise has an exponent of 0.
- pink noise: a signal with a 1/f power spectrum. Pink noise has an exponent of 1.
- brown noise: a signal with a 1/f^2 power spectrum. Also called red noise.

- random walk
- A random process that describes a path of a succession of random steps.