1. Implementing STFT via CWT Framework
By replacing the variable-scale kernels of CWT with a fixed-scale complex exponential function,
STFT can be perfectly implemented as a special case within the same convolution-based computational framework.
(1) Mathematical Perspectives on STFT
(2) Mathematical Perspective for Implementing STFT via CWT/FCWT
While a standard CWT adaptively adjusts window lengths according to scale(frequency),
the STFT implementation within this framework maintains a fixed window length across all frequencies (f1 to f8).
2. Principle
By substituting variable-scale wavelets with fixed-length STFT kernels (windowed sinusoids),
the STFT can be seamlessly implemented within the CWT or FCWT framework.
This approach leverages the high-speed computational engine of FCWT to perform short-time spectral analysis at a constant resolution.
3. Why Unified FCWT/STFT
We are now capable of implementing the STFT by leveraging the existing CWT/FCWT engine.
This unification maximizes computational efficiency by processing both STFT and CWT through a single, high-performance FFT engine.
It offers seamless flexibility to switch between fixed and multi-resolution analysis without redundant framework overhead.
Radar Sensor SoC & Module
WiFi IoT Module
5G/LTE/CAT-M1/NB-IoT
WiSUN/HaLow/Thread Module
