Audio_signal_processing

# Audio signal processing **Audio signal processing** is the branch of [[Signal_processing|signal processing]] devoted to the electronic manipulation of sound: filtering, transforming, compressing, synthesizing and analyzing audio signals, the electrical or numerical stand-ins for the pressure wave of [[Sound|sound]] itself. A microphone turns that wave into a voltage, and from that point on, a tone control, a broadcast transmitter, a hearing aid and a music streaming service are all, at bottom, pieces of audio signal processing. The same operation can run in either of two domains. An analog processor reshapes the voltage directly, with resistors, capacitors and active devices standing in for the mathematics; a digital processor runs arithmetic on samples of that voltage taken at a fixed rate. The two domains meet at a converter that measures one and rebuilds the other. The microsim on this page builds the simplest processing chain there is: a synthesized harmonic tone pushed through a first-order low-pass filter and an output gain stage. Dragging the cutoff frequency, the source's harmonic content and the gain shows, in the time waveform and the frequency spectrum together, the property every linear, time-invariant effect shares — it can only reshape and delay energy already in the signal, and can never add energy the source did not have. ## History Systematic processing of audio signals began with the telephone network, whose amplifiers, loading coils and filters were analog circuits shaping a voice-frequency voltage decades before "signal processing" was a course title. A landmark in treating speech itself as a signal to be pulled apart and rebuilt was Homer Dudley's vocoder work at [[Bell_Labs|Bell Labs]], demonstrated to the public as the Voder at the 1939 New York World's Fair: a keyboard-operated synthesizer that built voice-like sound from a small set of resonance controls, foreshadowing every source–filter model of speech used since.[^dudley1939] The move to digital audio needed a theory of how densely a continuous signal must be sampled to be rebuilt exactly, given by [[Claude_Shannon|Claude Shannon]]'s 1949 sampling theorem, itself built on Harry Nyquist's earlier work on telegraph transmission.[^shannon1949] Digital processing became practical once a spectrum could be computed quickly: the Cooley–Tukey fast Fourier transform, published in 1965, cut the cost of a discrete Fourier transform from order N-squared to order N-log-N and made real-time digital filtering and analysis feasible outside a research laboratory.[^cooleytukey1965] Perceptual audio coding carried digital audio the rest of the way into everyday use, compressing a recording by discarding what the ear is least likely to hear; the resulting [[MP3]] format, a form of lossy [[Data_compression|data compression]] developed at the Fraunhofer Institute and standardized internationally, made digital music practical to store and transmit at ordinary bit rates.[^mp3cite] ## Types ### Analog An analog processor works on the [[Analog_signal|analog signal]] itself: a continuously varying voltage that stands in for the sound pressure wave at every instant. Tone controls, mixing consoles, tape saturation and most of a century of broadcast processing are built from [[Filter_(signal_processing)|filters]] made of resistors, capacitors, inductors and active gain stages, and their nonlinear cousins — a valve amplifier driven into clipping, or magnetic tape driven into saturation — add a characteristic, and often prized, [[Distortion|distortion]] rather than reproducing the input exactly. Everything an analog stage does happens in continuous time, at the speed of the circuit, with no notion of a sample. ### Digital A digital processor instead works on numbers: samples of the voltage taken at a fixed rate and held to a fixed resolution, produced by an [[Analog-to-digital_converter|analog-to-digital converter]] and turned back into a voltage, when needed, by a [[Digital-to-analog_converter|digital-to-analog converter]]. Between those two boundaries, [[Digital_signal_processing|digital signal processing]] is arithmetic: a filter is a short program — a [[Finite_impulse_response|finite impulse response]] is nothing more than a weighted sum of recent samples — and a spectrum is computed rather than swept out with a tuned circuit. Two constraints govern every digital audio system that an analog one never faces. The sampling rate must clear the signal's bandwidth by the [[Nyquist–Shannon_sampling_theorem|Nyquist–Shannon sampling theorem]] or frequencies fold back into the audible band as aliases, and every sample is rounded to a finite number of bits, a [[Quantization_(signal_processing)|quantization]] step that sets a noise floor no amount of later processing removes. Once a signal is a sequence of numbers, though, an effect can be made exact and endlessly repeatable in a way no analog circuit, with its component tolerances and drift, ever quite manages. ## Applications ### Audio broadcasting Radio and television transmission chains apply audio signal processing before a signal ever reaches a transmitter: level control keeps loud passages from over-modulating the carrier, and pre-emphasis boosts high frequencies before transmission so a matching de-emphasis filter at the receiver can pull them back down and, with them, pull down high-frequency noise picked up along the way — the same low-pass-and-gain logic the microsim on this page works through in miniature. [[Amplitude_modulation|Amplitude modulation]] and [[Frequency_modulation|frequency modulation]] radio, and their digital successors, each impose their own limit on how much of that processing a broadcaster can apply before the audio is audibly changed. ### Active noise control [[Active_noise_control|Active noise control]] processes a microphone's pickup of unwanted noise quickly enough to generate a matching waveform, inverted in phase, and add it back into the sound field so the two cancel. Noise-cancelling headphones and cabin-quieting systems in aircraft and cars are the familiar examples, and the technique works best on low-frequency, repetitive noise, where the inverted wave can be computed and reproduced before the original has moved on. ### Audio synthesis Synthesizing a voice or an instrument from parameters, rather than recording one, is audio signal processing run in reverse: a source signal rich in harmonics of a single fundamental frequency is shaped by a resonant filter standing in for a vocal tract or an instrument body, the source–filter model behind both the vocoder and much of speech synthesis.