Measurement of frequency deviation in FM signals

[nauman]

Hi all

Is there any way to measure frequency deviation in a recorded frequency modulated time domain data? The little research i have done on net mostly concerns with frequency deviation measurement using spectrum analyzer in real time i.e. data continuously received on spectrum analyzer while measuring deviation in carrier frequency.

If i record FM data using some digitizer and i know the carrier frequency, is it possible to measure frequency deviation using some fft technique on recorded data offline?

Thanks

 

[Baluncore]

Is there any way to measure frequency deviation in a recorded frequency modulated time domain data?

The FM carrier will have a stable amplitude, so given a time domain recording you might look at the zero crossings. The time between crossings in the record will have a maximum and a minimum value.

The reciprocals of twice those dtmax and dtmin values will give the maximum frequency deviation in the recording.

To find zero crossings more accurately, interpolate between adjacent points in the recording that have changing signs. You could then look at the statistical distribution of those half cycle times.

You do not need to digitise the RF carrier wave if you down convert it to an IF and digitise the input to the FM discriminator. You should not need to know the carrier wave frequency.

 

[sophiecentaur]

You should not need to know the carrier wave frequency.

Agreed. The spectrum of many FM signals has little or no energy at the carrier frequency.
If you look at the spectrum analyser picture (sinusoidal modulation is what to use) you will see various features.

is it possible to measure frequency deviation using some fft technique on recorded data offline?

If you have a time domain recording then you can give yourself the same information that a spectrum analyser shows you. You should look at a lot of different images of FM spectra that you can find all over the web.

Firstly, if you use a low modulating frequency with 'high' deviation (Hz per Volt of the modulating signal) you will see "angel's wings" with an almost continuous looking spectrum spread over a range with peaks on either side. The separation of those wings is an indication of the deviation and the total spread is the bandwidth of the signal. Precisely how this image is the result is a complicated business. Different spectrum analyser settings can produce different images but no need to worry too much about that.

Secondly, if you use a high modulating frequency and 'low deviation' , the spectrum will consist of identifiable lines which are spaced by the frequency of the modulating sinusoid. For very low modulation, you see just two 'sidebands' and the signal looks much the same as AM.

FM sidebands theoretically extend to infinity but of course you can limit the channel width, depending on what distortion you are prepared to tolerate. If you google Carson's Rule you will find a formula which tells you that the total required bandwidth of an FM signal.

There are several free Digital Signal Processing apps available but it's a long time since I used on so you will probably find something up to date with a friendly interface.

 

[tech99]

Hi all

Is there any way to measure frequency deviation in a recorded frequency modulated time domain data? The little research i have done on net mostly concerns with frequency deviation measurement using spectrum analyzer in real time i.e. data continuously received on spectrum analyzer while measuring deviation in carrier frequency.

If i record FM data using some digitizer and i know the carrier frequency, is it possible to measure frequency deviation using some fft technique on recorded data offline?

Thanks

You need to demodulate it, as deviation is proportional to voltage. This requires something giving voltage proportional to frequency. This can be done by clipping to a fixed amplitude followed by pulse counting to obtain pulses/second, either analogue or digital.

 

[sophiecentaur]

@nauman has not replied recently. He could help by re-stating his question in the light of what's been written so far.
The FM signal is a slippery little devil - much harder to quantify than an AM signal. For a start, Frequency Modulation nearly always uses pre- and de- emphasis because of the spectrum of the demodulated noise. In many ways, your regular FM signal is more of a Phase Modulated signal because of that. So we need to know exactly what that original post was actually about.

The display on a spectrum analyser will not tell you the deviation for just any signal. You can measure the 'occupied bandwidth' (between half power frequencies) of you can use the Bessel Zero method for calibrating low deviations. Anything a spectrum analyser can do can be done with computer software but you have to know what you actually want.

 

[alan123hk]

If i record FM data using some digitizer and i know the carrier frequency, is it possible to measure frequency deviation using some fft technique on recorded data offline?

Yes, I think theoretically, in some simple and special cases, FFT can be used to find the approximate frequency deviation.

 

[sophiecentaur]

Yes, I think theoretically, in some simple and special cases, FFT can be used to find the approximate frequency deviation.

I think you'd need to quote the "theory" you mention here.
If you know the bandwidth of the modulating signal (and, because the OP talks about a 'recording ', it's probably not a sinusoid), then you can measure the 3dB bandwidth of the signal (integration-based calculation) and subtract twice the modulating bandwidth. That will tell you, from Carson's Rule, what the peak to peak deviation is.
But that's a bit 'so what?' and not necessarily at all accurate because of the fact that the modulating signal is very likely pre and post filtered.

I think we have been asked the 'wrong question' or, at least an incomplete one. Time domain displays of FM signals are very hard to interpret because there is no 'envelope' as in AM.

 

[anorlunda]

This paper seems to address the difficulties that @sophiecentaur pointed out.

https://www.researchgate.net/figure/Frequency-Domain-Representation-of-an-FM-signal-modulated-by-three-sinusoids-with-K1-10_fig5_337533385

 

[Baluncore]

Time domain displays of FM signals are very hard to interpret because there is no 'envelope' as in AM.

