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.
Core Idea¶
A Log-Gabor filter has a Gaussian-shaped frequency response in log frequency, commonly combined with angular selectivity for image analysis. Multiplication in the Fourier domain selects a ratio-scaled frequency band; inverse transformation yields a localized oscillatory response with extended high-frequency tail and zero response at DC. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
The load-bearing residual is not the broad topic of signal processing. It is constant-ratio bandwidth frequency analysis with no DC response, often organized into scale-orientation banks.
Scope of Application¶
Log Gabor filter belongs to signal processing and is useful where the analyst can specify a one- or two-dimensional signal, Fourier frequency coordinates, center frequency, logarithmic bandwidth, orientation, a transfer function, and filtered responses, then evaluate the radial response is Gaussian as a function of log frequency around a positive center and vanishes at zero frequency under the defined convention. The scope is broad within that domain but bounded by the need for the radial response is Gaussian as a function of log frequency around a positive center and vanishes at zero frequency under the defined convention. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the radial response is Gaussian as a function of log frequency around a positive center and vanishes at zero frequency under the defined convention the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Log Gabor filter can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Log Gabor filter. Log Gabor filter compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: a one- or two-dimensional signal, Fourier frequency coordinates, center frequency, logarithmic bandwidth, orientation, a transfer function, and filtered responses. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the radial response is Gaussian as a function of log frequency around a positive center and vanishes at zero frequency under the defined convention independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of signal processing because they reuse a one- or two-dimensional signal, Fourier frequency coordinates, center frequency, logarithmic bandwidth, orientation, a transfer function, and filtered responses, Multiplication in the Fourier domain selects a ratio-scaled frequency band; inverse transformation yields a localized oscillatory response with extended high-frequency tail and zero response at DC., and type the carrier, state every parameter and convention in the definition, test that the radial response is Gaussian as a function of log frequency around a positive center and vanishes at zero frequency under the defined convention, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Log Gabor filter Domain-specific
Parents (1) — more general patterns this builds on
-
Log Gabor filter is a kind of Structural Filtering Prime
The proposed strict upward parent is
prime:structural_filtering.
Hierarchy path (1) — routes to 1 parentless root
- Log Gabor filter → Structural Filtering → Selection
Neighborhood in Abstraction Space¶
Log Gabor filter sits in a moderately populated region (49th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Wavelets & Time-Frequency Analysis (17 abstractions)
Nearest neighbors
- Gabor wavelet — 0.90
- Rectangular function — 0.89
- S transform — 0.89
- Discrete Fourier transform — 0.88
- Discrete-time Fourier transform — 0.88
Computed from structural-signature embeddings · 2026-09-08