I was always told to get 2.6 samples of the highest frequency.
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On Mon, Nov 22, 2021, 13:28 Tom Lee <tomlee@...> wrote: Which is why the Nyquist sampling constraint does not assume a sinusoid,
nor is it expressed in terms of the fundamental. It is properly
expressed in terms of the bandwidth (and not the 3dB bandwidth, nor in
terms of the maximum frequency). With a squarewave, even 10x can be
insufficient. And with impulses, it's even worse. The Nyquist criterion
is really quite straightforward. It's just that many have never bothered
to read what Nyquist actually said.
The sinewave example I gave is an example of "lies we tell to children"
to avoid the maths. When I follow that up with a lecture using the
proper maths, I point out that a sine occupies zero bandwidth, so
Nyquist actually tells us that we could sample it at an arbitrarily low
rate without losing any information at all, because a sinewave actually
has no information. Then that leads to a revisiting of aliasing,
sampling scopes, and compressed sensing, and also sets us up for an
extended discussion on Shannon channel capacity.
-- Cheers
Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
350 Jane Stanford Way
Stanford University
Stanford, CA 94305-4070
On 11/22/2021 13:15, David C. Partridge wrote:
Any assumption that you are looking at a sine wave is frankly na?ve.
From experience if you are using a DSO that's sampling at under 10x the fundamental frequency of a signal (e.g. 1GHz square wave sampled 5Gs/s),
then you are doomed to get an inaccurate signal representation.
David
-----Original Message-----
From: [email protected] <[email protected]> On Behalf Of Tom Lee
Sent: 22 November 2021 19:31
To: [email protected]
Subject: Re: [TekScopes] bandwidth
Steve,
I'm sorry to advise the others here to disregard your post. You have
made several profound misstatements here and elsewhere. If memory
serves, you once posted (maybe on HP groups.io) similar assertions. One
example you gave in support of your position was that of a sinewave
being sampled at slightly above the Nyquist rate, and you incorrectly
claimed there that the reconstruction had amplitude modulation. That
shows that you do not understand the role of the sinc interpolation
function. Properly applied, no such modulation results, and one obtains
perfect reconstruction. It's easier to see that from the frequency
domain.
If you wish to debate this, please do so off list to limit the thread
derail.
-- Tom
|
Re: TEKTRONIX 475 VOLTS/DIV
That is where the knobs stop in the 1x range. You should see that there are two small windows above the knob and behind the numbered collar. The "5" on the clear collar should stop above the left window (illuminated when scope is "on") situated behind the clear collar. The 10/20/50V ranges are attained by using a properly equipped TEKTRONIX 10X probe which will cause the left side window to go dark and the right side window behind the collar to then illuminate.
The Window to the left is illuminated when the scope is turned on (if the circuit and lamp are not damaged) and the Window to the right should come on when a TEKTRONIX 10X probe is used which connects the contact ring of the BNC to the ground through a spring loaded pin. This is called "probe coding". I hope My attempt to explain makes sense.
--
Michael Lynch
Dardanelle, AR
|
Which is why the Nyquist sampling constraint does not assume a sinusoid, nor is it expressed in terms of the fundamental. It is properly expressed in terms of the bandwidth (and not the 3dB bandwidth, nor in terms of the maximum frequency). With a squarewave, even 10x can be insufficient. And with impulses, it's even worse. The Nyquist criterion is really quite straightforward. It's just that many have never bothered to read what Nyquist actually said.
The sinewave example I gave is an example of "lies we tell to children" to avoid the maths. When I follow that up with a lecture using the proper maths, I point out that a sine occupies zero bandwidth, so Nyquist actually tells us that we could sample it at an arbitrarily low rate without losing any information at all, because a sinewave actually has no information. Then that leads to a revisiting of aliasing, sampling scopes, and compressed sensing, and also sets us up for an extended discussion on Shannon channel capacity.
-- Cheers
Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
350 Jane Stanford Way
Stanford University
Stanford, CA 94305-4070
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Show quoted text
On 11/22/2021 13:15, David C. Partridge wrote: Any assumption that you are looking at a sine wave is frankly na?ve.