I disagree.
You must focus on the zero crossings, and not on the level of the limiter. If you trigger an oscilloscope sweep on the rising edge of a carrier, you can watch a full cycle on the screen, then zoom into view the second rising edge.

If it is an FM signal, then the rising edge will vary in the time position it crosses the time axis. From that you can read the range of time variation of full cycles, then calculate the reciprocal to get the range of frequency deviation.

I say edge rather than zero crossing because the limiter is likely to have a flat topped signal, with steep transitions, so the exact zero reference will not be critical when measured over a full cycle.

I find analysis of real FM signals in the frequency domain more difficult since the spectrum contains varying combinations of modulation index dependent Bessel function envelopes.

Maybe we approach this problem differently because you could inject a test signal, while I was quietly verifying or investigating a target.

 

[sophiecentaur]

I disagree.
You must focus on the zero crossings,

Spot the zero crossings for anything other than a sinusoidal modulation and a low mod index? Can you do that? Plus you are ignoring the fact that pre-emph and a high deviation will cause the zero crossings to fill in the gaps between cycles.
There is an exception to my problem and that is to look at a high deviation FM TV signal. You can spot the peaks of energy at the peaks of the sync pulses and the blanking level - especially when there's no 'CEFAX type' data in the sync intervals. And that corresponds to 30% of the excursion from sync bottoms to peak white.
But, hey, why expect to be able to visually decode any form of modulation? AM is the only one you can hope to do that with. Where FM TV is concerned, the spec for deviation is based on what works (imo) and what fits into the channel passband with least distortion. with such a non-linear system as FM.

 

[alan123hk]

I think you'd need to quote the "theory" you mention here

There is no particular theory. Similar to what you mentioned, we can estimate the frequency deviation based on the frequency spectrum of the FM signal and the Carson rule. In the case of a single modulation frequency only, we don't even need to know the frequency of the modulating signal, because as long as the resolution is sufficient, we can see it directly from the spectrum.

But that's a bit 'so what?' and not necessarily at all accurate because of the fact that the modulating signal is very likely pre and post filtered.

As for pre-emphasis and de-emphasis, this is the audio signal processing before the modulator and after the demodulator. I don't understand why this affects the accuracy of using FFT to estimate the frequency deviation of the FM signal.

https://www.daenotes.com/electronics/communication-system/pre-emphasis-and-de-emphasis

 

[sophiecentaur]

As for pre-emphasis and de-emphasis, this is the audio signal processing before the modulator and after the demodulator. I don't understand why this affects the accuracy of using FFT to estimate the frequency deviation of the FM signal.

Again, you are right but that's not the whole story about using FM. Why use FM in the first place? What is the demodulated noise spectrum and why use pre and de-emphasis?
The actual context of the OP is still nagging at me, and that's the problem. It seems that the OP has a set of data for an FM signal with sinusoidal modulation. To find the deviation then why not just use DSP FM discriminator application? Does just looking at the FT of an FM help? The 'theory' works one way very easily (frequency modulator) and you can tell what the sideband levels will be. Working backwards (demodulator) is much harder.
When you are presented with a spectrum - as in the diagram below - with a range of sideband amplitudes. You then need to 'work backwards' from the Bessel graphs (below) to decide what deviation will give you measured sidebands lying on the appropriate Bessel curves. Do-able but an awful lot easier to approach it the other way round and show that the sideband levels are right for a chosen deviation. There will be software to do it for you, I'm sure.
Another approach would be to look at zero crossings of the time domain values (scope display). Measuring the range of spacings between zero crossings would give you a distribution with max and min phase values. That also would give the peak phase deviation (just another step to frequency deviation).

 

[sophiecentaur]

we can estimate the frequency deviation

I read this and a light came on in my head. People like to think about modulation as if that implies there actually is always a carrier. It's nice to be able to imagine a tuning knob being wave wobbled at an audio frequency but it doesn't take you far in getting to grips with what is involved in FM in general. There are many modulation systems that have no power at what is the nominal carrier frequency (including many values of FM frequency deviation). The carrier is only a way of thinking which, taking AM as a good example, gives us all a feeling that we know what's going on.

 

[Baluncore]

The actual context of the OP is still nagging at me, and that's the problem.

It must be over 30 years since frequency allocation mentioned “nominal carrier frequency”. What is now specified is the centre of the channel and the channel width. That becomes obvious when you look at SSB transmissions, where the suppressed carrier frequency can be outside the allocated channel.

Your FM “nominal carrier frequency” would refer to the centre frequency of the allocated channel. That would be the frequency of an unmodulated FM carrier. An FSK data stream might generate the signal by gating together only the two extreme 0 and 1 carrier frequencies, but spectral analysis during a transition would show some energy present at the centre of the allocated channel. If that was not so, the allocated channel would be too wide, or the data rate too low.

FM is a tricky carrier at the best of times, with too many possible implementations under the one umbrella. Looking for more possibilities to worry about seems unnecessary.

