Glossary

Glossary#

An alphabetical reference of the key terms in this book. Click a term to jump to where it first appears.

Note

The definitions on this page were AI-generated from the passage where each term first appears. They may contain mistakes. When in doubt, click the term to read it in context, and trust the book’s text.

A B C D E F G H IJK L M N O P Q R S T U V WXYZ

A

additive synthesis #: Building a periodic tone by summing \(K\) sinusoidal harmonics, each with its own amplitude \(a_k\) and initial phase \(\phi_k\). The fundamental \(f_0\) sets the pitch, and the relative amplitudes mostly set the timbre.
ADSR #: A common four-phase envelope shape: attack (rise from silence), decay (fall from the peak), sustain (hold steady while the note is held), and release (fade back to silence). Usually only the sustain stretches with note length.
aliasing #: Distortion that occurs when a signal is sampled too slowly, so frequencies above the Nyquist frequency masquerade as lower ones. A frequency \(f\) produces exactly the same samples as its aliases \(f + k f_s\) for any integer \(k\).
all-pass #: A filter that leaves the amplitude of every frequency unchanged and alters only the phase.
amplitude #: The peak deviation of a waveform from zero. A basic sinusoid \(a \sin(\cdot)\) stays within \([-a, a]\), and larger amplitudes sound louder.
amplitude modulation #: Multiplying a carrier by a modulator that oscillates around a nonzero average, \(\sin(\omega_c t)\,[1 + \sin(\omega_m t)]\). It equals ring modulation plus the carrier, so the spectrum keeps the carrier alongside two sidebands.
amplitude spectrum #: The magnitude \(|X(\omega)|\) of the Fourier transform, which tells how much of each frequency a signal contains. It is real and non-negative, and is used far more than the phase spectrum because the ear is largely insensitive to phase.
angular frequency #: Frequency measured in radians per second instead of cycles per second, \(\omega = 2\pi f\). It lets the basic sinusoid be written compactly as \(a \sin(\omega t + \phi)\).
anti-aliasing filter #: A filter applied before sampling (or before downsampling) that removes content above the Nyquist frequency, so that nothing is left to alias.
antinode #: A point halfway between the nodes of a standing wave, where the medium oscillates with the largest amplitude.

B

band-pass #: A filter that passes a band of frequencies around a center frequency and rejects everything else.
band-stop #: A filter that rejects a band of frequencies around a center frequency and passes everything else. Also called a notch.
bandwidth #: The width of a band of frequencies. For a band-pass filter it is \(f_H - f_L\), the distance between the two frequencies where the response crosses \(-6\) dB.
baseband #: The central, unshifted copy of a signal’s spectrum, spanning \([-f_{\max}, f_{\max}]\). Sampling replicates the baseband around every multiple of \(f_s\).
basic sinusoid #: The simplest periodic function, \(x(t) = a \sin(2\pi f t + \phi)\), with frequency \(f\), amplitude \(a\), and initial phase \(\phi\). It sounds like a pure tone, and any periodic sound can be built as a sum of basic sinusoids.
beat #: A symbolic unit of musical time referring to the underlying pulse, what you might tap your foot to.
bin #: One of the \(N\) evenly spaced analysis frequencies of the DFT, indexed by \(k\). Bin \(k\) sits at \(k f_s / N\) Hz, so adjacent bins are \(\Delta f = f_s/N = 1/T\) apart.
block #: The name for a frame in real-time audio. The audio system repeatedly asks a program for the next \(B\) samples, which is frame-based processing with \(N_H = N_F = B\).
butterfly #: The combining step of the FFT, which merges two half-size DFTs \(E[k]\) and \(O[k]\) into \(X[k] = E[k] + W_N^k O[k]\) and \(X[k + N/2] = E[k] - W_N^k O[k]\) in \(O(N)\) time.

