Hello,
Sounds like your referring to what's called a finite response filter or FIR. It takes in samples and passes those signals along (in a digital format) like a shift register (if your a digital guy) or a bucket brigade (for old analog guys ;).
The newest sample is always coming in one side of the sequence, while the oldest one is going to bit heaven. The number of samples being held, altogether, is referred to as the number of taps or filter length.
Now, comes the stranger part - why they call it taps. Essentially, you can make a great many different responses with this filter - some that seem almost impossible.
To do this your neighbourhood underpaid mathmatician (or over paid engineer with software) comes up with a table of values. There's one value for each "tap" (stored sample). Each time a new sample comes in, the DSP runs through every stored sample, multiplies it with the corresponding value from the table, and adds up the sum of all those multiplications. The total of all that addition is the output of the filter.
Having to multiplying every single sample and add it is a lot of work, considering the DSP must do so every single time a new sample comes in. So DSP are designed to be able both multiple and add in the same instruction. Also, they can do this to long strings of numbers (like all the samples you're holding) without having to be told over and over. Essentially they're told where to get it, how many to do, and chip will multiply and add till the sequence is done.
Now, as to the impulse response. If you have only one sample that has a value and all of the rest are zero, then that one sample would be an impulse. For an FIR filter, you would expect that impulse to come out looking different at different times depending on how far it's shifted through the taps and what the corresponding table value looks like. In any case, you know that once the impulse has shifted to the end of the filter, it's gone. Hence the expression "Finite" Impulse Response.
Some filters feed part of their output back into an earlier stage of the filter. Hence theoretically, an impulse will never altogether reach zero. It will keep getting smaller, but there's always a piece that's left over and it goes back in. Such filters are referred to as Infinite Impulse Response (IIR) filters. To me, these remind me more of my treasured analog filters, though of course you still have to go through some math to get one to work - sigh...
Well, as to application. The FIR filters are great. Not great. WONDERFUL, at communications processing. They have a lot of delay, going through all those taps, but they can filter a mesquito buzz out of a car crash. They can be updated in real time for noise cancelation and echo reduction. They're just good and wholesome. AND, if you know what you're doing they're not all that difficult to design.
As to IIR filters, well... They have a place. I like em as resonators and "digital" oscillators, and they're pretty good for lead-lag networks in control systems. FIR's have that whole thing with process delay, so generally they're not considered good stuff for closed loop control.
Well, I hope this helps a bit. I do ramble on at times...
Best Wishes and good luck on your work,
Mike
