Electrically tunable crystal band pass filters

[T3sl4co1l]

And, if we're talking bandpass filters (which in context of radio, means some offset between desired signal, IF passband, and BFO), then the impulse response is that of the envelope, not the carrier (which is obviously ringing quite a tremendous amount in absolute terms if it's a center frequency of say 4MHz and a bandwidth of 50Hz!).

We haven't heard any mention (read: I don't recall seeing it mentioned) what the received signal was, nor how it was determined to "not ring".  So far it sounds like it was just by ear, which I've tried to remind is a NOTORIOUSLY bad metric.  I don't recall any response on that, so I assume it's a point that's been ignored, presumably because the reader disagrees with what they presume is an insult to their perceptions, without even asking if it was intended as an insult, nor objectively gauging whether such a position is reasonable in the first place.

But I'd be glad to be corrected on those assumptions.

Tim

[rhb]

That is the classic definition of "ringing".  It's origins are a very messy bit of mathematics.

Your graphic shows the response to a Heaviside step function.  This is the classic test of oscilloscope AFEs.
ringinThe main cause of ringing is too steep a filter edge, though at a refined level the nature of the transitions matter.  Gaussian and Bessel filters behave the best, but it's a rare scope that looks good in the face of one of Leo Bodnar's pulsers.

Gaussian and Bessel filters don't ring, but the minimum phase constraint broadens the impulse response considerably c.f. Zverev. and the impulse response become symmetric with significant delay. Narrow BW conventional filters will muddy a fast CW signal a lot.


Model it in Octave or MATLAB.  Too much like a homework exercise from 305 years ago for me.

Reg

[mawyatt]

I'm trying to make the analog equivalent of the DSP in the Icom 705.

BTW  Gaussian filters very definitely ring in the time domain.  You're thinking of the symmetric zero phase time domain response.  But reality is minimum phase. I suspect the DSP version is zero phase, but an analog version can't be.

Completely wrong!! A Gaussian Filter has no time domain ring response period!! It can't exceed unity magnitude in a normalized step response and can't go negative in a normalized magnitude impulse response!!

The Impulse Response of a Gaussian Filter is in the form of e^-(t^2) which is bounded between 0 and 1 for all t.

The Step Response of a Gaussian Filter is in the form of (1+erf(t))/2 which is also bounded between 0 and 1 for all t, where erf(x) is the Error Function x and has limits of +-1 for all x.

BTW you can't implement an Ideal Analog Gaussian Filter, it requires and infinite number of elements to implement the exponential transfer function.

Best,

[rhb]

In the case of operators which are symmetric in both domains, the phase delay significantly lengthens the time domain response.

If 50  Hz wide filters are old hat, who made them?

[gf]

Gaussian and Bessel filters don't ring, but the minimum phase constraint broadens the impulse response considerably

A Gaussian filter still gives you the shortest possible rise time w/o overshoot in the step response. Any other filter that gives you the same rise time either has a wider bandwidth, or it overshoots.

The major drawback of a Gaussian filter is IMO the rather low selectivity. A compromise with little overshoot and much better selectivity are transitional filters like e.g. "Gaussian to 12dB", which start with an approx. Gaussian response in the passband and transition to Chebycheff in the stop band (see https://www.analog.com/media/en/training-seminars/design-handbooks/basic-linear-design/chapter8.pdf).

[rhb]

TANSTAFL

[rhb]

OK some order of magnitude calculations.

A 50 Hz wide Gaussian is 20 ms wide.  At 20 wpm each dit and space are 20 ms long.  If you try to send faster it all mashes together.  Symbols (.-) don't complete before the next one begins.  A computer can copy it, but not a human.

The thing which is so cool about twin pass band tuning is the time domain response is set by the width of the filters, not  the passband of the cascade.

Many  of the ham gear makers are doing this.  The first reference I can find is the Icom 7300, but I'm pretty sure Yaesu has a functional equivalent in the FTdx-101 from the video I watched.

I'd like to know who invented the architecture of overlapping isolated filters.  I am incredibly impressed by the digital version and very curious how well an analog version can do.  I've spent 40 years doing DSP.

Reg

[gf]

The thing which is so cool about twin pass band tuning is the time domain response is set by the width of the filters, not  the passband of the cascade.

I calculated/simulated this for two cascaded 10th order Butterworth bandpass filters, fc=10kHz, bw=500Hz (just an arbitrary example).
Take a look at the plots. The envelope's step response definitively does depend on the passband of the cascade.