C

carrier frequency #: In modulation synthesis, the frequency of the carrier, the signal whose amplitude or frequency is being modulated. Written \(\omega_c\) in radians per second or \(f_c\) in Hz.
circular buffer #: An array with a pointer to its oldest entry, used to implement a delay line. Each step reads the oldest sample, overwrites it with the newest, and advances the pointer, wrapping from the end back to the start.
comb filter #: A filter whose magnitude response has evenly spaced peaks, like the teeth of a comb. A feedback delay line of \(M\) samples is a comb filter that boosts whole-number multiples of \(\frac{f_s}{M}\) and rejects the frequencies in between.
commuted synthesis #: Reordering and regrouping the filters of a physical model (delays, losses, low-pass filters) into whatever order is cheapest to compute. This is valid because LTI filters commute, as long as we only listen at points the reordering does not disturb.
complex sinusoid #: The complex-valued signal \(a e^{j\omega t} = a\cos(\omega t) + j\,a\sin(\omega t)\). It is a vector of length \(a\) rotating around the complex plane, whose real part traces a cosine and whose imaginary part traces a sine.
constant overlap-add #: A property (COLA) of a window \(w\) and hop length \(N_H\) where the shifted windows sum to a non-zero constant at every sample. It guarantees that overlap-adding windowed frames reconstructs the signal up to a scale factor.
control point #: A pair \((t_i, a_i)\) that fixes an envelope’s value \(a_i\) at time \(t_i\). A piecewise-linear envelope interpolates linearly between consecutive control points.
convolution #: The operation \(y[n] = \sum_{k=0}^{K-1} h[k]\, x[n-k]\), written \(y = h * x\), which sums weighted, delayed copies of the input. Every LTI filter can be written as a convolution with its impulse response.
convolution reverb #: A reverb effect made by convolving a dry recording with the recorded impulse response of a real space, so it sounds as if it were played in that space.
convolution theorem #: The result that convolution in the time domain equals multiplication in the frequency domain: if \(y = h * x\), then \(Y[k] = H[k] \cdot X[k]\). Its dual says multiplication in time equals convolution in frequency.
critical sampling #: Sampling at exactly twice the highest frequency, \(f_s = 2 f_{\max}\). A component right at \(f_s/2\) may vanish depending on its phase, so perfect reconstruction is not guaranteed.
crossfade #: Gradually fading one piece of audio out while fading another in. Samplers crossfade at each wrap of a sustain loop to hide the mismatch between the loop’s end and its start.
cutoff frequency #: The frequency \(f_C\) marking the boundary between a filter’s passband and stopband. For a real filter it is conventionally where the response has fallen to a threshold such as \(-6\) dB.

D

dB SPL #: Decibels of sound pressure level, measured relative to the threshold of hearing \(p_0 = 20\) μPa, so \(\text{dB SPL} = 20\log_{10}(p/p_0)\).
dBFS #: Decibels relative to full scale, using the reference amplitude \(a_0 = 1\), so \(\text{dBFS} = 20\log_{10}(a)\). Values are normally negative, and 0 dBFS is the clipping point.
decibel #: A logarithmic unit (dB) that compares an amplitude \(a\) to a reference \(a_0\) as \(20\log_{10}(a/a_0)\). Doubling an amplitude adds about 6 dB, and multiplying it by 10 adds 20 dB.
delay line #: A filter that outputs its input \(M\) samples later, \(y[n] = x[n - M]\). In physical models it simulates the time a wave takes to travel through a medium.
depth #: In frequency modulation, the amount \(D\), in Hz, by which the instantaneous frequency wavers above and below the carrier frequency \(f_c\).
difference equation #: A formula that defines a filter by expressing each output sample \(y[n]\) in terms of input samples and possibly past output samples, such as \(y[n] = x[n] + x[n-1]\).
digital filter #: A function \(g\) that maps an array of input samples \(x\) to an array of output samples \(y\), written \(g : x \mapsto y\).
digital waveguide #: A physical model that represents the right-going and left-going waves on a string with two delay lines running in opposite directions. Reflections at the ends multiply by \(-1\), and summing the two lines at a point gives the string’s displacement there.
discrete Fourier transform #: The DFT, a version of the Fourier transform that a computer can evaluate on \(N\) samples, \(\texttt{DFT}(x)[k] = \sum_{n=0}^{N-1} x[n]\, e^{-2\pi j k n / N}\). It maps \(N\) samples to \(N\) complex bins.
drum machine #: A sequencer whose interface is a grid of steps. Each row is a drum sound, each column is a subdivision of a beat, and the musician switches cells on or off.
dynamic range #: The span between the quietest and loudest levels a system can represent or a listener can hear, measured in dB. Each bit of depth adds about 6 dB, so 16-bit audio has about 96 dB.

