Wave filter question (mainly for Joerg)

I'm taking the liberty of cross-posting this to the DSP group because you'll get a lot of good answers there, too.

I would look at either plain old bandpass filters of the form

(z+1)(z-1) H(z) = ------------------------- z^2 - 2 d cos(th) z + d^2

or I would consider modulating the incoming signal with inphase and quadrature versions of the tone you're looking for, and low-pass filtering the result.

Note that I do _not_ have the famous Goertzel filter on this list. Odd, that.

In the bandpass filter case you'll have to think carefully about the form of the filter; the states can easily overflow, and you sometimes need an astonishing precision to your variables for a high-Q filter.

If you are into tone detectors, don't use filters for detection. Filters are good to isolate the frequency spectrum of interest. Nothing more. If you want to detect a tone, you have to watch 3 parameters: frequency, allowed error and minimum duration. So what you want to know is whether the frequency of the signal is whithin spec. and how long the frequency is present. Both are easy to get from a signal.

Goertzel doesn't work for detecting tones reliably especially when a few percent of error is allowed.

Hi Nico,

How would you suggest obtaining "the frequency" (i.e., the major component of a signal) given that -- in a real system -- there's plenty of noise around? (Probably about 10dB SNR here...) What I'm used to in the continuous time domain is closer to what Tim suggested -- bandpass filter, rectify & low-pass filter the result. Frequencies error should be in the single-digit percentage ballpark, but may be as poor as, say, +/-10%.

I agree with both you and Tim that the Goertzel "filter" (the term filter being a bit of a stretch in my mind!) isn't at all robust.

Thanks for the help,

---Joel

Hello Joel,

Yes. You'll have to first design the analog structure and then transfer it. I don't know of any other design methodology.

Most of the stuff I have is in German so I guess that wouldn't help you. Professor Fettweis published his famous 1986 paper "Wave Digital Filters: Theory and Practice" which is still considered "the WDF paper". I don't have it but if you have access to IEEE-Explore you should find it.

I could send you some info about WDF. If interested let me know your real email address but it needs to be one where you can receive a huge file. Might be until tomorrow to get to the stuff though.

The design program I am using is the one from Professor Mildenberger:

There is also WDF design SW at Texas Instruments, from the group around Dr.Ulrich Kaiser. I only got it under the condition not to distribute but they told me that others can ask TI support for it. I like the Mildenberger SW better (but I understand German...)

Just don't expect any exhaustively documented software or fancy user interface. It's more like bare-bones race cars assuming you know how the fire extinguishing and all that works :-)

WDFs are pretty good at that if you have to do it on budget hardware, IOW when there are no leather seats and hardware multipliers. They are also very stable in the presence of disruptions, something that needs extra tricks on classical digital filters (but can also be done there).

Goertzel is another option as Tim mentioned. However, they will quickly clog your processor when you need to detect more than a handful of frequencies simultaneously. You'd have to "price out" whether a full FFT might be better in terms of economy.

Regards, Joerg

Thanks for the detailed reply, Joerg.

That's the paper I was looking for -- thanks for the title; I've downloaded a copy (it's old enough that it's scanned, but at least it's a PDF -- the copy with unknown whereabouts I have was Xeroxed...)

Let me digest a few other things first before you make the effort, but thanks for the offer. My real e-mail address is just removing "hates spam" at the end of snipped-for-privacy@yahoo.com.

Spanish I could do passably, but German... mmm... not so much. :-) I'll talk to TI and see what they have to say.

The hardware budget isn't tight, but there is plenty of noise (it's a wireless link). A full FFT might be worthwhile, since we actually have 17 tones to detect (not just 7 or 8 like DTMF does).

---Joel

Hello Joel,

That should give you the essence of wave digital filtering.

Ok, just let me know if you need more but with 17 tones I am not so sure WDF is the right approach.