From experience if you are using a DSO that's sampling at under 10x the fundamental frequency of a signal (e.g. 1GHz square wave sampled 5Gs/s), then you are doomed to get an inaccurate signal representation.
David
-----Original Message-----
From: [email protected] <[email protected]> On Behalf Of Tom Lee
Sent: 22 November 2021 19:31
To: [email protected]
Subject: Re: [TekScopes] bandwidth
Steve,
I'm sorry to advise the others here to disregard your post. You have
made several profound misstatements here and elsewhere. If memory
serves, you once posted (maybe on HP groups.io) similar assertions. One
example you gave in support of your position was that of a sinewave
being sampled at slightly above the Nyquist rate, and you incorrectly
claimed there that the reconstruction had amplitude modulation. That
shows that you do not understand the role of the sinc interpolation
function. Properly applied, no such modulation results, and one obtains
perfect reconstruction. It's easier to see that from the frequency domain.
If you wish to debate this, please do so off list to limit the thread
derail.
-- Tom
|
Re: TEKTRONIX 475 VOLTS/DIV
I assumed that someone would've answered you earlier, but I don't see any reply (but I only just got your post, so maybe relevant messages are stuck in the Great Cloud somewhere). In any case, the higher voltage ranges correspond to the scope being used with a 10:1 probe. The scope itself does not have those higher ranges. If you look carefully, there are two illuminators behind the knob skirts. The higher range one lights up when a 10:1 probe with the right dingus (to tell the scope that it's a 10:1 probe) is used. Random third-party probes rarely have this feature, so you have to keep the factor of 10 straight in your head. So, stop trying to rotate the knob further. :)
-- Cheers,
Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
350 Jane Stanford Way
Stanford University
Stanford, CA 94305-4070
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Show quoted text
On 11/19/2021 18:05, K Cleary via groups.io wrote: The VOLTS/DIV knob for Both channels 1 & 2 will not rotate past the 5 volt indicator. The lower ranges act normally.It would be nice to have the 10/20/50 Volt ranges working.
Searching 'here',it doesn't appear to be a common problem, but I have to ask, before I venture * inside *.
Any help is appreciated.
klc
|
Any assumption that you are looking at a sine wave is frankly na?ve.
From experience if you are using a DSO that's sampling at under 10x the fundamental frequency of a signal (e.g. 1GHz square wave sampled 5Gs/s), then you are doomed to get an inaccurate signal representation.
David
toggle quoted message
Show quoted text
-----Original Message----- From: [email protected] < [email protected]> On Behalf Of Tom Lee Sent: 22 November 2021 19:31 To: [email protected]Subject: Re: [TekScopes] bandwidth Steve, I'm sorry to advise the others here to disregard your post. You have made several profound misstatements here and elsewhere. If memory serves, you once posted (maybe on HP groups.io) similar assertions. One example you gave in support of your position was that of a sinewave being sampled at slightly above the Nyquist rate, and you incorrectly claimed there that the reconstruction had amplitude modulation. That shows that you do not understand the role of the sinc interpolation function. Properly applied, no such modulation results, and one obtains perfect reconstruction. It's easier to see that from the frequency domain. If you wish to debate this, please do so off list to limit the thread derail. -- Tom
|
Just acquired a TDS430a at auction that works but has damage to front and back bezels from a drop. Are these unobtinium? Especially the front bezel (it's intact except for the tabs that hold it secure but that lets it move out so the selection buttons don't contact well) Any suggestions for repair workarounds? or parts sources?
TIA!
Steve Shumaker
|
Hello everybody!
My 7104 started having problems in displaying traces and readout characters, it did not happen suddenly, sometimes after switching off and on again everything went back to normal operation.
ISSUES DESCRIPTION
Traces could be moved both vertically and horizontally, the horizontal part was all OK.
With (no difference between LEFT or RIGHT) and without a vertical plug in installed the traces were positioned half way between the top and the middle of the screen.
Focus had effect on traces and readout characters but it was difficult to focus them.
