The winner of the AES competition has a structure that does not qualify as a Feistel cipher, as explained in answers to this recent question.

However, most many of the AES candidates, and all 3 out of 4 some other finalists (Twofish, MARS) are Feistel ciphers, if we define that as a cipher transforming a block of data using a number of rounds which each can be expressed as:


split all the bits of the block $B_j$ into two disjoint portions $L_j$ and $R_j$ (typically of equal size);
compute some (typically round-dependent) function of $R_j$ and key with output $F_j$ of same width as $L_j$;
compute  $L_j'=L_j\oplus F_j$ where $\oplus$ is binary addition with removal of some carry bits (e.g. exclusive-OR, where all carry bits are removed);
recombine bits of $L_j'$ and the unmodified $R_j$ into a new block $B_{j+1}$.


Note: Serpent and RC6 can not be put in this framework (thanks to @Reid and @J.D. for pointing that). Neither can Rijndael/AES.

At the time of the AES competition, Feistel ciphers already enjoyed a well understood theory. In particular DES was among them, and essentially unbroken in practice except for its small key and block size. It would seem that proposing anything else than a Feistel cipher would be an uphill battle.

Yet, Rijndael won the AES competion, and does not fall under the above definition. Did a desirable characteristic of Rijndael made it preferred to the other candidates despite the apparent drawback of using a relatively untested structure? And if that characteristic could not be matched by a Feistel cipher, why?


Question: Demonstrating the effect of aliasing
Answer: I think you need to increase frequency of the size or use far larger steps in the sampling.

The aliasing does not appears if you have a very smooth function. For example, a constant function does not yield aliasing whatever sampling you use.