Prev: Discretization of nonlinear differential equation
Next: Interpolation
From: gretzteam on 17 Nov 2009 19:12
Hi,
In a very basic DDS, the first method used to reduce the ROM size is to
only store one quarter of the sine-wave. Although this sounds very obvious,
I cannot figure out how to do it without storing 1/4th + 1 location in the
ROM.

For example, say we start with a 10-bit address for the full table (1024
locations). Ideally, we want to use the top two bits to determine which
quadrant we are into, and the bottom 8 bits as the address in a
256-location ROM (not a 257 location ROM!!).

However, when implementing this, it really seems like I need to store the
value at pi/4 (256 in the example above), which makes the ROM 257 location!


Any idea?

Thanks!

Dave
From: glen herrmannsfeldt on 17 Nov 2009 20:07
gretzteam <gretzteam(a)yahoo.com> wrote:

> In a very basic DDS, the first method used to reduce the ROM size is to
> only store one quarter of the sine-wave. Although this sounds very obvious,
> I cannot figure out how to do it without storing 1/4th + 1 location in the
> ROM.

> For example, say we start with a 10-bit address for the full table (1024
> locations). Ideally, we want to use the top two bits to determine which
> quadrant we are into, and the bottom 8 bits as the address in a
> 256-location ROM (not a 257 location ROM!!).

Well, it is 1.0 which probably doesn't fit anyway. You know
it is 1.0 (or 0.99999) so just put that in.

> However, when implementing this, it really seems like I need to store the
> value at pi/4 (256 in the example above), which makes the ROM 257 location!

-- glen
From: Tim Wescott on 17 Nov 2009 20:18
On Tue, 17 Nov 2009 18:12:34 -0600, gretzteam wrote:

> Hi,
> In a very basic DDS, the first method used to reduce the ROM size is to
> only store one quarter of the sine-wave. Although this sounds very
> obvious, I cannot figure out how to do it without storing 1/4th + 1
> location in the ROM.
>
> For example, say we start with a 10-bit address for the full table (1024
> locations). Ideally, we want to use the top two bits to determine which
> quadrant we are into, and the bottom 8 bits as the address in a
> 256-location ROM (not a 257 location ROM!!).
>
> However, when implementing this, it really seems like I need to store
> the value at pi/4 (256 in the example above), which makes the ROM 257
> location!
>
>
> Any idea?
>
> Thanks!
>
> Dave

Do like Glen said, and hard-code one location.

Or store values at half-locations, i.e. pi * (1/2048, 3/2048 ...
2047/2048). Not only does this now wrap nicer, but you never have to
deal with 1 -- just 0.9999997.

--
www.wescottdesign.com
From: gretzteam on 17 Nov 2009 20:41
>Do like Glen said, and hard-code one location.
>
>Or store values at half-locations, i.e. pi * (1/2048, 3/2048 ...
>2047/2048). Not only does this now wrap nicer, but you never have to
>deal with 1 -- just 0.9999997.

Got it!
I guess this has a bunch of advantages!
1) Not storing 1.0 is a good one from the ROM width perspective.
2) The ROM address can be generated with a simple one-complement (inverse
all bits) when we detect the 2nd and 4th quadrant! Which also save the
extra address bit I needed!

Now it all sounds obvious, but I litterally spent the whole day on
this...should have posted earlier!

Thanks a lot!

Dave
From: Eric Jacobsen on 18 Nov 2009 01:10
On 11/17/2009 6:41 PM, gretzteam wrote:
>> Do like Glen said, and hard-code one location.
>>
>> Or store values at half-locations, i.e. pi * (1/2048, 3/2048 ...
>> 2047/2048). Not only does this now wrap nicer, but you never have to
>> deal with 1 -- just 0.9999997.
>
> Got it!
> I guess this has a bunch of advantages!
> 1) Not storing 1.0 is a good one from the ROM width perspective.
> 2) The ROM address can be generated with a simple one-complement (inverse
> all bits) when we detect the 2nd and 4th quadrant! Which also save the
> extra address bit I needed!
>
> Now it all sounds obvious, but I litterally spent the whole day on
> this...should have posted earlier!
>
> Thanks a lot!
>
> Dave

Sounds like a day well spent to me. Getting those insights into
implementation issues can help a lot in building efficient systems.

--
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com
 |  Next  |  Last
Pages: 1 2 3
Prev: Discretization of nonlinear differential equation
Next: Interpolation