02 · FOURIER TRANSFORM
FFT Visualizer
The Fast Fourier Transform decomposes a time-domain signal into its constituent frequency components. A 1024-point FFT reveals 512 frequency bins, each representing a narrow band of the audio spectrum from 0 Hz to the Nyquist frequency.
220 Hz
6
1024
Hann
03 · TEMPORAL SUSPENSION
Spectral Freeze
Spectral freeze captures a frame of frequency-domain data and sustains it indefinitely. The result is a pitched, reverb-like drone — the spectral snapshot of a transient instant held outside of time. Pioneered by Max Mathews at Bell Labs.
30%
0.20
0 st
04 · PHASE ANALYSIS
Phase Vocoder Explorer
The phase vocoder analyses overlapping short-time frames of audio, tracks instantaneous frequency via phase derivatives, and resynthesises at altered time and pitch. Decoupling time and pitch — the fundamental operation of modern timestretching.
1.00×
0 st
256
0 st
05 · IMPULSE RESPONSE
Convolution Engine
Convolution multiplies a signal's spectrum with an impulse response spectrum, stamping the acoustic character of any captured space onto any audio signal. Concert hall acoustics, hardware gear emulation, extreme creative processing.
Hall
2000ms
10ms
40%
06 · SPECTRAL INTERPOLATION
Spectral Morphing Systems
Interpolating between two spectral envelopes creates timbral transitions impossible in the time domain. Cross-synthesis stamps the frequency character of one sound onto the temporal energy of another — voice shaped by string, thunder becoming piano.
Violin
Synth
50%
0%
07 · PRACTITIONERS
Spectral Artists
Jean-Claude Risset
Computer Music Pioneer · IRCAM
Curtis Roads
Microsound · Granular Theory · UCSB
Tristan Murail
Spectral Music · IRCAM · Composer
Gérard Grisey
Founder · Spectral Music Movement
Kaija Saariaho
Spectral + Electronics · Helsinki
Spectral de la Salle
Institut de Recherche Musicale
Philippe Manoury
Live Electronics · IRCAM · Score
Peter Norvig
FFT Signal Analysis · AI Research
08 · REFERENCE
Spectral Lexicon
FFT (Fast Fourier Transform)
Algorithm computing the Discrete Fourier Transform in O(N log N) time. Converts N time-domain samples into N/2 complex frequency-domain bins, each representing amplitude and phase at a specific frequency.
Spectral Freeze
Capturing a single FFT frame and continuously resynthesising it. Creates sustained, pitch-stable drones from any transient moment. Implemented in Max/MSP pfft~, Ableton Grain Delay, Paul's Extreme Stretch.
Phase Vocoder
Analysis/resynthesis system tracking instantaneous frequency via phase differences between overlapping FFT frames. Enables independent time and pitch manipulation — the basis of modern audio timestretching algorithms.
Short-Time Fourier Transform
FFT applied to windowed segments of a signal, producing a time-frequency representation (spectrogram). The window size determines frequency vs. time resolution — a fundamental tradeoff governed by the Heisenberg uncertainty principle.
Convolution
Mathematical operation multiplying two signals' frequency spectra. In audio: stamps the impulse response of any acoustic space onto a source signal, creating reverberation that perfectly emulates that environment.
Impulse Response
The response of a system to a Dirac impulse (infinitely short, infinitely loud click). Captures the complete acoustic character of a space or device. Convolved with any audio to impose that character.
Spectral Morphing
Interpolating between the spectral envelopes of two sounds, gradually transitioning timbre from one to the other. Creates hybrid timbres impossible to achieve through synthesis alone.
Cross-Synthesis
Using the spectral envelope of one sound to filter another — the frequency character of a vowel imposed on a string quartet, thunder's spectral shape stamped onto a piano chord.
Window Function
Taper applied to each FFT frame to reduce spectral leakage. Hann (cosine bell), Hamming, Blackman, and Kaiser windows trade main-lobe width against side-lobe suppression.
Spectral Leakage
Energy from one frequency bin appearing in adjacent bins due to non-integer periods within the FFT window. Minimised by windowing functions at the cost of frequency resolution.
Bin
A single frequency-domain sample output by an FFT. An N-point FFT produces N/2 bins, each representing a frequency range of (sample_rate / N) Hz. Bin width determines frequency resolution.
Overlap-Add (OLA)
Method for time-domain reconstruction from overlapping STFT frames. Modified frames are added with the correct overlap to produce continuous output. The basis of spectral processing and resynthesis.
Spectral Subtraction
Noise reduction technique estimating noise spectrum from a silent frame and subtracting it from subsequent frames in the frequency domain. Creates characteristic artefacts (musical noise) when pushed aggressively.
Formant
Resonant peak in a spectral envelope, primarily associated with vowel sounds in voice. Formant shifting independently from pitch is a key application of phase vocoder technology — voice character without pitch change.
Partial
An individual sinusoidal component in a complex sound. Harmonic partials have frequencies that are integer multiples of the fundamental; inharmonic partials create bell-like, metallic, or noisy timbres.
Resynthesis
Reconstructing a time-domain signal from spectral analysis data. Allows independent manipulation of amplitude, phase, and frequency of individual partials before reconstruction — additive synthesis from analysis.
Spectral Centroid
The weighted mean frequency of a spectrum — the "centre of mass." Perceptually correlates with brightness. High spectral centroid = bright sound; low = dark, dull. Fundamental audio feature for classification.
Spectrogram
2D representation of spectral content over time: x-axis = time, y-axis = frequency, pixel brightness = amplitude. The primary visual representation of audio in spectral editors (iZotope RX, Spectral Layers).
Pitch Detection
Estimating the fundamental frequency of a pitched sound from its spectrum — either via autocorrelation (YIN algorithm), cepstrum analysis, or machine learning models trained on labelled pitch data.
Cepstrum
The Inverse FFT of the log magnitude spectrum. The quefrency peak indicates the fundamental period of a pitched signal. Used for pitch detection, formant analysis, and echo removal algorithms.
Mel Spectrogram
Spectrogram with frequency axis warped to the Mel scale — perceptually uniform frequency spacing. The primary input representation for most deep learning audio models (speech recognition, music classification).
MFCC
Mel-Frequency Cepstral Coefficients — compact spectral shape representation derived from the Mel spectrogram's cepstrum. Standard feature set for speech recognition, timbre classification, and audio ML since the 1980s.