The readout characters were all aligned at the bottom line, no matter if related to LEFT/RIGHT vertical or A/B horizontal plug ins; bottom line was not at the bottom of the screen, but 1 inch above.
The readout characters were not readable, changing plug in settings had effect, something changed.
In some cases some weird readout characters were displayed.
The front panel readout controls were working correctly.
FIRST CHECKS AND FIXES
I¡¯ve changed all the electrolytic and tantalum capacitors and also 2 MKT in the Main Interface board, in total 77 capacitors;
in the PSU I could not find replacements for the 3 blue big ones (C1216, C1217 and C1354) that could fit so I only tested them for capacitance and leakage current, capacitances are in spec for all of them, the high voltage rated ones are OK while the low voltage one (for the +5V) rail has a slightly high leakage current but it can still do its job;
in the Low Voltage Regulators board there was a 40K (R1446) resistor of the -50V regulator out of tolerance that prevented to have a correct value when setting the +50V (it was at -52.6V with +50.0V), I changed both 40K resistors with 0.1%, 0.5W metal film ones;
in the Low Voltage Regulators board there was a missing nut on Q1494 (-15V power regulator) preventing a good thermal contact with the heat sink, it probably run (very) hot but it was still working fine;
I¡¯ve adjusted the two PSU voltages (+109V and +50V) and checked all other ones, they are all in spec within 0.05V;
there was a leaking electrolytic capacitor in the Vertical Amplifier on the -15V line (C897), I cleaned with IPA all the area around it;
I¡¯ve checked all transistors for shorted/not functioning ones, not with a curve tracer as I do not have one;
I¡¯ve fixed a couple of issues of the moving connectors in the right (B) horizontal plug of the Main Interface board;
I¡¯ve changed 5 contact pins of the plug in connectors because they were some irreparably damaged;
I¡¯ve fixed a shorted cable from the right (B) horizontal plug of the Main Interface to the Horizontal Amplifier, there was no problem before removing the Main Interface board, short circuit appeared after reinstalling it, the internal wire was touching the cable shield;
I¡¯ve checked all coaxial cables for shorts/broken connections and sprayed their connectors with contact cleaner before replacing;
I¡¯ve cleaned with IPA all HYPCON and hybrid ICs contacts and tested for good electrical connection, by the way I found as a fix for contact issues to leave the elastomer in IPA for some hours and then to bend the contacts a little from both the inner and outer side, this fixed a problem with the 7B15 contact failure raising after 20 minutes of use;
I¡¯ve cleaned all transistors and ICs sockets and their pins with contact cleaner (I had troubles with IPA), then tested for good electrical connection;
I¡¯ve cleaned all connectors and PCBs;
I¡¯ve changed the left vertical plug in slide guide because the outer edge was broken preventing a secure locking in the bay of the plug in module;
I¡¯ve changed all bulbs of the trigger source push buttons and that of the power on indicator, there were only two broken bulbs, but while changing them the filament of other two broke so I decided to change all of them.
ANALYSIS
At this point the 7104 was really shiny, with all lights working and half a can of contact cleaner used to clean contacts but the issue was still there.
If I swapped the two Vertical Amplifier input signal wires the trace did not move from its position, so the issue was not in the Vertical Channel Switch.
Disconnecting the Readout board had no effect, the trace did not move from its position, so the issue was not in the Readout for what is related to trace position.
SOLUTION
At this point I focused on the vertical amplifier, given that all transistors were OK, I started checking the opamps: I begun from the readout signal amplification and phase inversion LF351 (U705).
I did not have on hand a LF351 so, because it is not too critical, I used instead a LM318. With the new opamp in place the readout traces were now fine, not anymore all aligned at the bottom, but all of them in the right place.
But still the signal traces were not in the right position, with strange spikes and with a limited bandwidth.
I changed the feedbeside LF315 (U782) with another LM318 and the signal traces were now clear, noiseless, not bandwidth limited and in their correct position.
I then decided to change all opamps on that board just to be sure to avoid future issues, so I purchased 3 x LF351 and 1 x MC1458.
The broken connectors in the Main Interface board were dedicated to the readout signals, this explained the fuzzy/strange characters sometimes displayed.
