> If simply comparing two algorithms by the number of operations needed to
> compute a sample, would you include delays in filters as an operation? I'm
> just wondering as some papers about FFT only include real multiplications
> and additions as operations.
>

It depends whether you are conducting an academic study or a
real-world engineering.
In the very past you had to know how much time a MUL operations
required compared to a SUM, nowadays they are very similar as they are
hardware implemented, even on microcontrollers such as Arduino's
Atmel.

Anyway, for academic stuff what I usually do (based on what currently
people do) is summing together all real sums and multiplications into
one number. If you have complex data operations, then 1 complex SUM =
2 real SUM, 1 complex MUL = 4 real MUL + 2 real SUM. As for divisions
you can either indicate them as another count, or put them together
with SUM and MUL in the global flops count. This way, however you
can't be too abstract and have to take some reference values. I take
the instruction manual of the target architecture and give an estimate
of the number of clock cycles, then compare this to SUM or MUL clock
cycles.
Finally, for the delays, sometimes I indicate the size of the memory
to allocate.

Differently, if you are working on an engineering project, you should
really take care of all pointer arithmetics, value copying, memory
swapping. These can usually go in parallel with the arithmetic
operations (if your code is nice) but you never know. Memory
operations have a severe effect on embedded systems as the system can
stall for many cycles waiting for the data to come. Definitely
divisions are a nightmare on embedded processors and you should just
try to avoid them at all costs (unless you are using a whole DSP for a
digital effect). On x86 forget all the above and write your code as
ugly as possible, you'll never incur in bottlenecks :P :P :P (joking,
but really you have no big issues with divisions and memory ops
there).

Hope this helps.
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