| Popis: |
The Heisenberg Uncertainty Principle provides a well-known constraint on time-frequency analysis. In FIR digital filtering, the concept is normally tangentially addressed through the FIR design via windowing methods, where the normal filtering constraints (passband ripple, stopband rejection, and the width of the transition region) all conspire, with the appropriate window function, to determine an appropriate filter length. However, there is a second implication of the Uncertainty Principle that also ties the wordlength of the FIR digital filter implementation to the (normalizing) sampling frequency, f s . As the sampling frequency f s increases, the quality of the digital filter must correspondingly increase, because the passband band-width decreases. It is well known in classical FIR window designs that this necessitates a longer filter. But, it also necessitates a more precise amplitude representation. We develop this unstudied problem both theoretically and physically in this paper. We give a basic result that can be used to predict, and thus to compensate, for this problem. We find that for fixed point implementations of even low sample rate audio systems, the impact is significant. |
