
doi: 10.5772/15902
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.
Quaternionic Windowed, Fourier Transform
Quaternionic Windowed, Fourier Transform
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