Higher upsampling with minimum phase downsampling produces more aliasing

robert bristow-johnson <rbj@audioimagination.com> wrote:

(snip)
> this would work for a single sine wave in the wavetable.  i think 
> i came across this before in the context of non-musical 
> use (like it was an "NCO" or "DDS" or whatever they're calling 
> it nowadaze).  you can have a sin and cos table (it can be the 
> same table) for "t" and then another sin and cos table 
> for "delta_t" and do
 
>    sin(t + delta_t)  =  cos(t)*sin(delta_t)  +  sin(t)*cos(delta_t)
 
> where delta_t is smaller than the difference between adjacent t values 
> in the first table.

I have the data sheet for sin lookup ROM from the days when ROMs
used 12V power.  To get more bits out of the available ROMs, they
did just that. Though at some point cos(delta_t) is 1.

So, just a few (not very big) ROMs and a TTL adder, for pretty many
bits of sin(x).

-- glen