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Log Sampling in Time and Frequency: Preliminary Theory and Application

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The impulse response of real-world physical systems decays faster at high frequencies than low frequencies. This is due to the approximately constant Q behavior of the resonators that often make up these systems. Considerable efficiency can be obtained in digitizing, storing, and manipulating impulse-response data that has been sampled at a rate that starts high initially, and then falls inversely with time. This paper explores the concept, and develops an efficient log-log time-frequency transform that converts back and forth directly between log-spaced time samples and log-spaced frequency samples. A very efficient FIR convolver/equalizer configuration with logarithmically spaced time taps is described.

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