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Interpolating Linear- and Log-Sampled Convolution

This paper describes a class of FIR filter/convolvers based on interpolation that allow sparse specification of the filter’s impulse-response waveform or equivalently its frequency spectrum in both linear-and log-spaced domains. Interpolation allows the filter 's impulse response or frequency response to be specified in significantly fewer samples. This is turn means that farless filter taps are required. Linear-and log-sampled interpolating filter/convolvers can further be categorized into two types: Type 1, interpolation in time, and Type 2, interpolation in frequency. Type 1 provides direct specification of the filter’s impulse response in linear or log time, while Type 2 allows direct specification of the complex (real-imaginary) frequency response of the filter in linear or log frequency. Each form of filter vastly reduces the number of filter taps but greatly increases the processing complexity at each tap. Efficient implementations of the log-spaced filter-convolvers are presented which use multiple asynchronous sample-rate converters. This paper is a continuation of the author 's" Log Sampling "paper presented to the AES in Nov. 1994. This paper represents work in progress with a conceptual description of the convolution technique with minimal mathematical development.

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