I had real hard times with poor contacts after reassembling the boards. Before I experienced no issues in use. Fortunately I decided to work on one board at a time so, if something went wrong I could focus on only one board and its connections. The strangest issue came up when I worked on the Display Control one (A/B intensity, focus and astigmatism), after replacing it intensity controls were swapped (A controlling B and B controlling A) and not properly functioning¡ it was just a bad connection between this board and the Mode Switch one but it took me hours to figure out.
7104 finally fixed after 3 months since I started repairing/restoring it and 1.5 years since I stopped using it.
THOUGHTS
This repair ended up in an almost full restoration (only calibration is missing), but what I still have to understand is what caused two LF351s failing at the same time on the same board, I¡¯m afraid there is something wrong somewhere else I still have to find, the leaking electrolytic capacitor was on the -15V rail that might explain U705 failure, but not that of U782 that only has +15V supply, maybe the missing nut on the -15V power transistor caused spikes on this rail¡ no idea.
Hope this helps someone having same troubles.
|
Just acquired a TDS430a at auction that works! but has damage to front and back bezels from a drop. Are these unobtinium? Especially the front bezel (it's intact except for the tabs that hold it to the face. That lets it move out so the selection buttons don't contact well) Any suggestions for repair workarounds? or parts sources?
TIA!
Steve Shumaker
|
The VOLTS/DIV knob for Both channels 1 & 2 will not rotate past the 5 volt indicator. The lower ranges act normally.It would be nice to have the 10/20/50 Volt ranges working.
Searching 'here',it doesn't appear to be a common problem, but I have to ask, before I venture * inside *.
Any help is appreciated.
klc
|
475 Scope VOLTS/DIV Problem
I can't get eother Chanel 1 or 2 VOLTS/DIV
|
Just acquired a TDS430a at auction that works but has damage to front and back bezels from a drop.? Are these unobtinium??? Especially the front bezel? (it's intact except for the tabs that hold it secure but that lets it move out so the selection buttons don't contact well)?? Any suggestions for repair workarounds? or parts sources?
TIA!
Steve Shumaker
|
Re: [HP-Agilent-Keysight-equipment] Removing the Adhesive From Hell
I've used 3M surface mark remover: To clean up equipment and it's worked pretty well. You need to wear gloves when you use it because it can irritate your skin. Eric KI7LTT On Mon, Nov 15, 2021, 7:31 AM Brad Thompson <brad.thompsonaa1ip@...> wrote: Hello--
I'm restoring an older piece of equipment that was festooned with
tan-colored
masking tape. I'm able to scrape away most of the crumbling tape-- but
not its adhesive.
Applying Goo-Gone works but not well (softens the glue) snd it doesn't
remove
do a good job of removing adhesive from one's fingers.
Recommendations are welcome.
Thanks, and 73--
Brad AA1IP
|
Hello everybody
My 7104 started having problems in displaying traces and readout characters, it did not happen suddenly, sometimes after switching off and on again everything went back to normal operation.
ISSUES DESCRIPTION
Traces could be moved both vertically and horizontally, the horizontal part was all OK.
With (no difference between LEFT or RIGHT) and without a vertical plug in installed the traces were positioned half way between the top and the middle of the screen.
Focus had effect on traces and readout characters but it was difficult to focus them.
The readout characters were all aligned at the bottom line, no matter if related to LEFT/RIGHT vertical or A/B horizontal plug ins; bottom line was not at the bottom of the screen, but 1 inch above.
The readout characters were not readable, changing plug in settings had effect, something changed.
In some cases some weird readout characters were displayed.
The front panel readout controls were working correctly.
