Electronics > RF, Microwave, Ham Radio

How to sample FM

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mariolucas75:
Dear All,

I am not sure whether this is the right place to post a question (may be it should go beginners section)...

To sample a signal it is needed to have a sampling rate at least twice as the signal frequency... suppose i want to capture high frequency signal ~ 100Mhz so what does it mean - my SDR should have 200 Ms/s (mega samples / sec) rate ?

If I have a FM signal - lets say carrier freq is 100Mhz and after modulation bandwidth  is +  - 100 Khz either side, so it means that my signal will have chunks of frequencies - min 100Mhz-100khz and max 100Mhz+100Khz... and i want to view  / visualize this signal in time domain..... in another words something like a "spring with compressed coils or stretched coils".... so to sample that signal and try to visualize it do i need sampling rate two times (~ 200 Ms /s ) more ? Or how to do it ?

Pls help

RoGeorge:
If f0 is 100MHz with +/-100kHz deviation, than we can translate the spectrum around 0Hz, so we will have \\$\Delta f = 200kHz\\$ which will require a Nyquist sampling at 400 kilosamples/s (400kSa/s).

If I got your question wright, what you are looking for is decimation.

In decimation, if it were to have all the samples taken at 200 MSa/s, than we can simply keep only each 50th sample and discard the other samples.  That way we would get the same samples as if it we were sampling at 400 kSa/s (every 50th because 200 MSa/s = 200_000 kSa/s = 50 * 400 kSa/s).

Keep in mind that decimation will fold down other spectral components into the same band, so usually this is done by first applying a low pass filter over all of the high speed 200 MSa/s samples, and only after filtering we can throw away the rest of the samples and keep only each 50th sample after low pass filtering the original high speed signal.

The low pass filter in this numerical example must be at 200kHz, to cut out any higher spectral components.  This is necessary only if higher than 200kHz frequencies are present in the FM signal, because by decimation all other multiple of 200kHz bands (e.g. 400kHz-600kHz, or 91.8MHz to 92.0MHz, etc.) will be folded into the first 200kHz, too, and there is no way to distinguish which is which.

mariolucas75:
Dear RoGeorge,

So it is possible to view real-time FM station signal obtained through rtl-sdr in time domain as a signal with chunks of different frequencies like a "spring with compressed or stretched  coils" (the way FM is symbolically drawn in books ) ?

Or how to do it....

Sorry if my question sounds silly ... i am new but desperately want to learn this.....

srce:

--- Quote from: mariolucas75 on September 22, 2021, 10:45:22 am ---To sample a signal it is needed to have a sampling rate at least twice as the signal frequency... suppose i want to capture high frequency signal ~ 100Mhz so what does it mean - my SDR should have 200 Ms/s (mega samples / sec) rate ?

If I have a FM signal - lets say carrier freq is 100Mhz and after modulation bandwidth  is +  - 100 Khz either side, so it means that my signal will have chunks of frequencies - min 100Mhz-100khz and max 100Mhz+100Khz... and i want to view  / visualize this signal in time domain..... in another words something like a "spring with compressed coils or stretched coils".... so to sample that signal and try to visualize it do i need sampling rate two times (~ 200 Ms /s ) more ? Or how to do it ?

--- End quote ---
You could do it by sampling at 200MS/s, but this isn't the way most radios work.

They work by mixing the received signal with a 100MHz local oscillator which downconverts the 100MHz signal to baseband, so you get a signal 200kHz wide centred at 0Hz (Or a low IF such as 1MHz). Thus your ADC only needs to run at 2 MHz not 200 MHz. The circuitry for this is inside your SDR.

--- Quote from: RoGeorge on September 22, 2021, 12:43:21 pm ---If f0 is 100MHz with +/-100kHz deviation, than we can translate the spectrum around 0Hz, so we will have \\$\Delta f = 200kHz\\$ which will require a Nyquist sampling at 400 kilosamples/s (400kSa/s).

If I got your question wright, what you are looking for is decimation.

In decimation, if it were to have all the samples taken at 200 MSa/s, than we can simply keep only each 50th sample and discard the other samples.  That way we would get the same samples as if it we were sampling at 400 kSa/s (every 50th because 200 MSa/s = 200_000 kSa/s = 50 * 400 kSa/s).

Keep in mind that decimation will fold down other spectral components into the same band, so usually this is done by first applying a low pass filter over all of the high speed 200 MSa/s samples, and only after filtering we can throw away the rest of the samples and keep only each 50th sample after low pass filtering the original high speed signal.

The low pass filter in this numerical example must be at 200kHz, to cut out any higher spectral components.  This is necessary only if higher than 200kHz frequencies are present in the FM signal, because by decimation all other multiple of 200kHz bands (e.g. 400kHz-600kHz, or 91.8MHz to 92.0MHz, etc.) will be folded into the first 200kHz, too, and there is no way to distinguish which is which.

--- End quote ---

if you want the ~100MHz +/-100kHz signal from your 200MSa/s, you a bandpass filter around ~100MHz not a lowpass before decimation...