Number of DFT (FFT) Points Required for a Specific Frequency Resolution for an Oversampled Signal

I have a bandpass signal centered at 2 MHz and bandwidth of 50 kHz (the signal frequency varies from 2 MHz - 25 kHz to 2 MHz + 25 kHz). This signal is being sampled at 10 MHz. I want a frequency resolution of 100 Hz in FFT.

I want to know:

1. 
   

   How many samples of the signal should I take to achieve this frequency resolution.

   
   


2. 
   

   What should be the number of points in FFT for this frequency resolution.

   
   

My thoughts:

Minimum frequency in the bandpass signal = 1.975 MHz.

To complete one period of the minimum frequency = 5.0633e-07 seconds.

No of samples in 5.0633e-07 seconds = 5.0633 ~ 6 samples.

So at least 6 samples should be taken to complete one cycle of min frequency.

Now the frequency resolution is 100 Hz.

Since the sampling frequency is 10 MHz, Maximum frequency can be detected is 5 MHz.

So 5MHz/100Hz = 50000 points will be there in first half of FFT.

Second half of the FFT is redundant (complex conjugation of the first half).

So I should take 2*50000 = 1,00,000 point FFT (2^17 = 131072 point FFT) for the above specifications.

Will this work?

Answer

1. The resolution in the DFT is given by: $ \frac{{F}_{s}}{N} $.
   Hence you need 10e6 / 100 = 100,000 samples to get the resolution you want.


2. You may bring the signal to the baseband (demodulation) and then you'll need a lower frequency of sampling to achieve what you want.
   Since the effective bandwidth of the signal is (Two Sided) 50 [KHz], it can be sampled at $ {F}_{S} = 50 [KHz] $ and only 500 samples would be required for the asked resolution.