E

envelope #: A function \(\text{Envelope}(t)\) with values in \([0, 1]\) that is zero outside a finite time window. Multiplying a sustained tone by an envelope shapes its loudness over time and turns it into a finite sound event.
Euler’s formula #: The identity \(e^{j\theta} = \cos\theta + j\sin\theta\). It places \(e^{j\theta}\) on the unit circle at angle \(\theta\) and links polar and rectangular form.
event #: Something that happens at a specific point in time and carries parameters describing it, such as a note with a pitch and a duration. In Pyquist an event is a pair of a time and a dict of keyword arguments.

F

fast Fourier transform #: The FFT, a divide-and-conquer algorithm that computes the DFT exactly in \(O(N \log N)\) time instead of \(O(N^2)\), by splitting it into two half-size DFTs over the even- and odd-indexed samples.
feedback coefficient #: One of the weights \(a_j\) in a recursive difference equation that multiply past outputs \(y[n-j]\).
feedforward coefficient #: One of the weights \(b_i\) in a difference equation that multiply the current and past inputs \(x[n-i]\).
filter #: Broadly, any function that takes a signal as input and produces another signal as output. In everyday usage the word is shorthand for a linear time-invariant filter, which reshapes a sound’s spectrum.
finite impulse response #: FIR, an impulse response that ends after finitely many samples. A filter with only feedforward coefficients has one, equal to those coefficients.
foldover #: Aliasing of frequencies just above the Nyquist frequency, in \([f_s/2, f_s]\), which reflect back below it as if the Nyquist frequency were a crease in a folded sheet of paper.
Fourier series #: The result that any periodic signal with fundamental frequency \(f_0\) can be written as a constant plus a sum of sinusoids at integer multiples of \(f_0\), \(x(t) = a_0 + \sum_{k} a_k \sin(2\pi k f_0 t + \phi_k)\).
Fourier transform #: The function \(X(\omega) = \int_{-\infty}^{\infty} x(t)\, e^{-j\omega t}\, dt\), which maps each angular frequency to a complex number describing how much of that frequency \(x(t)\) contains and at what phase. It works by multiplying the signal by a phasor and integrating over time.
frame #: A contiguous chunk of \(N_F\) samples extracted from a signal. The \(k\)-th frame starts at sample \(k \cdot N_H\), so \(x_k[n] = x[k \cdot N_H + n]\).
frame length #: The number of samples \(N_F\) in each frame.
frame rate #: The number of frames per second, \(f_s / N_H\) for a signal sampled at \(f_s\) with hop length \(N_H\).
frame-based processing #: A family of techniques that chop audio into chunks called frames and analyze or manipulate those frames. It lets us work at musically intuitive rates of tens to hundreds of times per second.
frequency #: The number of cycles a periodic signal completes per second, measured in Hertz. The fundamental frequency is the reciprocal of the fundamental period, \(f_0 = 1/t_0\), and is the property most strongly tied to perceived pitch.
frequency domain #: A view of a sound in terms of how much of each frequency it contains, such as its amplitude spectrum. It complements the time-domain waveform \(x(t)\).
frequency modulation #: Synthesis in which a modulator varies the carrier’s frequency over time, giving \(\sin(2\pi f_c t + \frac{D}{f_m} \sin(2\pi f_m t))\). At audio rates it creates a theoretically infinite series of sidebands at \(f_c \pm k f_m\) from just two oscillators.
fundamental period #: The smallest positive \(T\) for which a periodic signal satisfies \(x(t + T) = x(t)\), written \(t_0\). It is the duration of one cycle.

G

grain #: A tiny slice of sound, typically tens of milliseconds long, used as the building block of granular synthesis.
granular synthesis #: Chopping a sound into many grains, then transforming and rearranging them (changing their order, amplitude, duration, pitch, or density) to build a new sound.

H

Hann window #: A window shaped like a raised cosine that tapers smoothly from zero at both ends to a peak in the middle. Its spectrum has much smaller side lobes than the rectangular window’s, so it causes less spectral leakage.
Hertz #: The unit of frequency, abbreviated Hz. One hertz is one cycle per second.
high-pass #: A filter that passes frequencies above its cutoff and rejects those below, for example to remove low-frequency rumble.
hop length #: The spacing \(N_H\), in samples, between the start of one frame and the start of the next.

