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The next question is what type of resolution do you want from your spectrum?
Lets say you do use a 100MHz ADC to sample the signal, and you use digital demodulation and decimation to select a 10MHz band. What type of resolution would you like, eg. 1MHz, 100kHz?
You can convert a sequence of time samples into a power spectrum by either lag correlation, or by using the discrete Fourier transform to implement the correlation operation.
You can implement a lag correlator using delays (registers) and multipliers or logic elements configured to act as multipliers. Depending on the signals you are looking at, it may be possible to use low bit width multiplications (which do not require actual multipliers). If however you plan on correlating tones or signals with a lot of RFI, if you sample too coarsely, you will generate harmonics. If your signals are noise-like, then coarse quantization just makes the signals noisier (lower efficiency), but this may be acceptable if you have time available to integrate (average) and recover a SNR that is acceptable.
You can implement a discrete correlation using an FFT. The discrete correlation of an N-point sequence has 2N-1 points. If you want to reproduce this correlation identically using an FFT, you have to pad an N-point sample sequence to at least 2N-1 points, then Fourier transform, and then take the magnitude squared. Many applications can get by with just taking the FFT of an N-point sequence and then taking the magnitude squared of that sequence. In your case, it would be sufficient to use an FFT core, and take the magnitude squared of the output and sum a sequence of outputs to improve the signal-to-noise. Once you read the data out, you can divide by the integration time to normalize it. You will likely need to scale the data into an appropriate power scale.
An N-point FFT will give N/2+1 unique frequency channels, frequency channels 0 to N/2. An (N/2+1) lag autocorrelation, for lags 0 to N/2, can reproduce this same spectrum.
If you want 100kHz resolution for a sampling frequency of 20MHz (10MHz bandwidth sampled), then you want at least 100 channels. Because you are time-limiting your spectra to N-lags, your spectrum will be convolved with the sinc-response of this effective rect function. To improve resolution, you can take the lag response, or the inverse Fourier transform of the averaged spectra, and apply a window function, eg. Hamming window, then Fourier transform to spectra. This window will reduce the sidelobes in the spectra, but it will make the frequency channels wider. So if you want 100kHz resolution in the spectra, you'll need more channels, eg. 200-channels.
If you would like some references on digital signal processing, just ask.
Cheers,
Dave
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Hello Dave,
Thanks for all,
I would like a reference on digital signal processing, because I didn't understand very well what you said.
thanks
Honored Contributor
