region of convergence of z transform - why bother

Started by December 11, 2018
```Yes I understand the theory, left handed and right-handed sequences. we can=
have two z transfer functions the same but one is left hand sided and the =
other right.
A great deal is spent explaining this but exactly what is the use in the fi=
rst place of left-handed sequences as they are non-causal. I see in countle=
ss book examples of sequences going backwards in time - find the z-transfer=
function!

Now for optimal filtering I agree we need this (Wiener), but for what other=
application do we need left-handed sequences? Usually in control-theory we=
only use the one-sided z-transform. I suppose in DSP we can have some long=
positive and negative sided sequence and we delay the left-handed one and =
shift it into the right, but that just becomes an FIR filter + delay.

```
```On Tuesday, 11 December 2018 00:04:43 UTC-5, gyans...@gmail.com  wrote:

>  I suppose in DSP we can have some long positive and negative sided sequence and we delay the left-handed one and shift it into the right, but that just becomes an FIR filter + delay.

Well, in image processing the "time" access is really the x or y axis. So it makes perfect sense to have "non-causal" systems there.

```
```On Friday, January 4, 2019 at 6:19:48 AM UTC+13, Peter K. wrote:
> On Tuesday, 11 December 2018 00:04:43 UTC-5, gyans...@gmail.com  wrote:
>
> >  I suppose in DSP we can have some long positive and negative sided sequence and we delay the left-handed one and shift it into the right, but that just becomes an FIR filter + delay.
>
> Well, in image processing the "time" access is really the x or y axis. So it makes perfect sense to have "non-causal" systems there.

Oh agreed! I never do image processing so never thought of that one
```
```On 1/4/19 3:13 PM, gyansorova@gmail.com wrote:
> On Friday, January 4, 2019 at 6:19:48 AM UTC+13, Peter K. wrote:
>> On Tuesday, 11 December 2018 00:04:43 UTC-5, gyans...@gmail.com  wrote:
>>
>>>   I suppose in DSP we can have some long positive and negative sided sequence and we delay the left-handed one and shift it into the right, but that just becomes an FIR filter + delay.
>>
>> Well, in image processing the "time" access is really the x or y axis. So it makes perfect sense to have "non-causal" systems there.
>
> Oh agreed! I never do image processing so never thought of that one
>

Also, even if the axis is time, not all processing is real-time.  Lots
of video/audio manipulation gets done offline where non-causality isn't
a deal breaker.

--
Rob Gaddi, Highland Technology -- www.highlandtechnology.com
Email address domain is currently out of order.  See above to fix.
```
```On Saturday, January 5, 2019 at 12:55:03 PM UTC+13, Rob Gaddi wrote:
> On 1/4/19 3:13 PM, gyansorova@gmail.com wrote:
> > On Friday, January 4, 2019 at 6:19:48 AM UTC+13, Peter K. wrote:
> >> On Tuesday, 11 December 2018 00:04:43 UTC-5, gyans...@gmail.com  wrote:
> >>
> >>>   I suppose in DSP we can have some long positive and negative sided sequence and we delay the left-handed one and shift it into the right, but that just becomes an FIR filter + delay.
> >>
> >> Well, in image processing the "time" access is really the x or y axis. So it makes perfect sense to have "non-causal" systems there.
> >
> > Oh agreed! I never do image processing so never thought of that one
> >
>
> Also, even if the axis is time, not all processing is real-time.  Lots
> of video/audio manipulation gets done offline where non-causality isn't
> a deal breaker.
>
> --
> Rob Gaddi, Highland Technology -- www.highlandtechnology.com
> Email address domain is currently out of order.  See above to fix.

But unless you run the data backwards through an uncausal filter, usually we move the uncausal part to make it causal. When you say lots, I can't think of many. Smoothing is one but we can delay the noncausal part and shift it to the right. But ok, point taken. I should have said real-time filters.
```