Wavelets & Time-Frequency Analysis

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Abstractions about wavelet families, time-frequency representations, spatial-frequency filtering, multiscale transforms, and related sensing or imaging methods.

17 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.

• Absorbing boundary condition — An artificial computational boundary rule designed to let outgoing waves exit a truncated domain with minimal reflection.
• Discrete wavelet transform — Decompose a sampled signal into multiscale approximation and detail coefficients through paired analysis filters and decimation, with reconstruction governed by the chosen wavelet filter bank and boundary convention.
• Dual wavelet — A wavelet family biorthogonal to a primal wavelet family so analysis coefficients and synthesis functions reconstruct signals even when the basis is not orthonormal.
• Gabor wavelet — A complex sinusoid localized by a Gaussian envelope, providing near-minimal joint uncertainty in position or time and spatial or temporal frequency.
• Log Gabor filter — A band-pass signal filter whose transfer function is Gaussian on a logarithmic frequency axis, providing no DC component and flexible bandwidth for localized multi-scale analysis.
• Mathieu wavelet — A wavelet family constructed from periodic Mathieu functions and their associated filter coefficients.
• Modified Morlet wavelet — A localized oscillatory analyzing function formed by multiplying a cosine carrier by a hyperbolic-secant envelope and normalizing it for wavelet use.
• Non-separable wavelet — A multidimensional wavelet whose analyzing function or filter bank cannot be factored into tensor products of lower-dimensional wavelets.
• Pansharpening — Fuse a high-spatial-resolution panchromatic image with lower-spatial-resolution multispectral bands to estimate imagery that combines fine spatial detail with retained spectral information.
• S transform — A time–frequency transform combining a frequency-dependent Gaussian window with Fourier phase reference to localize nonstationary signal content.
• Spatial frequency — The rate at which a periodic or sinusoidal component repeats per unit distance, represented by reciprocal wavelength or angular wavenumber under an explicit cycles-versus-radians convention.
• Spline wavelet — A wavelet whose scaling functions or wavelets are constructed from spline spaces, combining multiresolution structure with piecewise-polynomial regularity.
• Standing wave ratio — The ratio of maximum to minimum standing-wave amplitude on a transmission line, quantifying impedance mismatch between line and load.
• TDR moisture sensor — A sensor that infers material moisture from the travel time and reflection of an electromagnetic pulse along embedded or contacting transmission-line probes.
• Time–frequency analysis — Represent a nonstationary signal jointly over time and frequency so changing spectral content, transients, and localization tradeoffs remain visible instead of being collapsed into one global spectrum.
• Time–frequency representation — A representation that distributes a signal’s amplitude, energy or power jointly over time and frequency.
• Transfer matrix — The block-Toeplitz linear operator induced by a refinement mask whose eigenstructure characterizes refinable functions and their regularity.