I

impulse response #: A filter’s output when fed the unit impulse \(\delta\). It fully characterizes an LTI filter, and for the convolution \(h * x\) it is just \(h\).
impulse train #: A function that is 1 at every sampling instant \(t = n/f_s\) and 0 everywhere else, written \(\text{Ш}_{f_s}(t)\). Sampling can be modeled as multiplying a signal by an impulse train.
index of modulation #: In frequency modulation, the unitless ratio \(I = D/f_m\) of the depth to the modulating frequency. Larger \(I\) spreads energy into more sidebands, with roughly \(I + 1\) audible on each side of the carrier.
infinite impulse response #: IIR, an impulse response that never ends. Recursive filters generally have one because feedback keeps copying past outputs forward.
initial phase #: The constant offset \(\phi\), in radians, that shifts where a sinusoid starts within its cycle. Changing it has almost no audible effect.
instantaneous phase #: The total phase of a sinusoid at time \(t\), \(\theta(t) = \omega t + \phi\), in radians. It grows by \(2\pi\) every period, and the sinusoid can be written \(x(t) = a \sin(\theta(t))\).
inverse DFT #: The IDFT, which exactly reconstructs \(N\) time-domain samples from \(N\) DFT coefficients via \(\texttt{IDFT}(X)[n] = \frac{1}{N}\sum_{k=0}^{N-1} X[k]\, e^{+2\pi j k n / N}\).
inverse FFT #: The IFFT, a fast algorithm that computes the inverse DFT in \(O(N \log N)\) time using the same divide-and-conquer strategy as the FFT.

K

Karplus-Strong algorithm #: A plucked-string synthesis algorithm that fills a feedback delay line with a burst of white noise and recirculates it through a low-pass filter and a gain, \(y[n] = x[n] + g \cdot \tfrac{1}{2}(y[n - M] + y[n - M - 1])\). The delay \(M = \mathrm{round}(f_s / f)\) sets the pitch.

L

linear #: A property of a filter \(g\) that respects gain and mixing, so \(g(A x) = A\, g(x)\) and \(g(x_1 + x_2) = g(x_1) + g(x_2)\).
linear time-invariant #: Describes a filter (LTI) that is both linear and time-invariant. LTI filters can only boost or attenuate frequencies already present, and every LTI filter is a convolution with its impulse response.
low-pass #: A filter that passes frequencies below its cutoff and rejects those above, making a sound darker or more muffled.

M

mode of oscillation #: A standing wave that an object supports. On a string of length \(L\) with fixed ends, the modes have wavelengths \(\lambda_i = \frac{2L}{i}\) and frequencies \(f_i = i \cdot \frac{v}{2L}\), which are harmonics.
modulating frequency #: In modulation synthesis, the frequency of the modulator, the signal that alters the carrier. Written \(\omega_m\) in radians per second or \(f_m\) in Hz.
modulation synthesis #: A family of techniques that affect a property of one signal, the carrier, with another oscillating signal, the modulator. It produces rich, time-varying spectra from only a few oscillators.
multisampling #: Recording an instrument at several pitches across its range and repitching whichever recording is closest to the target pitch. Keeping the shift small keeps the result realistic.

N

node #: A point on a standing wave that never moves. On a string, nodes occur every half wavelength, and fixed ends are always nodes.
notch #: Another name for a band-stop filter, especially one that removes a narrow band such as a single hum frequency.
Nyquist frequency #: Half the sampling rate, \(f_s/2\). It is the highest frequency that can be unambiguously represented in a signal sampled at \(f_s\).
Nyquist-Shannon sampling theorem #: The theorem that a signal with no content above \(f_{\max}\) can be perfectly reconstructed from its samples, provided \(f_s > 2 f_{\max}\).

O

order #: The number of samples of memory a filter needs, equal to the largest delay in its difference equation, \(\max(M, L)\).
overlap #: The fraction of a frame shared with the next frame, \(\frac{N_F - N_H}{N_F}\). It is non-zero when the hop length is shorter than the frame length.
overlap-add #: Reassembling a signal from frames by shifting each frame \(x_k\) back to its position \(k \cdot N_H\) and summing, \(\hat{x}[n] = \sum_k x_k[n - k \cdot N_H]\).

