Home > On-Demand Archives > Talks >

## Interpolated FIR (IFIR) Digital Filters

Rick Lyons - **Watch Now** - DSP Online Conference 2024 - Duration: 25:38

This presentation delves into the theory, operation, and design of very efficient linear-phase interpolated FIR (IFIR) digital filters.

**Harry**

**RichardLyons**Speaker

Hello Harry. You're right in that a detailed comparison of narrowband 'IFIR filters', narrowband 'multi-rate FIR filters', and narrowband 'Frequency Sampling filters' would be useful. Creating such a comparison would require a fair amount of effort.

I hadn't seen your referenced MATLAB "Narrow Transition-Band FIR" web page before today. Sadly I don't have the MATLAB toolbox to run the code on that web page. However, I'm suspicious of that MATLAB IFIR filter example. The first thing that troubled me was that the IFIR example had the desired passband ripple and stopband attenuation specified to a precision of one ten thousandth of a dB! No practicing DSP engineer would specify those desired parameters to such an unrealistic precision.

The second thing that troubled me about that MATLAB IFIR filter example was that the IFIR's Image Reject filter magically turned out to be a "5th band" FIR filter having four out of every five coefficients being zero-valued. What are the chances this was accidental(!)? Yep, that MATLAB IFIR filter example troubles me.

Postscript: Thinking more about this, I'll assume that the MATLAB IFIR example was written by Mathworks employee Ric Losada who is indeed a very skilled DSP engineer.

**Hilmar**

Great talk, very thorough, informative, and hands on. I really enjoyed it.

Last year, I gave a presentation on Warped FIR filters , which is a close cousin. Instead of replacing the single tap delays with longer delays, you replace it with an first order allpass. Instead of squeezing and replicating the original spectrum, this warps the frequency axis so you only end up with a single image and don't need the rejection filter. The warped image is probably less steep, so I actually have no idea which method would be more efficient in your example.

Off course, both a multi-tap delay and a 1st order allpass are "general allpass" filters. It may be fun to explore combining the two: Higher order allpasses would give you warping AND image replication. Maybe there is an optimum there somewhere.

**RichardLyons**Speaker

Hello Hilmar. Sadly I'm not familiar with Warped FIR filters. Because of you have some learning to do. I thought there was a presentation on Warped FIR filters, by Hilmar Lehnert, in this conference, but now I can't find that presentation.

**Hilmar**

Yep, that was me last year: See https://www.dsponlineconference.com/session/Introduction_to_Warped_FIR_Filters

VERY similar concept: replace the delays in the FIR filter with something else and see what happens :-)

**RichardLyons**Speaker

Hello Hilmar. OK, great. I'll watch your presentation. Thanks a lot.

Thank you for this really interesting presentation. I wonder how IFIR filters compare with multi-rate FIR filters (decimation followed by interpolation). MATLAB's online documentation includes an article "Efficient Narrow Transition-Band FIR Filter Design", which looks at both architectures. In their one specific example, the multi-rate FIR filter requires fewer multiply-accumulates per input sample than the IFIR filter. But I suspect IFIR would come out on top in other scenarios. Now, I wish I knew how to choose!

Thanks again for sharing this really fascinating filter architecture!