## SNR of a pulse

## SNR of a pulse

(OP)

I have a system where I'm receiving pulses and I'd like to quantify the signal to noise ratio for the pulse.

Are there any standards calculations for determining the signal to noise ratio of a pulse? In a CW (continuous wave) system I'll take the ratio of the RMS (root mean square) voltage of the signal and divide it by the noise (also in RMS).

If I do this for a pulse, I have to throw some assumption in for the repetition of the pulse; a pulse with a slower repeition rate will have a lower RMS value than a pulse with a faster repetition rate. That make sense for a continuous time system, but not for an aquisition system with a fixed time window.

For example, i have two systems that measure the pulse. One collects data for 10 times the duration of the pulse and the other system collects data for 40 times the duration of the pulse. They both measure the same pulse, but one reports a RMS value 4x what the other reports.

I could measure the RMS is a fixed window around the pulse to eliminate this variation but that gets a bit too application specific and could introduce error if my fall time slows down. Is there a standard technique that I'm missing?

Another technique would be to divide the rms value by the acquisition window width. That will give me a constant value in Vrms/sec; strange units though and a quick test didn't give me the results I expected...

Can anyone recommend any good books on pulse analysis?

Are there any standards calculations for determining the signal to noise ratio of a pulse? In a CW (continuous wave) system I'll take the ratio of the RMS (root mean square) voltage of the signal and divide it by the noise (also in RMS).

If I do this for a pulse, I have to throw some assumption in for the repetition of the pulse; a pulse with a slower repeition rate will have a lower RMS value than a pulse with a faster repetition rate. That make sense for a continuous time system, but not for an aquisition system with a fixed time window.

For example, i have two systems that measure the pulse. One collects data for 10 times the duration of the pulse and the other system collects data for 40 times the duration of the pulse. They both measure the same pulse, but one reports a RMS value 4x what the other reports.

I could measure the RMS is a fixed window around the pulse to eliminate this variation but that gets a bit too application specific and could introduce error if my fall time slows down. Is there a standard technique that I'm missing?

Another technique would be to divide the rms value by the acquisition window width. That will give me a constant value in Vrms/sec; strange units though and a quick test didn't give me the results I expected...

Can anyone recommend any good books on pulse analysis?

## RE: SNR of a pulse

SNR = Pulse amplitude (peak) / noise floor amplitude (all in dBx)

You need to watch out for bandwidth - make sure your test bandwidth is the same as the actual receiver bandwidth, including same shape factor.

## RE: SNR of a pulse

## RE: SNR of a pulse

## RE: SNR of a pulse

I've avoided this technique because if I applied it to a sine wave it would report a SNR that is almost 3 dB (1.414x) better than a SNR with rms ratios (the noise floor is only meaningful in RMS so I can't take a signal-peak to noise-peak ratio). That just doesn't seem correct.

## RE: SNR of a pulse

## RE: SNR of a pulse

## RE: SNR of a pulse

e.g. a system where the digital pulses were

a few millivolts in the noise of a few volts and the raw

-- uncorrected -- error rate better than 1 in 1 million.

To give any help we need much more data ( see my FAQ )

What is the data frequency, amplitude, clock rate ?

Modulation rules ?

What is the noise spectrum like? Is there any dominant

source ?

What kind of error probability can you afford per bit

without redundancy based error correction?

What kind of estimated volume ?

The probability that I van help you is almost 1 if you answer

but without further data you are beyond help.

----------------------------

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## RE: SNR of a pulse

This is an analog system, not digital (bits). Defining the SNR is more of an engineering function to qualify the data coming out of the algorithm (okay, the answer is digital) that processes the pulses. I need the analytical technique, not a hardware solution (volume).

This system has an analog signal coming in with about 40 dB of dynamic range (by my present qualification techniques). It gets sampled at 1 MSPS and is easily averaged (1000x) to a SNR of better than 70 dB (i.e. the noise spectrum is white). The frame rate is 100 Hz with data collected for about half the period of a frame.

If there are standard algorithms for this then I'm looking for the technique behind the algorithm.

I've also calculated this another way (I think this was while I was beyond...) - treating the noise as a sinewave so I could estimate a noise peak voltage by multiplying the rms voltage by 1.414. I then took the ratio of the signal peak (averaged) to the background noise peak. This result is about 5 dB off from my SNR calculated with RMS values. I want better accuracy than that (I'll settle for 1 dB) so I'm looking for a proven technique to remove this uncertainty.

## RE: SNR of a pulse

In this case, RMS just adds a layer of confusion.

I've already mentioned some gotchas:

Bandwidth and filtering reducing noise floor in your receiver but not your measurement tools.

If SNR is low, remember to account for S+N/N.

## RE: SNR of a pulse

Is there a technique to calculate the pulse power directly from the pulse peak/shape? Maybe if I integrate the pulse over time ((vpeak^2/R)*time) and then average it across the pulse width. This still seems dependent upon the amount of time I average across; that's the problem I started with for RMS! Any suggestions?

