Sampling frequency of modulated signal

A very naive question... A signal with bandwidth of 20 MHz is modulated using a carrier of 1 GHz. What will be the sampling frequency? I was asked this question during an interview. I answered 2 GHz but the interviewer said it will be 40 MHz. Can anyone explain it? Thanks.

1 Answer

Nyqvist-shannon sampling theorem only says that your sampling frequency should be greater than twice the bandwidth of the signal and not twice the carrier frequency of the signal. Hence you can modulate your 20 MHz signal at any carrier frequency you need and still get back your original signal by sampling at greater than 40 MHz. Hence you need not sample at 2GHZ for recovery of signal, you can do away with a sampling frequency greater than 40 MHz itself For a more clear understanding refer to bandpass sampling.

http://en.wikipedia.org/wiki/Undersampling

• Depending on what is meant by modulation, a baseband signal of bandwidth $20$ MHz might give a passband signal of bandwidth $40$ MHz, and depending on what is meant by sampling might need sampling at a rate greater than $80$ MHz. – Dilip Sarwate May 2 '14 at 13:59
• @DilipSarwate Did you mean if double sideband modulation is used,it might require a sampling frequency greater than 80MHz. – Karan Talasila May 2 '14 at 17:56
• Yes, that is what I meant. The question asked by the interviewer is ambiguous at best and what the interviewer gave as the answer is for a specific case of single-side band AM. There is also ambiguity with regard to what is meant by sampling. Are these complex-valued samples or real-valued samples? This too can affect the answer. – Dilip Sarwate May 2 '14 at 18:38
• @DilipSarwate Yes the interviewer is referring to single sideband AM. With regard to real samples or complex valued samples, complex valued samples occur only when you use IQ modulation for which sampling frequency can be equal to bandwidth though the total no of samples is still the same for given bandwidth since you have to sample I channel and Q channel. IQ modulation can be used for the Frequency modulation and phase modulation case. Correct me if I am wrong so that i can make the edit. – Karan Talasila May 3 '14 at 2:15