If the two filters are tuned to the same center frequency, the -3dB cascade bandwidth is ~456Hz, the envelope rise time is approx. 2.3ms, but (as expected) there is some overshoot.

The narrowest -3dB cascade bandwidth I could achieve was approx. 100Hz, when the two filters are de-tuned approx. +-250Hz.

[ If I de-tune more than +-250Hz, then the overall -3dB bandwidth of the cascade becomes wider again, with a dip in the center. Even though it is a 10th order bandpass, it still has a limited roll-off in the stopband, which eventually determines the narrowest achievable bandwidth for the de-tuned cascade. With 10th order Butterworth bandpass filters as used in this example, a cascade passband narrower than approx. bw/5 is obviously not possible. ]

Now the important point: The envelope rise time of the de-tuned cascade is no longer 2.3ms, but now it is approx. 6.9ms. And it does not ring any more, because the frequency response of the cascade rolls off softly near the center (not a flat top anymore -- see plot). If the time domain response of the cascade would be determined only by the time domain response of the wide-band filters (as you claim), then we would not see a different time domain response now. But we do see a much slower response with the 100Hz cascade bandwidth than with 100% overlap.

For comparison, an ideal Gaussian bandpass with 100Hz BW would have ~6.65ms envelope rise time. So the resulting rise time of ~6.9ms comes indeed close to Gaussian, but it still does not beat a Gaussian. As you said, there is no free lunch. Regardless how you do it ("twin" or otherwise), you cannot outwit the trade-off between rise time (pulse width), overshoot and bandwidth. The frequency domain transfer function of the cascade is still the product of the transfer functions of the two filters, and the impulse response of the cascade is still the inverse Fourier transform of the cascade's transfer function. Even a filter realized as a combination of two de-tuned partially overlapping wide-band filters cannot outwit that.

EDIT: Attached Octave script

Code: [Select]

pkg load signal

fc = 10000
bw = 500
detune = 0
f1 = fc - detune
f2 = fc + detune

points=2000
fs=100000

t = [0:points-1]/fs;
signal = sin(2*pi*fc*t);

[b1,a1] = butter(5,[(f1-bw/2)/(fs/2) (f1+bw/2)/(fs/2)]);
[b2,a2] = butter(5,[(f2-bw/2)/(fs/2) (f2+bw/2)/(fs/2)]);

[H2,f2] = freqz(b2,a2,fs,fs);
[H1,f1] = freqz(b1,a1,fs,fs);

figure 1
plot(f1,20*log10(abs(H1.*H2)))
xlabel("Hz")
ylabel("dB")
grid on

figure 2
plot(1000*t,filter(b1,a1,filter(b2,a2,signal)))
xlabel("ms")
grid on


[rhb]

Edit: Complete rewrite

I'd  always said exactly the same thing until I used the TPBT feature on an Icom 705 to completely reject a stronger signal 30 Hz away on one side and another 50 Hz on the other side on the waterfall display from the station I was copying! 

I spent my career doing this.  I was introduced to DSP in 1982 and took two semesters of "Integral Transforms" taught by Bill Guy at Austin using Churchill's "Operational Mathematics".  You can't do that!   It won't work.  But I was listening to the result.

You tell me how they make it work.    Here's my best explanation:

D(w) = B(w)*d(w-w0) . B(w)*d(w-w1) =? B(w)**2*d(w-w0)*d(w-w1) = B(w)**2*d(w-w3)

where d(w) is a delta function in the frequency domain that performs the shift and all the normal Fourier theorems apply.


I thought I'd see if tunable crystal filters would work with an emitter followers  to provide isolation to recreate what they are doing in DSP for use in a portable QRP rig as a means of reducing the current drain.

Here's the work needed to properly simulate this.  It's a huge number of figures to generate :-(  Probably need Smith charts to do it right.


The filters:

a 500 Hz BW Nth order filter with an Fc of 5 MHz

a 50 Hz BW Nth order filter with an Fc of 5 MHz

a pair of N/2 order 500 Hz BW filters with F1L=4.999525 F1H=5.000025 F2L=4.99975 F2H=5.000475

Work needed:

design filters 

plot the filter operator in frequency and time showing phase and complex impedances

generate a random set of sine waves which span the BW of the filters

plot the responses in time and frequency

modulate the sine waves with a 2 Hz square wave (CW keying "5" at 25 wpm)

plot the responses

[rhb]

Go to a ham radio store during an HF CW contest in your region and ask to be shown the Icom 7300 or 707 TPBT feature in operation.

