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what are second order terms in undersampling

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pankaj jha

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hello all !!!

I am reading "Filter Basics: Anti-Aliasing" a tutoral by Maxim (https://www.maximintegrated.com/en/app-notes/index.mvp/id/928).

I am confused in the section of undersampling.
I am attaching the image of the pdf of the section where I am confused.

The tutorial says "Undersampling at 4MHz yields first-order sum and difference terms (f1 + f2 and f1 - f2) of 14MHz and 6Mz, and second-order terms (2f1, 2f2, 2f1 + f2, f1 + 2f2, | 2f1 - f2 |, | f1 - 2f2) | of 8MHz, 20MHz, 18MHz, 2MHz, 24MHz, and 16MHz. "

I am OK with the "first-order sum and difference terms".

I am confused as to how to justify the second order terms? where do they come from? any formula/expresssion? any book or website is welcome.


 

Code: 
df = n*f1 + m *f2 (n, m = 0, +/-1, +/-2 ..)
Second order terms have n or m = +2 or -2
 

Hi FvM !!!
Thanks for your reply.
I understand sampling (normal or undersampling) as summation of shifted versions of the input. Even the expressions for the sampled signal do not show anything like the equation you've mentioned.
Kindly elaborate on the equation. If possible, can you give me the source of this equation.
I want to understand it completely.
 

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