FIRST CHECKS AND FIXES
I¡¯ve changed all the electrolytic and tantalum capacitors and also 2 MKT in the Main Interface board, in total 77 capacitors;
in the PSU I could not find replacements for the 3 blue big ones (C1216, C1217 and C1354) that could fit so I only tested them for capacitance and leakage current, capacitances are in spec for all of them, the high voltage rated ones are OK while the low voltage one (for the +5V) rail has a slightly high leakage current but it can still do its job;
in the Low Voltage Regulators board there was a 40K (R1446) resistor of the -50V regulator out of tolerance that prevented to have a correct value when setting the +50V (it was at -52.6V with +50.0V), I changed both 40K resistors with 0.1%, 0.5W metal film ones;
in the Low Voltage Regulators board there was a missing nut on Q1494 (-15V power regulator) preventing a good thermal contact with the heat sink, it probably run (very) hot but it was still working fine;
I¡¯ve adjusted the two PSU voltages (+109V and +50V) and checked all other ones, they are all in spec within 0.05V;
there was a leaking electrolytic capacitor in the Vertical Amplifier on the -15V line (C897), I cleaned with IPA all the area around it;
I¡¯ve checked all transistors for shorted/not functioning ones, not with a curve tracer as I do not have one;
I¡¯ve fixed a couple of issues of the moving connectors in the right (B) horizontal plug of the Main Interface board;
I¡¯ve changed 5 contact pins of the plug in connectors because they were some irreparably damaged;
I¡¯ve fixed a shorted cable from the right (B) horizontal plug of the Main Interface to the Horizontal Amplifier, there was no problem before removing the Main Interface board, short circuit appeared after reinstalling it, the internal wire was touching the cable shield;
I¡¯ve checked all coaxial cables for shorts/broken connections and sprayed their connectors with contact cleaner before replacing;
I¡¯ve cleaned with IPA all HYPCON and hybrid ICs contacts and tested for good electrical connection, by the way I found as a fix for contact issues to leave the elastomer in IPA for some hours and then to bend the contacts a little from both the inner and outer side, this fixed a problem with the 7B15 contact failure raising after 20 minutes of use;
I¡¯ve cleaned all transistors and ICs sockets and their pins with contact cleaner (I had troubles with IPA), then tested for good electrical connection;
I¡¯ve cleaned all connectors and PCBs;
I¡¯ve changed the left vertical plug in slide guide because the outer edge was broken preventing a secure locking in the bay of the plug in module;
I¡¯ve changed all bulbs of the trigger source push buttons and that of the power on indicator, there were only two broken bulbs, but while changing them the filament of other two broke so I decided to change all of them.
ANALYSIS
At this point the 7104 was really shiny, with all lights working and half a can of contact cleaner used to clean contacts but the issue was still there.
If I swapped the two Vertical Amplifier input signal wires the trace did not move from its position, so the issue was not in the Vertical Channel Switch.
Disconnecting the Readout board had no effect, the trace did not move from its position, so the issue was not in the Readout for what is related to trace position.
SOLUTION
At this point I focused on the vertical amplifier, given that all transistors were OK, I started checking the opamps: I begun from the readout signal amplification and phase inversion LF351 (U705).
I did not have on hand a LF351 so, because it is not too critical, I used instead a LM318. With the new opamp in place the readout traces were now fine, not anymore all aligned at the bottom, but all of them in the right place.
But still the signal traces were not in the right position, with strange spikes and with a limited bandwidth.
I changed the feedbeside LF315 (U782) with another LM318 and the signal traces were now clear, noiseless, not bandwidth limited and in their correct position.
I then decided to change all opamps on that board just to be sure to avoid future issues, so I purchased 3 x LF351 and 1 x MC1458.
The broken connectors in the Main Interface board were dedicated to the readout signals, this explained the fuzzy/strange characters sometimes displayed.
I had real hard times with poor contacts after reassembling the boards. Before I experienced no issues in use. Fortunately I decided to work on one board at a time so, if something went wrong I could focus on only one board and its connections. The strangest issue came up when I worked on the Display Control one (A/B intensity, focus and astigmatism), after replacing it intensity controls were swapped (A controlling B and B controlling A) and not properly functioning¡ it was just a bad connection between this board and the Mode Switch one but it took me hours to figure out.
7104 finally fixed after 3 months since I started repairing/restoring it and 1.5 years since I stopped using it.