Then tell me how it works.  Because I've always been told it can't be done.

Reg

[T3sl4co1l]

Keep in mind they could be doing further audio processing, emphasis, expanding, noise gating, etc. I kind of doubt that's actually the case, but it's a possible explanation for intelligible (to a human) results when the code is otherwise digitally resolvable.  That is, it's not pulling information out of nowhere (bandwidth), it's expanding apparent bandwidth by nonlinear methods.

Tim

[rhb]

Let's consider 3 signals at 5.000020, 5.000050 and 5.000100 MHz.

Let's have 2 filters.  One has a pass band of 500 Hz from 4.999575 to 5.000075.   Filter the signal composed of the 3 sine waves with the filter.  That leaves 2 signals at 5.000020 and 5.000050.  The signal at 5.000100 has been removed from the signal.

I now pass that signal through a 2nd filter with a pass band from 5.000025 to 5.000575.  That leaves just the signal at 5.000050.

How does the 2nd filter know that the signal has been through the first filter and the upper signal removed?  How is this different from using only the 2nd filter and turning off the signal source?

Serious question.  I want to know the answer.  This confounds all I've believed for 40+ years.  It raises serious question about the statements about commutation and association Norbert Weiner set forth in the 40's.

I'm a seismic guy.  We are the lineage that originated DSP.  We could use a 125 Hz Nyquist system..  An individual modern seismic survey is a $10-30 million operation to acquire and process.

The correct equation is D(w) =[S(w).B(w)*d(w-w0)] . [B(w)*d(w-w1)]

where S is the input signal.

I am working on implementing this using crystal filters, but have 500 crystals to measure.

I'd love to have someone else do the computer simulation stuff and let me sniff solder fumes and test the results.  I did the computer stuff for a very long time.  My blood lead levels are too low ;-)

Reg

[David Hess]

Go to a ham radio store during an HF CW contest in your region and ask to be shown the Icom 7300 or 707 TPBT feature in operation.

Then tell me how it works.  Because I've always been told it can't be done.

Told that what cannot be done?

Twin passband tuning sure works.  I described it in an earlier post and have used it many times.

The implementation requires fine tuning of the local oscillator frequencies so it was a pretty late development.  Most radios just get by with IF shift tuning which does the same thing and works the same way but is limited to a fixed IF filter width.

[rhb]

It's the mathematics that is the problem.

What's the correct equation to describe the situation?

Edit:

This has really become an issue with me.  I agree with gf and David Hess. 

All my life I was taught that if you had an underdetermined system of equations there were an infinite number of solutions.  In 20004 David Donoho of Stanford proved that was rarely the case if the solution of Ax=y was sparse.  That is most of the entries in x were zero.  Thus you could solve NP-Hard problems in L1 time *most* of the time.  And if you couldn't, well you couldn't.

[rhb]

OK

@gf and I generally agree about the mathematics.   Though there are a lot of nuances to consider.

@David Hess and I agree about the filter performance.

Which leaves the question of the correct mathematical description.  Without that, there is no way to design an analog filter to replace the digital filter.  Analog filters must be causal and that implies minimum phase.

I've put forth an equation in standard transform notation.

So how do we reconcile this apparent conflict?

Reg

[gf]

Keep in mind they could be doing further audio processing, emphasis, expanding, noise gating, etc. I kind of doubt that's actually the case, but it's a possible explanation for intelligible (to a human) results when the code is otherwise digitally resolvable. That is, it's not pulling information out of nowhere (bandwidth), it's expanding apparent bandwidth by nonlinear methods.

I think of a simple comparator, which recovers rectanglular pulses from the pulse-shaped ones ¹⁾

Pulse shaping on the TX side also plays a role. If the signal is already properly band-limited, you can even send it through a brickwall filter (a little bit wider than the signal's occupied bandwidth), and the brickwall filter won't add additional ringing.

