sinewt

Sinewt is a term that appears in informal or exploratory discussions of waveform modeling and time–frequency analysis. It does not have a single established definition in formal mathematics, but is commonly used to describe a sine wave whose amplitude is modulated by a window or weight function, producing a finite-duration burst rather than an infinite periodic signal.

Mathematically, sinewt is often defined as sinwt(x) = sin(x) · w(x), where w(x) is a real-valued window function. A typical and widely used choice is a Gaussian envelope w(x) = exp(-x^2/(2σ^2)), with σ controlling the width of the envelope. Other smooth, even windows such as the Hann or Hamming windows may also be employed. The exact form of w(x) determines the time localization and spectral characteristics of the resulting signal.

Properties of sinewt follow from its components. If w is even, then sinwt is an odd function. Because w is generally not periodic, sinwt is not strictly periodic and often has finite energy, especially when w(x) → 0 as |x| → ∞. The function is primarily a tool for illustrating how windowing affects the behavior of a sine signal in the time and frequency domains.

Applications include modeling short-duration carriers in signal processing, studying spectral leakage, and teaching concepts related to modulation and time–frequency resolution. In such uses, sinewt helps demonstrate how a base sinusoid can be localized in time through windowing.

History and usage notes indicate that sinewt is not part of a formal mathematical canon; it is a descriptive construct used in examples, simulations, and pedagogical discussions to contrast pure sinusoids with windowed, time-localized equivalents.