This discussion brings back memories of when I worked on FIR filter design many years ago, and I would add the following to the simple aspects that can be understood without math.
The digital signal is of course a string of numbers representing samples from the analog waveform, just like the numbers coming off a music CD. The FIR filter works on some number N of the latest signal samples and uses all these N numbers to compute one output number. Then the oldest remembered number is dumped, and a new sample is entered, and the process repeats. Suppose there is a step change in the input samples. This will not reach its full impact on the output until the new sample level has propagated into all of the memorized samples that are used to compute the output. The FIR filter has a delay which is roughly the number N times the sample interval. However, it doesn't remember anything beyond this time span, as nothing except the past N samples can affect each output value. Now, suppose we change the computation of output samples so that this rule is broken. Just as an example, say that we use the N latest inputs as before, but also take the previous OUTPUT value into account when we compute the next output value. Now, that previous OUTPUT value is affected by at least one older input value, so the new output value is affected by more than N input values. This effect compounds, so that every output value theoretically is affected by all old input values. Thus an Impulse on the input keeps on infinitely affecting the output (theoretically). Hence "Infinite Impulse Response". The flanks of a FIR bandpass filter get steeper with increasing number N of input samples used in the calculation of each output. This results in increasing delay. We just don't hear the other station immediately. Obviously there is a tradeoff between delay and selectivity. The other day a list member posted carefully measured selectivity curves of the K3 with various DSP filter widths and roofing filters (along with similar measurements on 1000MP). I just glanced over the graphs, but to me it looked like the K3 DSP filter flanks were far from "brick wall" in terms of shape factor; off the top of my head, the crystal filters may have been sharper than the DSP in terms of skirt falloff for a given bandwidth setting. This brings new light on the debate as to whether you really need those extra roofing filters. I am sure that the K3 designers made an intelligent decision as to the tradeoff between DSP passband shape and DSP delay. Does anyone know the number of N for the current FIR filters? I assume that the sampling frequency would be about 30 kHz for the 15 kHz IF frequency. Erik K7TV >The infinite response of the IIR filter is usually not, in and of >itself, a problem. Even an FIR filter has to have a long "tail" >(ringing) in order to get a good shape factor. An FIR and IIR filter of >the same bandwidth and shape factor will tend to have similar ringing >characteristics out to the point where the FIR filter's ringing ends >(and the IIR filter's ringing continues). But the ringing is often >inaudible by that time anyway. > >Al N1AL -- View this message in context: http://n2.nabble.com/Question---for-Educational-Purposes-tp580366p580996.html Sent from the Elecraft mailing list archive at Nabble.com. _______________________________________________ Elecraft mailing list Post to: Elecraft@mailman.qth.net You must be a subscriber to post to the list. Subscriber Info (Addr. Change, sub, unsub etc.): http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/subscribers.htm Elecraft web page: http://www.elecraft.com