EDIT:

¹⁾ For instance, if root raised cosine pulses with alpha=0.5 are turned into rectangular pulses with a comparator at 50% threshold, the resulting edge jitter is still only (roughly) 10% of the symbol width (see timing jitter of the 50% crossings in the attached eye diagram). So I guess the "crisp" rectangular dits recovered by the comparator should be well recognizable (if this speed can be recognized by a human at all, and granted that the signal is not too noisy). At 50 baud (20ms symbol duration) and with alpha=0.5, the occupied bandwith of these RRC-shaped pulses is only +-37.5Hz from the center. Maybe even a smaller alpha (-> smaller BW) is still feasible (I just calculated for 0.5).

EDIT: Sorry, was too good to be true. Had a typo in the calculation. I'll re-calculate and update the message when I find some free time.
False Alarm.

[mawyatt]

..... We are the lineage that originated DSP. .....

That is questionable since DSP concepts were developed for telephone line digital communications back in 40s and 50s at Bell Labs, and later became known as MODEMs that were part of the US air defense system called SAGE in 50s, and AT&T offered commercial versions of these in the 50s. Pagers were also in use in the 50s.

Had the honor of working along side Dr William Acker, a brilliant DSP guru that was behind the world leading high thru-put Group Data Modems at Honeywell in the 60s & 70s with his key patents in DSP based channel equalizers, later became Paradyne and eventually acquired by AT&T.

So Digital Signal Processing has been around for a long long time, likely preceding the transistor, although not generally known in the early days specifically as DSP, just another useful means of signal processing.

Best,

[rhb]

..... We are the lineage that originated DSP. .....

That is questionable since DSP concepts were developed for telephone line digital communications back in 40s and 50s at Bell Labs, and later became known as MODEMs that were part of the US air defense system called SAGE in 50s, and AT&T offered commercial versions of these in the 50s. Pagers were also in use in the 50s.

Had the honor of working along side Dr William Acker, a brilliant DSP guru that was behind the world leading high thru-put Group Data Modems at Honeywell in the 60s & 70s with his key patents in DSP based channel equalizers, later became Paradyne and eventually acquired by AT&T.

So Digital Signal Processing has been around for a long long time, likely preceding the transistor, although not generally known in the early days specifically as DSP, just another useful means of signal processing.

Best,

Norbert Weiner developed the foundations of DSP on contract to the Navy in 1940.  It was known as "the yellow peril" during the war because of the classified color and the difficulty of the mathematics. It was published in 1949 as "The Smoothing, Interpolation and Extrapolation of Stationary Time Series"

The oil industry immediately jumped on it and funded the Geophysical Analysis Group with 8 students.  Enders Robinson and Sven Treitel wrote a series of papers on DSP which appeared in Geophysics that were reprinted  as the Robinison-Treitel  Reader and widely distributed by seismic service companies.

Here's a more detailed story from the man who did the first deconvolution by hand on paper after digitizing the traces by hand in the summer of 1952.
 
https://library.seg.org/doi/10.1190/1.2000287


My PhD supervisor at Austin was a member of GAG, Milo Backus.  So yes, reflection seismologists originated DSP.  We were the only users that could work with a 125 Hz Nyquist.

[mawyatt]

Interesting read, was not aware of GAG involvement!!

Altho should have been since a former colleague (Prof at Cornell) father, Dr Peter Molnar at Colorado, won the Crafoord Prize in Geoscience in 2014

Thanks for the info

Edit: BTW the colleague at Cornell, Dr Al Molnar, he's the academic emphasis behind the Polyphase Mixer, Mixer-First, N-Path Mixer, whatever you want to call it. If you check the IEEE papers mentioned, you'll find he's one of the original authors.

Best

[rhb]

I have by any definition a *large* DSP library.  One of the the things I find *really* annoying is the general failure by the EE community to acknowledge what they owe the oil industry.

TI didn't start by building modern high speed wide word ADCs.  They started by building 250 Sa/s 16 bit ADCs which they sold for princely sums when they started building them in the 60's.

It's an interesting counter example to industry exploiting defense research.  Though Weiner's assignment was to figure out where to point an antiaircraft gun.  So it's defense exploiting industry exploiting defense.  And there's no another layer of industry exploiting defense.

FWIW I created an example of a pair of overlapping filters today using a 1 Hz resolution frequency domain with a 10 MHz Nyquist array and trapezoidal filters.

Have Fun!
Reg

Edit:  The norm today for an offshore survey is 5-6 sets of parallel lines with stations on 6.25 m or less spacing x 100-200 m (to keep the dozen 10-20 km long cables they are towing from tangling).  It takes several months to acquire the 10-12 TB of data and typically 6-9 months to process it.  Total bill for the project will run around $30-50 million.  These are done when it's time to decide where to place the wells.

