Signal Processing

Analog signals vary continuously, discrete-time signals exist at selected instants, and digital signals quantize values into a finite code alphabet; sampling and quantization are separate operations with different irreversible failures.

Sampling replicates a signal's spectrum at every multiple of the sample rate; aliasing is what happens when those copies overlap and fold high frequencies irreversibly onto low ones. Shannon's exact statement, the folding arithmetic, anti-alias filtering, oversampling, clock jitter, deliberate undersampling — and the same failure in metrics pipelines and images.

Quantization replaces an interval of input values with one code; its step sets the ideal error bound, while noise, nonlinearity, clipping, correlation, reference error, and converter architecture decide real dynamic range and effective bits.

A spectrum computed from a finite noisy record is an estimate, not a direct view of an infinite signal. This entry derives leakage from time-domain truncation, compares window tradeoffs, distinguishes bin spacing from resolution, and gives reproducible periodogram and Welch workflows with correct units.

The two filter families and what separates them — finite convolution with exactly linear phase versus feedback with poles you must keep inside the unit circle — and the result every metrics dashboard runs into: an exponential moving average is a one-pole IIR filter whose lag is exactly (1-α)/α samples, so more smoothing always buys more delay.

Filter design turns passband, stopband, phase, latency, and numerical constraints into coefficients that still meet the requirement after implementation. This entry connects FIR window and equiripple methods with analogue-prototype IIR design, bilinear prewarping, second-order sections, and verification against the original mask.

Acoustic systems exchange pressure and particle motion with electrical or digital signals. This entry derives level, impedance, intensity, spreading and near/far-field behavior, then connects them to microphone and loudspeaker directivity, sensitivity, loading, calibration, and room measurement.

Hearing maps a time-varying pressure field through a nonlinear, frequency-selective and adaptive biological system. This entry explains cochlear filtering, threshold and loudness, simultaneous and temporal masking, pitch, binaural localization, and the limits of standardized perceptual metrics.

Sonar estimates objects and environments from underwater sound, where refraction, absorption, surface and bottom interaction, reverberation, and platform self-noise dominate the link. This overview connects active and passive sonar equations to hydrophones, arrays, pulse compression, Doppler, cavitation, calibration, and a complete detection budget.

Image compression removes spatial redundancy and, for lossy coding, perceptually less important precision. This entry follows prediction, color transforms, chroma subsampling, block transforms, quantization and entropy coding; contrasts JPEG, PNG, WebP, JPEG 2000 and AVIF; and shows how to evaluate rate, artifacts, metadata and decode constraints together.

Speech codecs exploit vocal-tract structure, perceptual tolerance, and packet timing rather than treating voice as arbitrary audio. This overview connects PCM, LPC/CELP and transform coding to modern Opus and EVS operation, and makes bitrate, frame size, delay, packet loss, bandwidth, and tandem transcoding explicit tradeoffs.