It helps to have a glass of Spaten Optimator beforehand (Trader Joe's has it). Just don't drive after that :-)

If you can allow for a DSP or uC with a HW multiplier I'd consider the FFT. Look at the bandwidths you want for each tone. If they are all grossly different the FFT might become a bit large and you have to do binning. Sometimes individual DFTs (which is what the Goertzel essentially is) can be easier. The nice feature about FFTs and DFTs is that you can use a "routine in a can" for most architectures whereas something like a WDF usually needs to be coded by hand from scratch, more work.

Noise is one thing but more worrisome would be hard signal drop-outs. That can throw DFT stuff and especially IIR filters off the rocker. WDFs are said to be more tolerant against that but I never had a case where that was too much of a concern. Although it was nice to see how they never had a continuous little oscillation trailer when shorting the input for a brief moment.

Regards, Joerg

How about measuring the frequency (zero crossings)? Or using an adapted FFT which gives you precise frequency information

Hello Nico,

Zero crossers work nicely in a low noise environment put they really fall apart on noisy channels. Been there a lot, mostly for vascular Doppler apps.

Err, analog filters have a tendency to be unconditionally stable. That is one of the traits they bestowed on the digital world with WDF. Probably they did so kicking and screaming ;-)

Regards, Joerg

Indeed. :-)

I was at the local Wal*Mart today, Joerg, and guess what they had on clearance? HDTV (ATSC) to composite/S-Video/component/etc. converter boxes, all of $129 each! I wouldn't be surprised if they're not being replaced by a newer model, but rather Wal*Mart just won't sell such converters given what I suspect was a rather low uptake rate. (Something that probably won't change for a handful of years, by which point converters might be... $49?)

A newbie-level question...

I have no clue what the HDTV format is like.

Is it possible to convert HDTV with a block converter so I can continue to use my old composite TV sets?

I have 7 sets, 5 of which are over ten years old ;-)

...Jim Thompson

Hi Jim,

"Jim Thompson" wrote in message news: snipped-for-privacy@4ax.com...

Natively it's an MPEG-2 (compressed video) bitstream. "They" (the broadcasters) have a choice of a handful of different resolutions (see

Generally speaking, most true HD shows use a 16:9 aspect ratio (so a 4:3 TV set ends up with horizonal bars across the top and bottom) whereas SD programs stick to 4:3 (so a 16:9 TV set ends up with vertical bars across the left and right... although most 16:9 TV sets have options to distort and/or crop the image to fit the screen in various ways).

That's what the box I was describing does, although of course the quality of the end result is going to be limited by the analog connection -- hence the reason these boxes have component video outputs. I'd expect that with only composite inputs on a TV, the main features you'd get would be the elimination of show and ghosts rather than any noticeable resolution improvement (so probably no real benefit at all if you already have cable TV...).

If you visit antennaweb.org it'll show you nearby HDTV transmitters (and the bearing and distance to them); it looks like you have many to choose from there in Phoenix!

---Joel

Happened to stumble across Wal*Mart's web page with the converter box in question:

Now $129 on clearance at a Wal*Mart near you! (Although I believe that Wal*Marts set their clearance prices individually, so some could be higher or lower...)

Over-the-air is of no value to me... I have a serious mountain range in the way. I'm presently on Cox Cable Basic... I take no pay channels.

...Jim Thompson

Are you sure? At 10dB SN ratio the dominant frequency will still dictate the zero crossings. I have had excellent results with tone detectors based on zero crossings in telecommunications systems.

Perhaps filters is a field where there is not much to gain. But that is not the point I tried to make :-)

Hello Nico,

If you enter the world of correlators then, of course, analog is mostly out of range.

Regards, Joerg

In my experience digital filters are just as stable as analog ones as long as they are not oversteered and there is enough head room for the filter's Q factor. The latter is easely overlooked.

just widen the bandwidth (of the "filter") by using a window, then Goertzel

is more "error tolerant".

Gerold Schrutz

Still, the error margin will be smaller for high amplitude signals than for low amplitude signals.