So, the set of equations that I suggested elsewhere pretty much implement what you claim to want, you can use d = 2^-N, which implies a shift, and
-- as I stated -- you can use some delay in the "servo to average value" step.
So what's your problem again?
Equations reiterated:
u: input y: output x: state variable
y[n] = u[n] - x[n-1] x[n] = d * y[n]
-- Tim Wescott Wescott Design Services http://www.wescottdesign.com
Something can't be right with these equations.
Let us say we have had signal for awhile with a DC component.
u[n] now goes to that value.
By definition, y[n] should be 0, and thus so would x[n]
if u[n+1] has that same value again, y[n+1] = u[n+1] and not 0 as required,
The equations I tend to use for something like this is:
y[n]= u[n] = x[n-1] x[n] = x[n-1] + k*y[n]
(k being some power of 0.5 so the multiply is a shift.) x often needing additional fractional bits, especially if k is very small.
op links to this doc
looking into above document I got a bit curious; to get rid of truncation dc
bias why add fraction of truncation when you can just use rounding to nearest integer or to nearest even.
Kaz
--------------------------------------- Posted through
Not knowing your exact requirements, the simplest I can see would be a running average of a large number of samples, and subtract that.
E.g total = total + sample(n) - sample(n-2048), output = sample-total/2048.
The division would be a bit shift, and the 2k of samples could be held in a ram block.
It is pretty trivial to show that DC would be blocked, and signals at f/2048 will not be attenuated (as the average would be zero).
It would also be very fast and have minimal latency, however it would introduce some phase distortion as it isn't symetrical.
If that is an issue for your application, then a way around it would be to total over 2047 samples, and subtract the total from 2047*sample(n-1024), then divide by 2048 (once again this can be implemented with addition, subtraction and bitshifts). The output will be slightly attenuated (by 1/2048), but no phase distortion would occur. It will also have a latency of 1024 cycles or so.
Mike
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