# NeuroDSP Glossary¶

The following is a glossary of neuroscience and digital processing related terms that are used in NeuroDSP, as well as links to some external resources for learning DSP.

## General¶

- periodic
Properties or components of a signal that are rhythmic.

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

## Digital Signal Processing¶

Digital Signal Processing (DSP) is an area of science & engineering related to the computational analysis of digital signals.

For a collection of openly available resources for learning DSP, check out this list.

If you want to start with a general introduction to DSP, check out Seeing Circles Sines and Signal or for more in-depth descriptions, check out The Scientist and Engineers Guide to Digital Signal Processing.

- 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).

## Units¶

- 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.

## Filters¶

There are some available (pay-walled) articles that present overviews and guides to filters, including:

this guide on using filters for electrophysiological data

this primer on when, how, and why to use filters

For an open, in depth, and code-driven tutorial, 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.

## Rhythms & Bursts¶

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

## Time Frequency¶

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 occurrences 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 distance.

- 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.

## Spectral¶

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 a frequency representation.

- 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 neighboring entries.

- coefficient of variation
A standardized measure of dispersion, as the ratio of the standard deviation to the mean.

## Simulations¶

For an overview of the aperiodic signals available 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, technically, 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 powerlaw of the form \(1/f^\chi\), where \(\chi\) refers to the exponent of the powerlaw.

- colored noise
The ‘color’ of noise refers to the 1/f exponent of the power spectrum of a noise signal.

white noise: a signal with a \(1/f^0\) power spectrum, which is flat with equal power across all frequencies

pink noise: a signal with a \(1/f^1\) power spectrum

brown noise: a signal with a \(1/f^2\) power spectrum, sometimes also known as red noise

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