The imaging step, the digital equivalent of holography, compute is  7-10 days on 10-20 thousand cores.

[rhb]

Keep in mind they could be doing further audio processing, emphasis, expanding, noise gating, etc. I kind of doubt that's actually the case, but it's a possible explanation for intelligible (to a human) results when the code is otherwise digitally resolvable. That is, it's not pulling information out of nowhere (bandwidth), it's expanding apparent bandwidth by nonlinear methods.

I think of a simple comparator, which recovers rectanglular pulses from the pulse-shaped ones ¹⁾

Pulse shaping on the TX side also plays a role. If the signal is already properly band-limited, you can even send it through a brickwall filter (a little bit wider than the signal's occupied bandwidth), and the brickwall filter won't add additional ringing.

EDIT:

¹⁾ For instance, if root raised cosine pulses with alpha=0.5 are turned into rectangular pulses with a comparator at 50% threshold, the resulting edge jitter is still only (roughly) 10% of the symbol width (see timing jitter of the 50% crossings in the attached eye diagram). So I guess the "crisp" rectangular dits recovered by the comparator should be well recognizable (if this speed can be recognized by a human at all, and granted that the signal is not too noisy). At 50 baud (20ms symbol duration) and with alpha=0.5, the occupied bandwith of these RRC-shaped pulses is only +-37.5Hz from the center. Maybe even a smaller alpha (-> smaller BW) is still feasible (I just calculated for 0.5).

The IC-705 has the following IF BWs to choose from:

AM: 9kHz, 6 kHz & 3 kHz
SSB: 3kHz, 2.3kHz & 1.8kHz
RTTY: 2.4 kHz, 500 kHz & 250 kHz
FM: 15 kHz, 10 kHz & 7 kHz
DV:  15 kHz, 10 kHz & 7 kHz
CW:  1200 Hz, 500 Hz & 250 Hz

The Fc of both filters are individually adjustable in 50 Hz steps.  Clearly AM & SSB *must* be linear. 

FWIW The BW of a CW signal is 0.35/rise_time.  It's actually not the keying rate.  But the keying rate does set the maximum usable rise time.

[gf]

Clearly AM & SSB *must* be linear. 

Potential non-linear processing was rather meant in the baseband, after demodulation. For instance I see now way how linear processing could re-sharpen the pulse edges once they have been blurred and high frequencies have been completely eliminated. However, non-linear processing can do that, re-introducing high frequencies.

I'd  always said exactly the same thing until I used the TPBT feature on an Icom 705 to completely reject a stronger signal 30 Hz away on one side and another 50 Hz on the other side on the waterfall display from the station I was copying!

At which data rate? Still 50 baud (= 20ms symbol duration = 60 wps), or slower?

[T3sl4co1l]

Clearly AM & SSB *must* be linear. 

Potential non-linear processing was rather meant in the baseband, after demodulation. For instance I see now way how linear processing could re-sharpen the pulse edges once they have been blurred and high frequencies have been completely eliminated. However, non-linear processing can do that, re-introducing high frequencies.

Quite.  And, without measurements, we're merely left to speculate what the actual response is.

As you're [rhb] well aware, DSP can be changed at the flick of a bit; a filter doesn't need to be consistent across modes (or time or space for that matter; we're not restricted to LTI systems here!).  It might be easier that way, but it could also be that they went to the trouble of computing coefficients live, instead of literally shifting center frequencies around.  Analytic filter design might've been hard back in the day (for certain values of "day"; it's really not that new), but it's entirely understood now, and eminently computable.  It could even be that they detect the kind of program matter (not actually very hard in context of full modern computing, but again -- even less likely in an embedded context I would guess), and apply other kinds of filtering (including nonlinear effects as above) to improve legibility.

Tim

[mawyatt]

Recall a non-linear device used in very early telephone and radio called a "coher" or something similar. Evidently had almost magical properties based upon lightly compressed carbon particles as in a current/voltage dependent resistor, altho can't remember details (OK I'm old, but not that old!!).

Best,

[tggzzz]

Recall a non-linear device used in very early telephone and radio called a "coher" or something similar.

https://en.wikipedia.org/wiki/Coherer

I'm old enough to remember (when I was a kid) reading about them in very old books