[^johnson013] For a fundamental of 110 hertz, a typical adult male pitch, the waveform repeats roughly every 9 milliseconds, and the resonant filter's peaks — the formants — sample that harmonic series far more finely for a low voice than for a high one, since a higher fundamental spaces the harmonics further apart under the same fixed set of resonances.[^johnson013] The same idea, run as [[Speech_coding|speech coding]], represents a voice by the parameters of that model instead of by its waveform, at a small fraction of the bit rate plain sampling needs. ### Audio effects Most of what a listener would call "an effect" is a deliberate, audible piece of processing rather than an attempt at transparency: [[Dynamic_range_compression|dynamic range compression]] narrows the gap between the loudest and quietest passages, [[Reverberation|reverberation]] adds the reflections of a room the original recording did not have, and equalization reshapes the balance between frequency bands. All three can be built from the same low-pass-and-gain building block the microsim demonstrates, chained and parameterized differently. ### Computer audition Machine listening asks a computer to do what a listener does without thinking: find the pitch of a note, separate a voice from background noise, or recognize a word. A common way to estimate pitch is to correlate a segment of the waveform with a copy of itself shifted by a lag and look for the lag of the strongest match; on a segment sampled at 44.1 kilohertz, a peak at a lag of 101 samples implies a fundamental frequency near 437 hertz, with the neighboring lags of 100 and 102 samples bracketing it between roughly 441 and 432 hertz.[^downey058] This autocorrelation approach pins pitch far more finely than a spectrum of the same short segment can resolve it, which is why pitch detectors favor it over reading a peak off a [[Spectrogram|spectrogram]]. A related technique, the [[Cepstrum|cepstrum]], takes the spectrum of the logarithm of the spectrum to separate a source's fine harmonic structure from a filter's broad resonances — the same source–filter split used above for synthesis, run here to analyze a recording instead of to generate one. [[Machine_learning|Machine learning]] and other [[Artificial_intelligence|artificial intelligence]] techniques now do much of this work statistically, trained on large collections of labeled audio rather than programmed with an explicit acoustic model. ## Microsims The primary microsim, *Audio signal processing*, builds an audio processing chain from two stages: a first-order low-pass filter set by a cutoff-frequency control, and an output gain stage set in decibels. A third control, timbre, sets how quickly the harmonics of the synthesized source tone fall off, from a bright, sawtooth-like sound toward something close to a pure tone. Because a linear, time-invariant chain like this one can only redistribute energy already present, the spectrum bars can only shrink as the cutoff is lowered, never grow, and the time-domain waveform loses its sharp corners at exactly the harmonics the filter removes. A diagnostics readout tracks the spectral centroid — the signal's brightness — and the output level, both updating live as the controls move; in the sketch, the filter rolls harmonics above the cutoff off at 6 decibels per octave, the standard first-order rate. A companion three.js sketch renders a related idea in more depth: the spectrogram of a harmonic tone with added vibrato. *Try:* Lower the cutoff toward 120 hertz and watch the waveform round off while the spectrum bars duck under the rolloff curve, then raise the timbre control and watch the same cutoff remove far more of a brighter source. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Audio_signal_processing) : [Wikitube](https://en.wikitube.io/wiki/Audio_signal_processing) Skeleton mirrored at revision 1366840803. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Dynamic_range_compression]] - [[Reverberation]] - [[Active_noise_control]] - [[Digital-to-analog_converter]] - [[Spectrogram]] - [[Cepstrum]] - [[Nyquist–Shannon_sampling_theorem]] - [[MP3]] ## References The Fourier description of a harmonic tone and the roll-off of a first-order low-pass filter used in the microsim above are standard textbook material and are not separately footnoted, per the Wikitube style guide §6.1. [^dudley1939]: Dudley, H. "Remaking Speech." *Journal of the Acoustical Society of America*, 1939, 11(2), pp. 169–177. [^shannon1949]: Shannon, C. E. "Communication in the Presence of Noise." *Proceedings of the IRE*, 1949, 37(1), pp. 10–21. [^cooleytukey1965]: Cooley, J. W.; Tukey, J. W. "An Algorithm for the Machine Calculation of Complex Fourier Series." *Mathematics of Computation*, 1965, 19(90), pp. 297–301. [^mp3cite]: Citation needed: the exact year the Fraunhofer Institute's MPEG-1 Audio Layer III standard was finalized and the ".mp3" file extension adopted. [^johnson013]: Johnson, D. *Fundamentals of Electrical Engineering I*. 2014, p. 130 (source–filter speech model; formant filter; typical pitch periods). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. [^downey058]: Downey, A. *Think DSP: Digital Signal Processing in Python*. 2012, p. 71 (autocorrelation pitch estimate from the lag of the first strong peak). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python . CC BY-NC. ## Further reading - Don Johnson. *Fundamentals of Electrical Engineering I*. 2014. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 - Allen Downey. *Think DSP: Digital Signal Processing in Python*. 2012. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory*. 2026. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory