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In this paper, we seek to determine the adequate number of samples for an analog filter function f(t). The proposed approaches provide discrete filters that can be used for multiresolution analysis. We introduce two methods that provide sampling results for localization: one of them defines an approximate Nyquist rate, and the other samples in a manner that ensures time-frequency consistency between the generated samples and the analog filter function. The key contribution of the paper is that it establishes robust mathematical and programmable foundations for a previously established empirical method. Analytically, we show that the time-frequency method is based on minimizing aliasing while maximizing decimation. The method can be programmed by introducing a mean square error (MSE) threshold across scales. Afterwards, we provide the outcomes of experiments that demonstrate success of localization with the proposed time-frequency method.

Efficient Time and Frequency Methods for Sampling Filter Functions