THOUGHTS
This repair ended up in an almost full restoration (only calibration is missing), but what I still have to understand is what caused two LF351s failing at the same time on the same board, I¡¯m afraid there is something wrong somewhere else I still have to find, the leaking electrolytic capacitor was on the -15V rail that might explain U705 failure, but not that of U782 that only has +15V supply, maybe the missing nut on the -15V power transistor caused spikes on this rail¡ no idea.
I hope this helps someone experiencing the same issues
|
On Mon, Nov 22, 2021 at 12:33 AM, Jeff Dutky wrote:
TekWIki says that the 2440 is 300MHz (analog bandwidth) with 500 MSa/s
Hi Jeff: First of all... we (at least I) have to give a shout out to Claude Shannon... and at least one other! (Shannon, Armstrong, and Mason are absolute heroes of mine!) Next... the theorem named after Nyquist and Shannon only sets a sufficient condition (not a necessary one) for the sampling rate that will obtain/get all the 'information' in the analog (discrete-time) signal... under certain conditions... depending on the analog signal (like some of...band-limiting,finite band-with, existence of a Fourier transform which is bounded to zero outside a finite band-width, et. al.) The idea of the 'necessary' is there are/might be other ways to 'successfully' 'sample.' Putting all that aside (and one really shouldn't... IMO it's too important)... You have to have 'stored' enough sample points (even if you have the capability to get enough sample points)... you have to be able to store enough sample points (and display enough sample points), to 'faithfully' reproduce the signal. Peter Hiscocks (who has been mentioned on TekScopes) used to decry manufactures specing DSOs (or mixed signal scopes) with... shall we say... IHO&IMO inflated bandwidths. Obfuscating specs... was something major manufactures used to do. (I am not calling out any specific manufacturer.) We've got an old Instek DSO that's branded 150Mz EG25GS/s. (Is that 150 MHz and 25 GS/s? ... I think not!) Most Chinesium DSOs... these days (and for a while) have at least 10 to 20 times the sample rate as the band-width (required, according to Nyquist.) That's usually printed right on the front panel labelling. IME&IMO, Chinese engineers will sometimes risk burning down a house to save 1/2 cent (or less) on a lower power rated resistor. So give that inclination, what is it that they know about a DSO's performance, display fidelity, usability, and customer satisfaction?... when these guys routinely put out 200 MHz 2 GS/s DSOs, marketed as commodity items. -- Roy Thistle
|
Steve,
I'm sorry to advise the others here to disregard your post. You have made several profound misstatements here and elsewhere. If memory serves, you once posted (maybe on HP groups.io) similar assertions. One example you gave in support of your position was that of a sinewave being sampled at slightly above the Nyquist rate, and you incorrectly claimed there that the reconstruction had amplitude modulation. That shows that you do not understand the role of the sinc interpolation function. Properly applied, no such modulation results, and one obtains perfect reconstruction. It's easier to see that from the frequency domain.
If you wish to debate this, please do so off list to limit the thread derail.
-- Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
350 Jane Stanford Way
Stanford University
Stanford, CA 94305-4070
toggle quoted message
Show quoted text
On 11/22/2021 10:57, Steve Hendrix wrote: I don't have letters behind my name to make me an expert, but I did write an article some years ago for one of the trade journals, I forget which one, about the "Nyquist Frequency Fable". Two misconceptions are common:
1) That sampling at 2x the highest frequency present is adequate. What Nyquist actually says is the converse: sample any slower than that and you're guaranteed to get aliasing. As others have pointed out, around 10x the highest frequency is a good guide.
2) The theory behind the sampling theorem presumes sampling both real and imaginary parts at 2x the max frequency. In the time domain, the imaginary part is just phase-shifted by 90? from the real part. Thus to truly sample both real and imaginary parts at 2x the highest frequency, you're actually sampling (in the time domain) at 4x. This guarantees that you don't completely miss the signal by sampling exactly at the zero crossings.
So 4x is pretty much a minimum, and 10x is a good real-world guide. And remember that it's talking about the highest frequency component actually present. What's the highest frequency component in a perfect 1 KHz square wave? This is why you have to first filter in the continuous time domain BEFORE sampling.
