# Nyquest sampling criteria

Discussion in 'Wireless & RF Design' started by tomshong, Apr 10, 2012.

1. ### tomshong Thread Starter Member

Oct 6, 2011
36
0
Hi experts,

I was looking thru some of my old notes from school, and I came across the topic of Nyquest sampling criteria.

When I studied it, I was taught, for an analog signal to be accurate represented in the digital domain, it needs to be sampled at twice the frequency.

So, a input signal at 1 Mhz, feeding into a ADC, it will need to be sampled at 2 Mhz, ie, 2 Msps

Recently, I start digging around and did my research, and this is what I am begin to wonder:

It is the BANDWIDTH of the input that needs to be less than ½ of the sampling frequency. So given the same ADC above with 2 Msps, if the signal is 1 Ghz, as long as its BANDWIDTH is less than 2 Mhz. the signal can be properly captured in the digital domain.

What do you think? Please advise.

Tom

2. ### Kermit2 AAC Fanatic!

Feb 5, 2010
4,158
1,125
No.

With sample rates lower than the freq. of interest, an aliased(false) signal is created with a freq. lower than the one of interest. With the extreme difference in sample rate and data in your example several false signals would probably be discerned by the ADC

3. ### MrChips Moderator

Oct 2, 2009
19,129
6,148
What you are referring to is called the corollary of the Nyquist Theorem.

You almost have the right idea but you are out by a factor of 2. The bandwidth (starting from 0 Hz) must be less than 1MHz if the sampling frequency is 2Msps.

The Nyquist Theorem states that the sampling frequency must be at least twice the maximum input frequency.

The corollary of the Nyquist Theorem states that there must be no input frequency that is greater than one-half of the sampling frequency.

To meet this criteria, one must implement a low-pass filter to limit the bandwidth of the input signal otherwise one ends up with aliasing. Hence, this filter is called an anti-aliasing filter.

Edit: After reading Kermit's post and rereading the OP, I now see what you're getting at with BANDWIDTH.

There are situations where one can intentionally violate the Nyquist Theorem. This can occur in frequency conversion where you can move the signal to a different Nyquist zone. In this case the signal must be BANDWIDTH limited.

Since I noticed this post is in "Radio and Communications", this is a typical application where a high frequency carrier in an upper Nyquist zone is down converted to baseband.

Last edited: Apr 10, 2012