P

passband #: The range of frequencies that a filter lets through.
periodic #: A signal \(x(t)\) is periodic if it repeats exactly after some fixed time \(T > 0\), so that \(x(t + T) = x(t)\) for all \(t\).
phase #: A sinusoid’s position within its cycle, measured in radians. The book distinguishes the constant initial phase \(\phi\) from the time-varying instantaneous phase \(\theta(t)\).
phase increment #: In wavetable synthesis, how far the read position advances through the table per output sample, \(\Delta m = f_0 M / f_s\). It is usually not an integer, so reads often land between table entries.
phase spectrum #: The angle \(\angle X(\omega)\) of the Fourier transform, giving the phase of each frequency component in \((-\pi, \pi]\). It matters mainly when reconstructing a signal from its spectrum.
phase vocoder #: A spectral-processing algorithm that time-stretches audio without changing its pitch by interpolating STFT frames. It resolves the \(2\pi\) ambiguity in each bin’s phase by predicting how much the phase should advance over one hop.
phasor #: Another name for a complex sinusoid \(a e^{j\omega t}\), pictured as a vector of length \(a\) rotating counterclockwise once every \(1/f\) seconds. Like the basic sinusoid, it is a function of time.
physical modeling synthesis #: Synthesizing sound by directly simulating the physics of an instrument, so that properties like harmonics emerge on their own instead of being synthesized explicitly.
pitch class #: The set of all frequencies separated from \(f\) by whole numbers of octaves, \(\{f \cdot 2^i \mid i \in \mathbb{Z}\}\). Listeners hear its members as the same note in different registers.
polar form #: Writing a complex number by its magnitude \(r\) and angle \(\theta\), as \(z = r e^{j\theta}\). In polar form, multiplication multiplies magnitudes and adds angles.
polyphonic #: Having many notes sound at the same time. A score represents this with multiple events that share a timestamp.

Q

quality factor #: Written \(Q\), a measure of a band filter’s selectivity, equal to center frequency over bandwidth, \(Q = f_C / (f_H - f_L)\). A high \(Q\) gives a narrow resonant peak and a low \(Q\) a broad, gentle one.
quantization #: Rounding each sample to one of a finite set of levels so it can be stored in \(b\) bits. Unlike sampling, it is lossy and cannot be undone.
quantization noise #: The irreversible rounding error introduced by quantization, heard as noise. Each additional bit halves it, lowering it by about 6 dB.

R

rectangular form #: Writing a complex number as \(z = x + jy\), with real part \(x\) and imaginary part \(y\). Also called Cartesian form.
rectangular window #: The simplest window, equal to 1 on the interval of interest and 0 outside. Analyzing any finite stretch of audio implicitly applies one, and its abrupt edges cause strong spectral leakage.
recursive filter #: A filter whose difference equation also uses past outputs \(y[n-j]\), not just inputs. Feedback lets it achieve good frequency responses with few coefficients, but its impulse response is generally infinite.
resampling #: Changing the sample rate of already-sampled audio by reading it at interpolated fractional positions. Lowering the rate requires anti-alias filtering first.
Riemann sum #: An approximation of an integral as a sum of thin rectangles. The book uses it to turn the phase integral \(\int_0^t \omega(\tau)\, d\tau\) into the running sum \(\theta[n] = \theta[n-1] + \omega[n]\,\Delta t\) over samples.
ring modulation #: Multiplying two sinusoids, \(\sin(\omega_c t) \sin(\omega_m t)\). The result contains sidebands at the sum and difference frequencies \(\omega_c \pm \omega_m\), while the original frequencies disappear. Slow modulation is heard as tremolo.

