  This paper presents a new family of localized orthonormal bases - sinlets -
which are well suited for both signal and image processing and analysis.
One-dimensional sinlets are related to specific solutions of the time-dependent
harmonic oscillator equation. By construction, each sinlet is infinitely
differentiable and has a well-defined and smooth instantaneous frequency known
in analytical form. For square-integrable transient signals with infinite
support, one-dimensional sinlet basis provides an advantageous alternative to
the Fourier transform by rendering accurate signal representation via a
countable set of real-valued coefficients. The properties of sinlets make them
suitable for analyzing many real-world signals whose frequency content changes
with time including radar and sonar waveforms, music, speech, biological
echolocation sounds, biomedical signals, seismic acoustic waves, and signals
employed in wireless communication systems. One-dimensional sinlet bases can be
used to construct two- and higher-dimensional bases with variety of potential
applications including image analysis and representation.
