Electronic – Relationship of FFT Size, Sampling Rate and Buffer Size

The maximum sample rate of the device is 2Mhz, this is just something else that I don't understand, how can I detect 100Mhz+ signal if the maximum sample rate is 2Mhz ?

You can't, at least not unambiguously if there are other signals that are of a lower frequency in the input.

Anyway, if I understand correctly, the maximum frequency in FFT is 1Mhz, via nyquist, my question is, how can I find the bin that corresponds to the 148Mhz signal ? I can see a spike that corresponds to the signal but I want to be able to index into the bins and find it.

Probably reason why you see a spike that corresponds to the signal is because you're experiencing aliasing. There's no way to unambiguously detect the \$148.369\text{ MHz}\$ signal without a sufficiently high sample rate. It could actually be a much lower frequency signal.

For example, if I try to sample a \$2\text{ kHz}\$ sine wave signal with a sampling rate of \$1.5\text{ kHz}\$, the ADC reconstruction of the signal might end up actually being \$0.5\text{ kHz}\$, so there's no way to tell the difference between a \$2\text{ kHz}\$ or a \$0.5\text{ kHz}\$ signal using only the data acquired by an ADC. That's why ADCs are often used with an analog low-pass antialiasing filter to avoid the problem.

If you want to detect this \$148.369\text{ MHz}\$ signal, you need to either sample the signal at more than twice that frequency (the more, the better), or use an alternative strategy that does not involve directly looking for the \$148.369\text{ MHz}\$ signal.

For example, you can mix the signal with another (sine wave) signal generated by a local oscillator and look for the beat frequencies instead of the \$148.369\text{ MHz}\$ signals. You can then use an ADC and antialiasing filter filter to look for them. A proper choice of the local oscillator frequency would create beat frequencies much less than the sampling rate of the system.

This is actually the technique used in some (all?) radios to tune to a specific frequency, called heterodyning.

One usually needs to acquire multiple samples per waveform period to get good results from an FFT. The Nyquist limit of 2 samples per period is a lower bound but usually 10 samples per period or more is what is practically used. So to analyze a 64Hz signal you probably want to acquire samples at a rate of 640Hz or more.

Also (up to a point) you will get better results when measuring actual periodic signals if you acquire multiple waveform periods worth of samples. You will need to determine what window size makes the most sense for your application but to capture 1Hz signals I would suggest capturing somewhere around 10s worth of data.

So basically you need to acquire samples at a high rate relative to your highest frequency and for a long time relative to your lowest frequency to get good results. This mandates that there will be some sort of processing delay that will be a multiple of the period of your lowest frequency. This does not however prevent you from performing that processing as often as once every sample time.

So if you want to analyze the frequency components of a signal as it changes over time, and you want to see what the FFT looks like at a high rate then you can just take in however many samples you need. Run the FFT. Shift all the samples over 1 position, and then take the FFT again at the next sample time.

EXAMPLE:
1) Sample at 819.2 samples per second with a time window of 10 s.
2) Let samples accumulate for 10 s (for a total of 8192 samples)
3) Run the FFT on 8192 samples.
4) Discard the first sample in the buffer, and keep the other 8191 samples shifting them over 1 position.
5) 1/819.2 seconds later add in the next sample to the end of the buffer and re-run the FFT.
6) Repeat steps 4-6 until you have completed your analysis.

This would give you an FFT that analyzes a sliding window of data 819.2 times a second

The processing power needed for the example would be approximately 13*8192*819.2 Multiply-Accumulate opeations per second (87 Million MACs/s). An ordinary PC could easily handle this. You can of course reduce the processing power by a factor of N by only running the FFT ever N samples (for example running it every 8 samples only requies 11M MACs per second).