Merge pull request #144 from neurodsp-tools/glossary

Add glossary

doc/glossary.rst

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+NeuroDSP Glossary
+=================
+
+The following is a glossary of neuroscience and digital processing related terms that are used in NeuroDSP.
+
+General
+-------
+
+.. glossary::
+
+    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
+-------------------------
+
+For a general introduction to digital signal processing, we recommend
+`Seeing Circles Sines and Signal <https://jackschaedler.github.io/circles-sines-signals/>`_
+by Jack Schaedler.
+
+.. glossary::
+
+    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
+-----
+
+.. glossary::
+
+    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
+-------
+
+For a guide on filtering, specific to electrophysiological data, check out this
+`paper <https://doi.org/10.1016/j.jneumeth.2014.08.002>`_ from the journal of neuroscience methods.
+
+For a more in depth tutorial, in code, check out the
+`MNE Filtering Tutorial <https://martinos.org/mne/stable/auto_tutorials/plot_background_filtering.html>`_.
+
+.. glossary::
+
+    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
+----------------
+
+.. glossary::
+
+    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 <http://www.scholarpedia.org/article/Hilbert_transform_for_brain_waves>`_
+  * See also this
+    `deep dive into Hilbert methods <http://www.rdgao.com/roemerhasit_Hilbert_Transform/>`_
+    from VoytekLab member Richard Gao.
+* wavelet based approaches.
+
+.. glossary::
+
+    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.
+
+Spectral
+--------
+
+Many of the spectral methods available are based on the Fourier transform, for which there is an
+`interactive guide <https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/>`_
+by Better Explained and an
+`explainer video <https://www.youtube.com/watch?v=spUNpyF58BY>`_
+by 3Blue1Brown.
+
+.. glossary::
+
+    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.
+
+Simulations
+-----------
+
+For an overview of the aperiodic signals avaible in terms of their 1/f characteristics, check out this
+`article <http://www.scholarpedia.org/article/1/f_noise>`_
+from scholarpedia.
+
+.. glossary::
+
+    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.