ランダムパルス列用ディジタルフィルタ

抄録

When we want to use digital filters to process random pulse train inputs, we encounter some difficulty since the instants of the random input pulses do not usually coincide with the sampling instants of the filters. But we can avoid the difficulty, if we assume that the responses of the digital filter to an arbitrarily located input pulse are equal to the sampled values of the responses of the analog filter, which is derived from the digital filter by impulse invariant transformation, to the same pulse. Using this relation, we can realize a kind of fast recursive filters as follows.
1. Design a usual recursive filter with required response characteristics. The parallel form realization is desirable for several reasons.
2. For each input pulse, compute initial values of this filter using the impulse invariant analog filter.
3. Compute further responses recursively, as usual, by solving the difference equations of the filter.
In most practical cases, the above filter is several times as fast as the direct convolution type filter.