Signal Processing & Spectral Estimation

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Abstractions about sampling, transforming, estimating, filtering, and compressing signals. They cover Fourier and time-frequency methods, arrival-angle estimation, noise spectra, resampling and smoothing, signal-to-noise measures, denoising, bit errors, and rate adaptation.

23 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Adaptive differential pulse-code modulation — A predictive audio coding method that quantizes sample differences while adapting the quantizer scale to recent signal behavior.
• Angle of arrival — The direction from which a propagating radio, acoustic, optical, or other wavefront reaches a receiver or sensor array.
• Blahut–Arimoto algorithm — A family of alternating iterative optimization algorithms for channel capacity and rate-distortion problems that updates distributions until the information-theoretic objective converges.
• Chirplet transform — A time-frequency transform correlating a signal with localized chirps whose frequency changes within each analysis atom.
• Colors of noise — A classification of stochastic signals by the frequency dependence of their power spectral density.
• Constant-Q transform — A time–frequency transform whose analysis bins maintain a constant ratio of center frequency to bandwidth, producing logarithmic frequency resolution.
• Discrete Fourier transform — An invertible linear transformation between a finite sequence and coefficients on equally spaced discrete frequencies.
• Discrete-time Fourier transform — A periodic continuous-frequency function obtained by summing a discrete-time sequence against complex exponentials, representing the sequence by its spectral amplitudes.
• Estimation of signal parameters via rotational invariance techniques — A subspace method estimating frequencies, directions, or delays from the eigenstructure relating two overlapping sensor or sample subarrays.
• Lanczos resampling — Signal resampling by convolution with a finite-windowed sinc kernel.
• Linear time-invariant system — A system whose input-output operator obeys superposition and commutes with time shifts, making its response representable by convolution with an impulse response under suitable conditions.
• Lulu smoothing — A nonlinear sequence smoother built from alternating local lower and upper envelope operators that remove impulsive noise while preserving step structure.
• Modified Wigner distribution function — A member of a modified quadratic time–frequency representation family designed to suppress the interference cross-terms of the Wigner distribution while retaining useful concentration.
• Oversampling — Sampling a signal substantially above its Nyquist rate to ease antialias filtering, distribute quantization noise and improve effective resolution after filtering or decimation.
• Peak signal-to-noise ratio — A logarithmic full-reference fidelity metric comparing the squared peak representable signal value with mean squared error between a reference and a reconstruction.
• Polyphase matrix — A matrix of polyphase filter components that represents a multirate filter bank, making downsampling structure, perfect reconstruction and efficient implementation algebraically explicit.
• Residual bit error rate — The probability that a received bit remains wrong after the system’s error-detection or correction process.
• Sampling (signal processing) — The representation of a continuous-domain signal by values taken at discrete time, space or other-domain locations.
• Sensitivity index — A signal-detection statistic measuring separation between signal and noise distributions in standard-deviation units, commonly denoted d-prime.
• Signal averaging — The recovery of a repeatable signal by aligning repeated observations and averaging them so uncorrelated zero-mean noise cancels.
• Total variation denoising — A signal-reconstruction method that balances fidelity to observed data against a penalty on total variation so noise is reduced while sharp edges are retained.
• Twiddle factor — A precomputed complex root-of-unity coefficient used to combine subtransforms in fast Fourier transform algorithms.
• Variable bitrate — An encoding mode that varies the number of bits assigned per time segment so complex content receives more data and simple content less at a targeted quality or average rate.