[time-nuts] DDS'ery

[Magnus Danielson]

On 06/21/2011 04:29 PM, Jim Lux wrote:
> On 6/21/11 6:14 AM, dk4xp at arcor.de wrote:
>> There is an excellent article about cordic on
>>
>> http://www.andraka.com/files/crdcsrvy.pdf
>
>
> Yes..good explanation..
>
> So, in the "general case" where you might want to rotate by an arbitrary
> angle at each time step, where the angle doesn't happen to be 1/2^n, you
> still need either multiple shift/add operations, or a multiply add.
>
> (i.e. it's no different than longhand multiplication... it takes N
> (optional) adds to multiply by an N bit precision number, or you
> cleverly parallelize/pipeline it).
>
> And, in a lot of applications, you'll need to still do a multiply by the
> "gain" (product of all those cos phi) term you factored out
>
> I can see that there could be advantages in implementation, but in the
> general case, is it actually that much more efficient?
>
> (in a CPU with no multiply, yes, it's a lot better, because it's
> essentially the same as doing long multiplication, but you get more done
> for the same amount of work)
>
> Maybe it's a "how many gates do you need for a given precision" sort of
> thing? Or the fact that it generates sin/cos together (which is very
> useful in some cases)
>
> in a random "give me the cos(theta)" sort of situation (e.g. a
> calculator), compared to computing the series expansion, clearly CORDIC
> is the way to go.
>
> But in a DDS, you're generating a continuous series of samples.
>
> I'll have to think about it.
>
> (and, because it's integrating a difference equation, CORDIC does have
> the accumulating roundoff, unless you compute each sin/cos from scratch
> each time)

You do calculate the sin/cos from scratch on each sample. The CORDIC 
add/sub strategy allows for pipe-line processing at sample rate and will 
take less real estate than equivalent LUT.

Do read the article that Bruce referenced.

You could also play a little with integrators and stuff to let the 
dynamics grow up if you can allow some upper frequency limitation.

Cheers,
Magnus