This Paper Introduces a Generalized Running Discrete Transform with Respect to Arbitrary Transform Basea, and Relates the Generalized Transform to the Running Discrete Fourier Z and Short-Time Discrete Fourier Transforms. Concepts Associated with the Running and Short-Time Discrete Fourier Transforms Such as 1) Filter Bank Implementation, 2) Synthesis of the Original Sequence by Summation of the Filter Bank Outputs, 3) Frequency Sampling, and 4) Recursive Implementations Are All Extended to the Generalized Transform Case. a Formula is Obtained for Computing the Transform Coefficients of a Segment of Data at Time N Recursively from the Transform Coefficients of the Segment of Data at Time N – 1. the Computational Efficiency of This Formula is Studied, and the Class of Transforms Requiring the Minimum Possible Number of Arithmetic Operations Per Coefficient is Described. © 1982, IEEE. All Rights Reserved.
J. A. Stuller, "Generalized Running Discrete Transforms," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 30, no. 1, pp. 60 - 68, Institute of Electrical and Electronics Engineers, Jan 1982.
The definitive version is available at https://doi.org/10.1109/TASSP.1982.1163848
Electrical and Computer Engineering
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01 Jan 1982