I once was asked by a manager type to digitally filter a pressure sensor that was pulsing (due to an upstream pump) at almost (but not quite exactly) our sampling frequency. It took a lot of effort to convince him that we really needed to add an analog filter upstream, since the sample rate was non-negotiable.
Steve Hendrix
At 2021-11-22 13:45, Dave Daniel via groups.io wrote:
The Nyquist sampling theorem (or Nyquist-Shannon or Whittaker-Nyquist-Shannon, etc., etc.) postulates that one must sample at a sampling rate of at least twice the highest frequency contained in the signal being sampled in order to prevent aliasing.
The sinc() function has an odd property where the highest amplitudes (i.e., extrema) coincide with the extrema of the cosine() associated with the sine() function used in the sinc() function, or something like that. I know that the sinc() function is associated with the use of Fourier analysis of a signal. We used it in the Partial Response Maximum Likelihood (PRML) read channel algorithm of high-end tape drives awhile back.
There are certainly people on this forum who can describe the sinc() function better than I can. Or look at the Wolfram, Eric Weisstein or Wikipedia websites.
DaveD
On 11/22/2021 11:52 AM, Jeff Dutky wrote:
(not that I really understand all the math)
a very simplistic analysis says that you would not be able to resolve a sine wave from discrete samples unless you had at least four (very well placed) samples per cycle. I would expect (again, not based on any real mathematical understanding) that you would really need more like ten samples per cycle at your maximum frequency.
I have heard (but, again, don't understand the math) that you can use some kind of interpolation (sine x over x?) to get better looking waveforms than you really have sampled data for, but I also understand that this is a relatively recent innovation on DSOs (i.e. within the past 20 years).
-- Jeff Dutky
--
This email has been checked for viruses by Avast antivirus software.
|
Re: USB interface for the DPO / P7001
Holger,
Well done; especially the wizard!
This might be the world¡¯s first time that USB has connected to magnetic core memory.
|
I don't have letters behind my name to make me an expert, but I did write an article some years ago for one of the trade journals, I forget which one, about the "Nyquist Frequency Fable". Two misconceptions are common:
1) That sampling at 2x the highest frequency present is adequate. What Nyquist actually says is the converse: sample any slower than that and you're guaranteed to get aliasing. As others have pointed out, around 10x the highest frequency is a good guide.
2) The theory behind the sampling theorem presumes sampling both real and imaginary parts at 2x the max frequency. In the time domain, the imaginary part is just phase-shifted by 90? from the real part. Thus to truly sample both real and imaginary parts at 2x the highest frequency, you're actually sampling (in the time domain) at 4x. This guarantees that you don't completely miss the signal by sampling exactly at the zero crossings.
So 4x is pretty much a minimum, and 10x is a good real-world guide. And remember that it's talking about the highest frequency component actually present. What's the highest frequency component in a perfect 1 KHz square wave? This is why you have to first filter in the continuous time domain BEFORE sampling.
I once was asked by a manager type to digitally filter a pressure sensor that was pulsing (due to an upstream pump) at almost (but not quite exactly) our sampling frequency. It took a lot of effort to convince him that we really needed to add an analog filter upstream, since the sample rate was non-negotiable.
Steve Hendrix
toggle quoted message
Show quoted text
At 2021-11-22 13:45, Dave Daniel via groups.io wrote: The Nyquist sampling theorem (or Nyquist-Shannon or Whittaker-Nyquist-Shannon, etc., etc.) postulates that one must sample at a sampling rate of at least twice the highest frequency contained in the signal being sampled in order to prevent aliasing.
The sinc() function has an odd property where the highest amplitudes (i.e., extrema) coincide with the extrema of the cosine() associated with the sine() function used in the sinc() function, or something like that. I know that the sinc() function is associated with the use of Fourier analysis of a signal. We used it in the Partial Response Maximum Likelihood (PRML) read channel algorithm of high-end tape drives awhile back.
There are certainly people on this forum who can describe the sinc() function better than I can. Or look at the Wolfram, Eric Weisstein or Wikipedia websites.
