Curiously, permutations created in this way ( and their circular shifts ) have been shown to be Costas arrays.
2.
Rotation ( which in the FFT is multiplication by a complex phasor ) is a circular shift of the component waveform.
3.
There are also compiler-specific intrinsics implementing circular shifts, like _ rotl8, _ rotl16, _ rotr8, _ rotr16 in Microsoft Visual C + +.
4.
In practice, it is more likely that \ g _ b will be a simple linear shift of \ g _ a, rather than a circular shift as required by the explanation above.
5.
Unlike an arithmetic shift, a circular shift does not preserve a number's sign bit or distinguish a number's exponent from its significand ( sometimes referred to as the mantissa ).
6.
If the images consist of a flat background, with all detail situated away from the edges, then a linear shift will be equivalent to a circular shift, and the above derivation will hold exactly.
7.
There are also'bidirectional'shift registers which allow shifting in both directions : L?! R or R?! L . The serial input and last output of a shift register can also be connected to create a'circular shift register '.
8.
Unlike an arithmetic shift, a logical shift does not preserve a number's sign bit or distinguish a number's exponent from its significand ( mantissa ); every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled, usually with zeros ( contrast with a circular shift ).
9.
When representing elements as a binary string ( e . g . in GF ( 2 3 ) the most significant bit represents ? 2 2 = ? 4, the middle bit represents ? 2 1 = ? 2, and the least significant bit represents ? 2 0 = ? ), we can square elements by doing a left circular shift ( left shifting ? 4 would give ? 8, but since we are working in GF ( 2 3 ) this wraps around to ? ).
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