Digital IIR Filter with variable cutting frequency

[therealpaulie]

Hi,

I want to design a IIR low pass filter with variable cutting frequency. The order should be > 10. Order 1 or 2 is simple to be made. But when it comes to order > 4 the equation are pretty big and it's not feasibly anymore.

I don't search for something very precises. I need resolution for the Fc (cutting frequency) and not accuracy. E.g.: to be able to vary Fc with one step = pi/64, but the actual value doesn't have to be pi/64.

I though about designing several filters (for example with Matlab) and save the coefficients to a RAM. There are two problems: 1. RAM is required and 2. I want to be able to adjust the filter Fc when the system works. And if I change the entire set of coefficients I could have jumps in the output signals.

It doesn't really matter what type of filter. I only need small ripple in pass band (Chebyshev -I- an example that doesn't fit).

Any link, any idea, any hint is welcomed.
Thanks,
Paulie

 

[FvM]

The order should be > 10. Order 1 or 2 is simple to be made. But when it comes to order > 4 the equation are pretty big and it's not feasibly anymore.

There's no such thing as a free lunch.
But basically the effort is increasing linearly. One more order means just one more denominator and numerator coefficient. So I don't exactly understand the problem.
Changing the filter setting abruptly must be generally expected to create unwanted output signals. Changing it slowly, using interpolated intermediate coefficients would be one option.

I only need small ripple in pass band (Chebyshev -I- an example that doesn't fit).

Chebyshev ripple can be made as low as you want it. But if you want 0.00x dB ripple, simply use butterworth.

 

[therealpaulie]

Hi,

Thanks for answer.

The problem, or how I see it, is the following:
- if I use a simple IIR filter (Direct Form I) i will need more than 25bits for storing the coefficients. I started with a simple Low Pass filter (1+z^-1)/(1-a x z^-1). But if I add more poles and zeroes I need more than 25bits to store the coefficients. For small Fc and high (4,5 and so on) filter order the coefficients are way to small (1 * 10^-5 or so).
- I wanted to implement a Chebyshev II or a Butterworth but the transfer functions are not that simple, and I didn't find out a way in which I can vary (liniary) only one parameter in order to change the Fc.

Paul

 

[FvM]

When saying the effort rises linearly, I didn't particularly consider coefficient ranges. I aggree, that they may effectively increase the effort when going to higher order. With a common filter prototype, I would expect all coefficients to change when scaling the frequency. I didn't yet hear of an elegant trick to overcome it. Perhaps other forum members know?