From: fisico32 on
Hello Forum,

I am dealing with a 2D function of time. A 1D function f(t) is symmetric
and even if f(t)=f(-t)

I am dealing with a function f(t1,t2) instead for which

f(t1,t2)=f(-t1, -t2).

In the plane t1-t2, how many possible symmetries with respect to vertical
planes can a function like f(t1,t2) have?
I guess it depends on the function. Is there a way using combinatorics to
find out the various combinations of the arguments t1,t2 to determine if
the function is "even"?

What does the concept of "even" function mean in 2D?

thanks,
fisico

From: dbd on
On May 28, 5:43 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
wrote:
> Hello Forum,
>
> I am dealing with a 2D function of time. A 1D function f(t) is symmetric
> and even if  f(t)=f(-t)
> ...

> What does the concept of "even" function mean in 2D?
>
> thanks,
> fisico

Is your question a (continuous/infinite) theoretical one or do you
want a (sampled/finite) DSP answer? Your first sentence is not true in
the finite sampled domain for some definitions of even.

Dale B. Dalrymple
From: Dirk Bell on
On May 28, 8:43 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
wrote:
> Hello Forum,
>
> I am dealing with a 2D function of time. A 1D function f(t) is symmetric
> and even if  f(t)=f(-t)
>
> I am dealing with a function f(t1,t2) instead for which
>
> f(t1,t2)=f(-t1, -t2).
>
> In the plane t1-t2, how many possible symmetries with respect to vertical
> planes can a function like f(t1,t2) have?
> I guess it depends on the function. Is there a way using combinatorics to
> find out the various combinations of the arguments t1,t2 to determine if
> the function is "even"?
>
> What does the concept of "even" function mean in 2D?
>
> thanks,
> fisico

Think in terms of symmetric "about" something. A number of obvious
symmetries can be defined for 2-D.

BTW for 1-D, what you described is even symmetic about the origin.

Dirk
From: Tim Wescott on
On 05/28/2010 06:55 AM, dbd wrote:
> On May 28, 5:43 am, "fisico32"<marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
> wrote:
>> Hello Forum,
>>
>> I am dealing with a 2D function of time. A 1D function f(t) is symmetric
>> and even if f(t)=f(-t)
>> ...
>
>> What does the concept of "even" function mean in 2D?
>>
>> thanks,
>> fisico
>
> Is your question a (continuous/infinite) theoretical one or do you
> want a (sampled/finite) DSP answer? Your first sentence is not true in
> the finite sampled domain for some definitions of even.

Which ones? Examples? AFAIK it's a universally accepted definition.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
From: dbd on
On May 28, 11:19 am, Tim Wescott <t...(a)seemywebsite.now> wrote:
> On 05/28/2010 06:55 AM, dbd wrote:
>
> > On May 28, 5:43 am, "fisico32"<marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
> > wrote:
> >> ...
> >> fisico

> > Is your question a (continuous/infinite) theoretical one or do you
> > want a (sampled/finite) DSP answer? Your first sentence is not true in
> > the finite sampled domain for some definitions of even.

> Which ones?  Examples?  AFAIK it's a universally accepted definition.

> Tim Wescott

DFT-even

Dale B. Dalrymple