DaveD
On 11/22/2021 11:52 AM, Jeff Dutky wrote:
(not that I really understand all the math)
a very simplistic analysis says that you would not be able to resolve a sine wave from discrete samples unless you had at least four (very well placed) samples per cycle. I would expect (again, not based on any real mathematical understanding) that you would really need more like ten samples per cycle at your maximum frequency.
I have heard (but, again, don't understand the math) that you can use some kind of interpolation (sine x over x?) to get better looking waveforms than you really have sampled data for, but I also understand that this is a relatively recent innovation on DSOs (i.e. within the past 20 years).
-- Jeff Dutky
--
This email has been checked for viruses by Avast antivirus software.
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The Nyquist sampling theorem (or Nyquist-Shannon or Whittaker-Nyquist-Shannon, etc., etc.) postulates that one must sample at a sampling rate of at least twice the highest frequency contained in the signal being sampled in order to prevent aliasing.
The sinc() function has an odd property where the highest amplitudes (i.e., extrema) coincide with the extrema of the cosine() associated with the sine() function used in the sinc() function, or something like that. I know that the sinc() function is associated with the use of Fourier analysis of a signal. We used it in the Partial Response Maximum Likelihood (PRML) read channel algorithm of high-end tape drives awhile back.
There are certainly people on this forum who can describe the sinc() function better than I can. Or look at the Wolfram, Eric Weisstein or Wikipedia websites.
DaveD
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On 11/22/2021 11:52 AM, Jeff Dutky wrote: (not that I really understand all the math)
a very simplistic analysis says that you would not be able to resolve a sine wave from discrete samples unless you had at least four (very well placed) samples per cycle. I would expect (again, not based on any real mathematical understanding) that you would really need more like ten samples per cycle at your maximum frequency.
I have heard (but, again, don't understand the math) that you can use some kind of interpolation (sine x over x?) to get better looking waveforms than you really have sampled data for, but I also understand that this is a relatively recent innovation on DSOs (i.e. within the past 20 years).
-- Jeff Dutky
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Re: USB interface for the DPO / P7001
Hi Nenad!
You can find many information about the P7001 (and other Tektronix gear) on Tekwiki:
The USB interface of a Teensy can behave like a very fast COM port / serial device. My plan is that most of the functionality should be accessible with the help of a simple terminal program. So it will be open to almost any type of program.
I am writing my own program that can communicate with some of the Tektronix digitizers from the 1970s / 1980s. It's called Oscar. Here is a screenshot:
Holger
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To sidestep the math, here's a graphing exercise that seems to work for my students: Draw a sine wave. Pick off N equally spaced samples per cycle, then try to reconstruct by eye the original sine from the samples. If N exceeds 2, you can do it. If N = 2, you can't (consider if the samples all happen to be at the zero crossings). If N is less than two, you can reconstruct a sine, but it will be at a lower frequency than the original waveform -- we call that aliasing, since the lower-frequency reconstruction is falsely passing itself off as the original (we exploit this in sampling scopes).
The reconstruction problem is really nothing more than an interpolation problem: "What is the ideal way to interpolate between the samples?" That's where the math comes in. Once you connect the math to filter design, you find that the ideal interpolator is a filter with constant transmission up to half the sampling frequency, and then infinite attenuation above it. The finite rolloff characteristics of practically realizable filters forces the use of N significantly in excess of 2.
-- Tom
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Prof. Thomas H. Lee
Allen Ctr., Rm. 205
350 Jane Stanford Way
Stanford University
Stanford, CA 94305-4070
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On 11/22/2021 08:52, Jeff Dutky wrote: (not that I really understand all the math)
a very simplistic analysis says that you would not be able to resolve a sine wave from discrete samples unless you had at least four (very well placed) samples per cycle. I would expect (again, not based on any real mathematical understanding) that you would really need more like ten samples per cycle at your maximum frequency.
I have heard (but, again, don't understand the math) that you can use some kind of interpolation (sine x over x?) to get better looking waveforms than you really have sampled data for, but I also understand that this is a relatively recent innovation on DSOs (i.e. within the past 20 years).
-- Jeff Dutky
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Gary Robert Bosworth
Michael W. Lynch
David C. Partridge