Abstract:
Signal processing is a fast growing area today and the desired effectiveness in utilization
of bandwidth and energy makes the progress even faster. Special signal processors have
been developed to make it possible to implement the theoretical knowledge in an efficient
way. Signal processors are nowadays frequently used in equipment for radio, transportation,
medicine, and production, etc.In this paper, by using the adjoint operator of the (right-sided) QFT, we derive the Plancherel
theorem for the QFT. We apply it to prove the orthogonality relation and reconstruction
formula of the two-dimensional quaternionic windowed Fourier transform (QWFT). Our
results can be considered as an extension and continuation of the previous work of Mawardi
et al. (2008).We then present several examples to show the differences between the QWFT and
the WFT. Finally, we present a generalization of the QWFT to higher dimensions.
