The z-plane's unit circle

Hi Guys,
   I've been thinking about digital oscillators 
with regard to their implementation in 
fixed-point systems.  It occurred to me that 
our lives would be much simpler if instead of 
having to worry about a z-plane circle we only 
had to be concerned with a z-plane rectangle.

[-Rick-]

On Thursday, December 13, 2012 6:00:21 AM UTC-5, Rick Lyons wrote:
> Hi Guys,
> 
>    I've been thinking about digital oscillators 
> 
> with regard to their implementation in 
> 
> fixed-point systems.  It occurred to me that 
> 
> our lives would be much simpler if instead of 
> 
> having to worry about a z-plane circle we only 
> 
> had to be concerned with a z-plane rectangle.
> 
> 
> 
> [-Rick-]

So what does the "corner" frequency represent??

Clay

This would make implementation a lot easier. There is the problem of the
time varying magnitude of the oscillator.

On 2012-12-13 12:00, Rick Lyons wrote:
> 
> Hi Guys,
>    I've been thinking about digital oscillators 
> with regard to their implementation in 
> fixed-point systems.  It occurred to me that 
> our lives would be much simpler if instead of 
> having to worry about a z-plane circle we only 
> had to be concerned with a z-plane rectangle.

What's the issue here?

Just change the "distance" function to a
proper one... :-)

bye,

-- 

piergiorgio

Rick Lyons <R.Lyons@_BOGUS_ieee.org> writes:

> Hi Guys,
>    I've been thinking about digital oscillators 
> with regard to their implementation in 
> fixed-point systems.  It occurred to me that 
> our lives would be much simpler if instead of 
> having to worry about a z-plane circle we only 
> had to be concerned with a z-plane rectangle.

Does that mean that unstable people think outside the box?
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

Am 13.12.2012 12:00, schrieb Rick Lyons:
>
> Hi Guys,
>     I've been thinking about digital oscillators
> with regard to their implementation in
> fixed-point systems.

What is the advantage of a digital oscillator against, say,
a DDS generator?

Thomas

I have used these on dsps with no sin table. They work great except if you change the frequency on the fly, the amplitude may change. Depends on when the coefficients change relative to the sine wave. 


Bob

On Thursday, December 13, 2012 2:30:40 PM UTC-5, Robert Adams wrote:
> I have used these on dsps with no sin table. They work great except if you change the frequency on the fly, the amplitude may change. Depends on when the coefficients change relative to the sine wave. 
> 
> 
> 
> 
> 
> Bob

It is easy to add amplitude stabilization to a digital resonator to solve that problem.

On 12/13/12 2:16 PM, Thomas Heller wrote:
> Am 13.12.2012 12:00, schrieb Rick Lyons:
>>
>> I've been thinking about digital oscillators
>> with regard to their implementation in
>> fixed-point systems.
>
> What is the advantage of a digital oscillator against, say,
> a DDS generator?

*what* is the difference?

i still haven't understood anyone who differentiates the concepts of 
"Direct Digital Synthesis" (whatever that means) and the good ol' 
"Numerically Controlled Oscillator" with the phase accumulator and such.

i realize that, for different waveforms, that there are different ways 
of doing things, like for a simple square wave, you can have a simple 
count-down timer and toggle the output, or for a pure sine, you can 
synthesize it from an equation (or equations) similar to

    y[n]  =  2 cos(omega) y[n-1]  -  y[n-2]

    (there's another pair of equations for quadrature synthesis)

and with the typical NCO, it's a phase accumulator with table lookup 
and, perhaps, some interpolation.

does not DDS include any of these methods?

Rick (and group), isn't this largely a solved problem?


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

"Thomas Heller" <theller@ctypes.org> wrote in message 
news:aiunsoF71noU1@mid.individual.net...
> Am 13.12.2012 12:00, schrieb Rick Lyons:
>>
>> Hi Guys,
>>     I've been thinking about digital oscillators
>> with regard to their implementation in
>> fixed-point systems.
>
> What is the advantage of a digital oscillator against, say,
> a DDS generator?

If you need more then 15..16 bits of accuracy, DDS - like generators are 
getting rather heavy and non-trivial.

Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com