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.

Version: v1 · 2026-09-08 · History
Domain-specific #: 5622
Origin domain: wavelet analysis and signal processing
Subdomain: wavelet analysis and signal processing

Core Idea¶

The construction is motivated by bright-soliton profiles and differs from the Gaussian-envelope Morlet wavelet; admissibility, center frequency, normalization and exact mean correction depend on the cited convention. A sech pulse localizes the function in time, a cosine carrier introduces a tunable oscillation, and scale and translation generate a family for correlating signals with similarly localized frequency content. 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.

Scope of Application¶

Modified Morlet wavelet belongs to wavelet analysis and signal processing and is useful where the analyst can specify the typed wavelet analysis and signal processing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the real or complex convention, time variable, carrier angular frequency, hyperbolic-secant envelope, normalization, zero-mean or admissibility condition, Fourier transform, center frequency and bandwidth, scale and translation, inverse-transform requirements and comparison with ordinary Morlet are explicit.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the real or complex convention, time variable, carrier angular frequency, hyperbolic-secant envelope, normalization, zero-mean or admissibility condition, Fourier transform, center frequency and bandwidth, scale and translation, inverse-transform requirements and comparison with ordinary Morlet are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

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 Modified Morlet wavelet. Modified Morlet wavelet 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: the typed wavelet analysis and signal processing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of wavelet analysis and signal processing because they reuse the typed wavelet analysis and signal processing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, A sech pulse localizes the function in time, a cosine carrier introduces a tunable oscillation, and scale and translation generate a family for correlating signals with similarly localized frequency content., and type the carrier, state every parameter and convention in the definition, test that the real or complex convention, time variable, carrier angular frequency, hyperbolic-secant envelope, normalization, zero-mean or admissibility condition, Fourier transform, center frequency and bandwidth, scale and translation, inverse-transform requirements and comparison with ordinary Morlet are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Modified Morlet wavelet Domain-specific

Parents (1) — more general patterns this builds on

Modified Morlet wavelet is a kind of Wave Prime

The proposed strict upward parent is prime:wave.

Hierarchy path (1) — routes to 1 parentless root

Modified Morlet wavelet → Wave

Neighborhood in Abstraction Space¶

Modified Morlet wavelet sits in a crowded region of the domain-specific corpus (33^rd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Wavelets & Time-Frequency Analysis (17 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08