S

sample-based synthesis #: Pre-recording musical material and manipulating it on the fly to change its expressive parameters, such as pitch, duration, and loudness. It sounds realistic and is cheap to compute, but uses a lot of memory.
sampling #: In the musical sense, lifting a clip of audio (a sample) from one recording and reusing it in another context, often with some manipulation. This is distinct from digital sampling in analog-to-digital conversion.
sampling rate #: The number of samples recorded per second, \(f_s\). Sampling a continuous signal \(x(t)\) gives \(x[n] = x(n/f_s)\).
score #: A symbolic description of music as a set of timed events. In Pyquist a score is a list of events, and it says when sounds happen while instruments decide what they sound like.
semitone #: A relative pitch unit, also called a step. Raising a frequency by \(k\) semitones multiplies it by \(2^{k/12}\), so 12 semitones make an octave.
sequencing #: Playing samples back in different orders or with different timing than in their original recordings, as when building new beats from fragments of old ones.
short-time Fourier transform #: The DFT of each frame of a signal, which shows how its frequency content evolves over time. Abbreviated STFT, it is invertible via overlap-add.
sideband #: New frequency content that modulation creates on either side of a carrier. Ring and amplitude modulation produce two sidebands at \(\omega_c \pm \omega_m\), while frequency modulation produces a whole series at \(f_c \pm k f_m\).
signal-flow diagram #: A directed graph showing how signals move through a system. Processing elements such as unit generators, multipliers, summing junctions, or delay blocks are connected by wires that carry signals between them.
spectral leakage #: The smearing of each true frequency into neighboring frequencies that comes from analyzing a finite, windowed slice of a signal. It happens because the spectrum is convolved with the window’s own spectrum.
spectral processing #: Transforming a sound into the time-frequency domain with the STFT, editing the spectral coefficients, and transforming back with the inverse STFT.
spectrogram #: A two-dimensional image of the STFT magnitudes, with time on the horizontal axis, frequency on the vertical axis, and amplitude (usually in log scale) shown as color.
standing wave #: A wave that oscillates in place rather than traveling. It forms when waves traveling in opposite directions, such as reflections on a string fixed at both ends, superimpose.
stopband #: The range of frequencies that a filter rejects.
subtractive synthesis #: Synthesis that starts from a harmonically rich source, such as noise or a sawtooth, and carves away frequencies with filters (often time-varying) to shape a timbre.
superposition #: The principle that when two waves overlap, the displacement of the medium at each point is the sum of their individual displacements. It is a physical example of linearity.
sustain loop #: A section \([t_s, t_e)\) of a recording’s sustain that is repeated as many times as needed to lengthen a note, while the attack and release play once.

T

tempo #: The rate of beats, usually measured in beats per minute (BPM).
timbre #: The attributes of a sound that let us recognize it as a distinct instrument or component, independent of pitch and loudness. In additive synthesis it is shaped mainly by the relative amplitudes of the harmonics.
time domain #: A view of a sound as a waveform \(x(t)\) that gives its amplitude at each instant. It mirrors how sound physically reaches our ears or microphones.
time stretching #: Changing the duration (and hence playback speed) of audio without changing its pitch. Granular synthesis does this by reassembling grains at a different hop length than the one used to extract them.
time-invariant #: A property of a filter for which delaying the input simply delays the output by the same amount, so filtering and delaying can happen in either order.
transcription #: Converting audio into a symbolic representation of its notes, such as a score. A crude version picks the loudest pitch in each STFT frame.
transition band #: The region between a real filter’s passband and stopband, where its response slides gradually from the cutoff level (such as \(-6\) dB) down to a fully rejected level (such as \(-60\) dB).
tremolo #: A performance technique that periodically varies a note’s amplitude while keeping its pitch constant. It can be synthesized with slow ring or amplitude modulation.

U

unit generator #: A reusable function that produces or processes sound, such as an oscillator, an envelope, or a multiplier. Unit generators are combined into larger topologies to build instruments and effects.
unit impulse #: The signal \(\delta = [1, 0, 0, \ldots]\), a single one followed by zeros. It is the identity for convolution, \(\delta * x = x\).
unstable #: Describes a recursive filter whose impulse response grows without bound instead of decaying, as with \(y[n] = x[n] + 1.1\, y[n-1]\).

V

vibrato #: A performance technique in which the fundamental frequency wavers periodically over time. It can be synthesized as frequency modulation with a slow, shallow modulator.

W

wagon-wheel effect #: A visual form of aliasing in which a spoked wheel on film appears to slow, stop, or spin backwards because the camera’s frame rate samples its rotation too slowly.
wave #: A disturbance that transfers energy through a medium, like a string or the air. Each particle of the medium is displaced temporarily and returns to rest, so the disturbance travels but the medium does not.
wavelength #: The distance \(\lambda\) a sinusoidal wave travels during one cycle, which is the distance between neighboring peaks. For frequency \(f\) and speed \(v\), \(\lambda = \frac{v}{f}\).
wavetable #: An array of \(M\) samples holding exactly one cycle of a waveform. It is computed once and then read repeatedly to produce a tone.
wavetable synthesis #: An efficient alternative to computing additive synthesis sample by sample. One cycle of the waveform is precomputed into a wavetable, which is then read repeatedly at the rate that gives the desired frequency.
white noise #: A random signal whose samples are independent and identically distributed with mean zero. Its spectrum is flat on average, so it excites all frequencies at once.
window #: A function that is zero outside an interval of interest and non-negative inside it. Multiplying a signal by a window restricts analysis, such as the DFT, to a finite segment.

Z

zero-pad #: To fill missing samples with zeros, as when a final frame runs past the end of a signal.