While I prefer to calculate this in the time domain, a frequency domain response could work too (now my pulse is made up of many sine waves and the peak to RMS conversion is easy). Now the question is how to scale a FFT to RMS:

A*cos(w) --> A (Vpeak)

A*cos(w) --> A*PI*(impulse(w)+impulse(-w) (FFT)

A*cos(w) --> A/sqrt(2) (Vrms)

So is it correct that Vrms = sqrt(2)/PI * FFT for a given frequency bin? If so then I can RMS-sum the FFT bins and I'll have the RMS value of my pulse. Ah, I believe this only works if I have constant phase across all the frequencies; otherwise the FFT components never cancel and I'll get an erroneously high value. Hmmm...

## RE: SNR of a pulse

You should be able to tweak a thresholding function to get the something like 0.1% false alarm rate, which is then TNR=5.3

TTFN

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## RE: SNR of a pulse

Find the peak power of your pulse (notice that this is extremely trivial). Estimate the peak power of your noise (only slightly less trivial). Voila.

If you're going to try to stick with RMS, then you need to make a series of measurements, and then calculate the Root Mean Square in the same manner as a 'True RMS' Fluke DVOM. The time would be across the pulse (maybe trim the edges), and then aim for a known empty spot (in the time domain) of roughly the same duration.

Or apply a empirically-determined fudge factor, ah - I mean 'calibration constant', to your initial approach.

## RE: SNR of a pulse

Gunnar Englund

www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

## RE: SNR of a pulse

Thanks for all your suggestions. Bouncing all these ideas back and forth has been been helpful.

As far as generating my own method, I think I'll normalize a sampled pulse and then run an FFT. At that point I can take the ratio between the peak voltage and the peak in the FFT and that will be my 'calibration constant'. I'll be able to track that from system to system and see how stable of a factor it is.

## RE: SNR of a pulse

in the case of old, analog AM determines -- the error rate.

The error rate in the case of digital communication is much

more complex -- e.g. in the sixties there was a Saturn fly-

by and the returned picture -- in spite of the ridiculously

low S/N were excellent.

In digital magnetic tape drive the read and write heads

are within .1", we write and read it back simultaneously

even during deceleration -- i.e. the frequencies are changing.

The write crosstalk may be 1000 times larger than the read

signal. Would you really expect acceptable error rate at

S/N = -60 DB -- ( yes, minus 60 )?

----------------------------

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## RE: SNR of a pulse

Let me give you a philosophical “aside” in a related area which may be of some relevance. You would think that pulse response of acquisition systems was an industry standard term relating to oscilloscopes for example. So we rate a pulse response in terms of rise-time. There you go, a single metric risetime. Of course most people use 10%-90% risetime, although a few with really nasty responses quote 20%-80% risetimes, but let’s not worry about that. What about overshoot? Is a 1ns risetime with 10% overshoot better or worse that a 1.2ns risetime with 1% overshoot? There is no industry standard measure for the “quality” of a pulse response. Certainly anyone would complain if their pulse risetime was 0.8ns but it had 15% overshoot and was ringing for 15ns.

So back to your system. You have a notionally rectangular pulse and you want to establish a performance metric for it, presumably in order to optimise the response. In other words you want to measure it, tweak something, and see if you get a “better” response. Let me refer you to an article I wrote about this subject, “In Search of an Optimum Optimiser”.

ht

It does not address your pulse problem directly, but gives you more of the philosophical background to your problem, which may be of some small assistance.

## RE: SNR of a pulse

Thus a new paradigm. I can measure the peak of my pulse, so I'll define my SNR as pulse peak over noise peak. If I use the standard sqrt(2) conversion from wideband noise peak to noise rms then I will have rms noise that I can compare from the time domain to the frequency domain. Hey, that's about what VE1BLL suggested back in May! Sometimes I'm just a little slow... (or was it the five other projects that popped up on my to-do list since then?).

Thanks all!

## RE: SNR of a pulse

TTFN

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## RE: SNR of a pulse

TTFN

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## RE: SNR of a pulse

Z

## RE: SNR of a pulse

http:/

I think the following is an update to his original text:

http

TTFN

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## RE: SNR of a pulse

The whole question is so application dependent, that a simple concise answer is not really possible.

But some sort of test specification could probably be devised to give a measurement of "db above not working" threshold that may be a useful yardstick ?

## RE: SNR of a pulse

You are correct that this is very application specific. Even in my system we have different applications on how the pulse is processed. Some applications are mainly concerned about the jitter and distortion on the pulse; other applications are more interested in the frequency content of the pulse.

At least now with this 'pulse peak vs. noise peak ratio (PPNPR) I have a tool that I can use to compare the effect of changes in/to the system (if we do that it will cost us x dB).

Z

## RE: SNR of a pulse

TTFN

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## RE: SNR of a pulse