 

[alan123hk]

The actual context of the OP is still nagging at me

First of all, I would like to say that many of the points you put forward are worthy of consideration and studying.

I admit that I have not considered why OP needs to use FFT to find frequency deviation and other alternative methods. Instead, I think from a relatively narrow perspective and try to answer the question simply and directly.

To find the deviation then why not just use DSP FM discriminator application? Does just looking at the FT of an FM help?

If the purpose is to perform a complete digital frequency demodulation to recover the original modulating signal, then I think the fast convolution should be used instead of the fast Fourier transform.

I read this and a light came on in my head. People like to think about modulation as if that implies there actually is always a carrier

Modern radio communication is constantly seeking to transmit the most information with the lowest power and narrowest bandwidth. For those useless things, whether it is the so-called carrier or anything else, they will try to get rid of it.

 

[sophiecentaur]

Your FM “nominal carrier frequency” would refer to the centre frequency of the allocated channel.

Yes. AM channels have a well defined Video Carrier that sits well to one side of the channel because AM TV uses Vestigial Sideband Modulation (VSB) The RF spectrum mirrors the baseband spectrum pretty well apart from the lower VSB.
It's only sound signals that have a (more or less) symmetrical waveform about zero but I spent a large part of my life looking at FM TV transmitted signals and, of course, the TV signal is very much asymmetrical (basically 0V to +1V peak sync level). After a lot of searching, I found an old photograph of the spectrum of a satellite broadcast TV signal - perhaps colour bar test signal, see below. You can identify the various parts of the signal in terms of the TV waveform. Because of the necessary pre-emphasis, the DC part of the video signal may have relatively low deviation and you can see the low frequency luminance steps as a set of lines, spread over a couple of MHz around the ref zero and possibly the sync pulses as a single line at around -2.5MHz. and the higher frequency parts of the baseband signal are more 'symmetrical' and premphasised so they appear as distant sidebands without the LF luminance levels (lines).
Why go to the trouble of using FM? The wider spectrum of the transmitted signal gives the 'FM Advantage' of an increased signal to noise ratio. Useful when satellite power sources are expensive.
You'll have to indulge me about this information but it really does demonstrate how the frequency deviation is almost anyone's guess except for the low frequency luminance part of the video. Enjoy decoding the message that the spectrum analyser tells us.

 

[Baluncore]

@sophiecentaur
No matter how confusing you try to make it, I am going to use a class C amplifier for my transmitter, and my receiver will have a really good flat topped limiting amplifier before the discriminator.
The only information remaining for the discriminator to extract will be in the timing of the zero crossings.
I can accumulate that range of time variation on a storage oscilloscope, then compute the maximum frequency deviation encountered during the observation from the bounds. For me the spectrum is an irrelevant complexity that can only lead to confusion.

 

[sophiecentaur]

No matter how confusing you try to make it, . . . . . .

Yep you're quite right. And this thread has been over-egged a lot (mea culpa).

Except that an optimal receiver / demodulator could do a better job with signal to noise performance, I think. However, there are better systems that FM these days, for carrying information. AM used to be referred to as Ancient Modulation and I wonder what the name for FM will be in the future.

 

[Averagesupernova]

AM used to be referred to as Ancient Modulation and I wonder what the name for FM will be in the future.

I recall SSB, or often shortened to just SB was referred to as 'slop bucket' modulation. Hams can be a strange bunch. Yes AM sounds better than SSB, but seriously, why should it matter considering what the HF bands are typically used for. I do know of guys that will get on 160 using AM for nightly chats, and I doubt they're stepping on anyone's toes anywhere.

 

[alan123hk]

AM used to be referred to as Ancient Modulation and I wonder what the name for FM will be in the future

Modern DAB/HD radio broadcasts use a rather complex digital modulation scheme called Orthogonal Frequency Division Multiplexing (OFDM), and I believe that traditional FM broadcasting may be phased out in the near future.

But I think narrowband frequency modulation is still an excellent modulation method, it can provide narrow bandwidth and good signal-to-noise ratio at the same time, and the transmitter and receiver can be made of relatively simple analog circuits.

 

[sophiecentaur]

But I think narrowband frequency modulation is still an excellent modulation method, it can provide narrow bandwidth and good signal-to-noise ratio at the same time, and the transmitter and receiver can be made of relatively simple analog circuits.

NBFM has a lot going for it. Life started with AM because a receiver could be made with a half dozen components. some nails and a wooden board. The AM transmitter was always a hot and sweaty beast but the broadcaster could afford it. FM requires a pretty fancy receiver, in comparison, and only the technically minded could ever make one (so Radio wouldn't have taken off the way it did with FM. The FM transmitter is a much less dramatic piece of kit so it's probably better suited to amateur use. The spectrum of AM and NBFM is almost indistinguishable; there are two (significant) sidebands and the only difference is the phase relationship between them and the carrier.

However, Wideband FM gives the real noise advantage because the demodulated signal from the discriminator is proportional to the deviation - no limit to SNR improvement, on the face of it. The only problem / advantage is that the service area falls off with a crash with wide channels. Good for planning a service, bad for would-be listeners beyond the planned area.