[sdiy] Shift-based IIR filters

[Scott Gravenhorst]

Tom Wiltshire <tom at electricdruid.net> wrote:
 >This topic has been discussed here before, but I wanted to draw
 >people's attention to the following discussion on StackExchange:
 >
 >
 >http://electronics.stackexchange.com/questions/30370/fast-and-memory-efficient-moving-average-calculation
 >
 >There's a very good explanation of how to do a single pole
 >RC-style IIR filter on a basic processor using downshifts for the
 >multiplication (one shift right is "x0.5", so you can get any
 >coefficient like 1/2^n without doing hard sums).
 >
 >Realising that a byte-shift is even more efficient than a bit
 >shift, I did a 8-bit input, 16-bit filter variable IIR filter
 >which provides a slow filter (since the coefficient is 1/256) and
 >only requires five instructions and two bytes of memory to
 >calculate. Cascade it if you need more rolloff.
 >
 >Enjoy,
 >Tom

Ah, yes, I've used this form.  Eric Brombaugh showed me this one some 
years ago for an FPGA synth project.

It's works fine as long as the cutoff you need is close enough using one 
of the shifted values, but if you need a variable cut-off, it loses 
resolution at one end...   0.5  0.25  0.125  0.0625  are rather large 
jumps.  After rewriting the synth code to share multipliers, I replaced 
this form with the standard   in*a0+z*b1  form because I needed a smooth 
linear change from low cutoff to high cutoff (such as is needed for 
portamento).

Useful nonetheless in many cases.

-- ScottG