The importance of crossover steepness

[gberchin]

Originally Posted by CopperTop

Yes, sorry. What is the best description? "Gaussian-derived"?

No, because that conflicts with the "Gaussian-derived" highpass section.

My vote is for "higher-order Gaussian-like". It's a mouthful, but at least it's not ambiguous.

Edit: I enclose the results for Gaussian-derived (not too late to change that wording) at 2.0 (indicated as "Gaussian"), 3.0 and 4.0. Even the difference between a true 2.0 and the previous example of order 1.98 (or was it 2.02?) is noticeable.

Thank you. It really shows how "special" the true Gaussian response is. Interestingly enough, in the higher-order Gaussian-like cases, the impulse response does not appear to be significantly better than what you call the "standard" filters, which are approximations to classical filters like Butterworth and Bessel.

[steph_tsf]

Apology my gross ignorance. How do you manage to get preshoot and ringing, with negative values, on your so-called "Gauss" lowpass ?

Here is the code I'm using for generating a Gauss FIR and I don't understand how to enhance it for getting preshoot and ringing.

Gauss = Me.FIR2_Box1.Text
FIR2_coeff(m) = 1
For i As Integer = 1 To n
arg = i / Gauss
val = Math.Exp(-arg * arg)
FIR2_coeff(m + i) = val
FIR2_coeff(m - i) = val
Next

Steph

[CopperTop]

Originally Posted by steph_tsf

How do you manage to get preshoot and ringing, with negative values, on your so-called "Gauss" lowpass ?

In post #72, gberchin provided this information, which is what I have been using:

The equation for the frequency response magnitude of a Gaussian lowpass filter is:
exp{+[|f/fc|^2]*ln(1/2)},
where |f/fc| means "absolute value". (I hope that I didn't mess that up; I worked it quickly on some scrap paper.) The highpass filter will be 1 minus the lowpass filter.

For higher-order "Gaussian-like" filters of order "N", the lowpass filter is:
exp{+[|f/fc|^N]*ln(1/2)}. Again, the highpass filter will be 1 minus the lowpass filter. I believe that the corresponding highpass filter will have an "Nth-order" slope.

[steph_tsf]

Originally Posted by CopperTop

In post #72, gberchin provided this information: magnitude of a Gaussian lowpass filter is: exp{+[|f/fc|^2]*ln(1/2)}

Now I understand, thanks. I'm attaching the corresponding design form.

[CopperTop]

Any experts on patents here?

Just looking at the Neville Thiele patent for crossover filter with notched response:
http://www.pat2pdf.org/patents/pat6854005.pdf

Claim 19 says the following

19. A method of tuning a filter system including a low pass filter having a response which rolls off towards a crossover frequency and a high pass filter having a complementary response which rolls off towards said crossover frequency such that the combined amplitude response of said filters is substantially constant at least in the region of said crossover frequency, said method including the steps of:
selecting a filter topology capable of realizing a low pass complex transfer function defined by a first numerator and a first denominator;
selecting a filter topology capable of realizing a high pass complex transfer function defined by a second numerator and a second denominator;
setting the second denominator so that it is substantially the same as the first denominator; and
setting the squared modulus of the sum of the first and second numerators so that it is substantially the same as the squared modulus of the first or second denominator.

I wasn't too bothered, because it's basically an analogue type implementation. But then claim 35 says

35. A method according to claim 19 wherein said low and high pass filters include digitally implemented filters.

I always wonder about this sort of thing. If we were to pursue our numerical iterative optimisation thing, and blundered into such a filter simply because it met the criteria we had set (for frequency response roll-off, overshoot, ringing duration, latency etc.) I presume we would be infringing said patent if we allowed it out into the wild..? (If not, there wouldn't be much use in patenting anything, as obviously our story about the computer having found the filter 'by accident' could just be us retro-fitting a story to having copied Thiele's filter.)

But supposing, instead, we sold a program, or an electronic box, with a user interface that allowed the user to specify basically any filter they wanted. How would the patent work with that sort of thing? Would the program have to mask out certain no-go areas that were covered by patents?

I'm just curious.

[puppet]

gberchin ... noticed that you had stated a relationship w/EV. I'm curious, if you know, as to how well their Bessel filters (2,3,4th order) found in the DX34A series digital processors approximate the idealized Gaussian filter(s)?

[gberchin]

Originally Posted by puppet

gberchin ... noticed that you had stated a relationship w/EV. I'm curious, if you know, as to how well their Bessel filters (2,3,4th order) found in the DX34A series digital processors approximate the idealized Gaussian filter(s)?

Puppet; sorry for the huge delay in response, but I stopped following this thread when it looked like it ended last July.

In answer to your question: If EV is still using the Bessel filters that I designed for the DSP56K processor family, then they are textbook implementations of analog Bessel filters converted to digital by means of the bilinear transform, with prewarping to match the analog prototypes at the -3 dB frequencies. Their precision and accuracy are very close to the maximum possible in a 24-bit context because extended-precision is used for the internal calculations. So, basically, they are about as good an approximation to Gaussian filters as 24-bit Bessel filters can be.

If EV has changed processors (or implementations), then I am unable to speak to what might be there.

[David_Web]

iDFT XO CGn does not work as it can not write to c:/iDFT_XO_CGn.txt
Creating a file with permission and ownership changes nothing as win7 won't allow it.
It is also bad practice to write there as EVE online found out when they modified autoexec.bat (which was their launch script) but accidentally took c:/ one instead.

[steph_tsf]

Originally Posted by David_Web

iDFT XO CGn does not work as it can not write to c:/iDFT_XO_CGn.txt

See revision in : iDFT-based XOs (FIR)
post #1
post #6
The file gets written in a more suitable directory.

[David_Web]

Thanks, didn't see that thread. I was using the version posted above in #144