Les Cargill <lcargill99@comcast.com> writes:

> Randy Yates wrote:
>> Les Cargill <lcargill99@comcast.com> writes:
>>
>>> Randy Yates wrote:
>>>> Les Cargill <lcargill99@comcast.com> writes:
>>>>> [...]
>>>>> Tim Wescott wrote:
>>>>>> Note that what I gave you was a 2-tap boxcar with a pole at z = 0;
>>>>>
>>>>> Yeah, it compares quite closely with a classic moving average.
>>>>
>>>> Boxcar, moving average - same damn thing.
>>>>
>>>
>>>
>>> Very similar - but not exactly the same.
>>
>> Les,
>>
>> What difference do you think exists?
>>
>
> Huh. Are they mathematically equivalent?

Hi Les,

I would say a discrete-time N-sample moving average filter
has z-transform

  H_ma(z) = (1 / N) * sum_{n = 0}^{N-1} z^{-n},

while an N-sample boxcar filter has z-transform

  H_bc(z) = A * sum_{n = 0}^{N-1} z^{-n}

So yes, except for possibly the scaling factor A.

I don't know why you brought Butterworth into it - those are IIR, while
these are FIR.
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

Cedron <103185@DSPRelated> wrote:

>>> ARMA = Autoregressive-moving-average

>It was enough to answer what the acronym stood for.  I glanced at the
>article, it did look fairly complicated.  I won't speculate on Eric's
>motivation, he would have to answer that.

We actually had a discussion here once about the so-called ARMA
filter and whether it is or is not complicated.  

I have used this filter topology many times, beginning when
I was a grad student and working on speech analysis/synthesis,
where it is (or was) popularly used.  Some filter designers have never
had ocassion to use it.  I believe it to have good precision
properties but there was no consensus formed in the discussion.

i.e. situation normal.

Steve

rickman  <gnuarm@gmail.com> wrote:

>On 5/31/2015 2:02 PM, Cedron wrote:

>> ARMA = Autoregressive-moving-average

>I'm glad that was enough for you.  The name didn't mean anything to me 
>until I read a bit about it.  A fairly complex topic really.  Nothing 
>like a simple moving average.  Not sure why Eric even brought it up.

I think, to point out that moving averages are not necessarily
rectangular, in at least some peoples' terminlogy.

True, but IMO it's a misnomer in cases such as "ARMA".  (e.g. why
not call direct-forms I and II moving averages also?  They are
all topologies of the same filter.)

Steve

Eric Jacobsen <eric.jacobsen@ieee.org> wrote:

> Plus there's the whole ARMA  thing, so it's been used in
> the lit for a long time to mean something other than a boxcar.

Does anybody but Mathworks call a lattice filter an "ARMA"?

Steve

On Sun, 31 May 2015 14:08:24 -0400, rickman <gnuarm@gmail.com> wrote:

>On 5/31/2015 2:02 PM, Cedron wrote:
>> [...snip...]
>>
>>>
>>> BTW, why would you use the abbreviation ARMA, even in this group,
>>> without explanation?  I bet I'm not the only one who had to look it up.
>>>
>>>
>>>> Just my dos centavos.
>>>
>>> Thanks, now I can have that operation I've been needing...
>>>
>>> --
>>>
>>> Rick
>>
>> I had to look it up, too.  I wouldn't have had to if you had copy and
>> pasted the answer when you did.
>>
>> ARMA = Autoregressive-moving-average
>
>I'm glad that was enough for you.  The name didn't mean anything to me 
>until I read a bit about it.  A fairly complex topic really.  Nothing 
>like a simple moving average.  Not sure why Eric even brought it up.

ARMA filters are a DSP topic that was hot-ish maybe a couple of
decades ago.   It is a fairly straightforward and contextually
relevant example of the use of the term Moving Average to mean
something other than a boxcar, which was a sort-of-joking response to
Randy stating that boxcar and moving average are the same thing.

It is just another example of how people can sometimes get hung up on
semantic issues due to terms that are overloaded. 

Can make for fun discussions. 

Not sure why that was complicated.




Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

>>
>> ARMA = Autoregressive-moving-average
>
>I'm glad that was enough for you.  The name didn't mean anything to me 
>until I read a bit about it.  A fairly complex topic really.  Nothing 
>like a simple moving average.  Not sure why Eric even brought it up.
>
>-- 
>
>Rick

It was enough to answer what the acronym stood for.  I glanced at the
article, it did look fairly complicated.  I won't speculate on Eric's
motivation, he would have to answer that.

Ced
---------------------------------------
Posted through http://www.DSPRelated.com

On 5/31/2015 2:02 PM, Cedron wrote:
> [...snip...]
>
>>
>> BTW, why would you use the abbreviation ARMA, even in this group,
>> without explanation?  I bet I'm not the only one who had to look it up.
>>
>>
>>> Just my dos centavos.
>>
>> Thanks, now I can have that operation I've been needing...
>>
>> --
>>
>> Rick
>
> I had to look it up, too.  I wouldn't have had to if you had copy and
> pasted the answer when you did.
>
> ARMA = Autoregressive-moving-average

I'm glad that was enough for you.  The name didn't mean anything to me 
until I read a bit about it.  A fairly complex topic really.  Nothing 
like a simple moving average.  Not sure why Eric even brought it up.

-- 

Rick

[...snip...]

>
>BTW, why would you use the abbreviation ARMA, even in this group, 
>without explanation?  I bet I'm not the only one who had to look it up.
>
>
>> Just my dos centavos.
>
>Thanks, now I can have that operation I've been needing...
>
>-- 
>
>Rick

I had to look it up, too.  I wouldn't have had to if you had copy and
pasted the answer when you did.  

ARMA = Autoregressive-moving-average

Ced
---------------------------------------
Posted through http://www.DSPRelated.com

>
>I'm being persnickety about "equivalent" and "very similar". They
>may well be functionally so similar as to be indistinguishable.
>
>-- 
>Les Cargill

Les,

These are worth being persnickety about.  Just as "exact" and
"approximate" are.

Moving averages are not just used by DSP engineers.  They are tools of
time series data analysis.  In the stock markets, it is known as
"Technical Analysis".  If you want to stretch the definition of financial
data as a "digital signal", fine, then you also have to call technical
analysts DSP engineers.

My opinion, if anybody cares about this humble bit twiddler's opinion, is
that "moving average" is a category and needs further specification to
indicate a particular type.  When somebody specifies a time period in
front of it, as in 100 day moving average, I think that is sufficient to
assume that it is an arithmetic moving average.

Ced

---------------------------------------
Posted through http://www.DSPRelated.com

Randy Yates wrote:
> Les Cargill <lcargill99@comcast.com> writes:
>
>> Randy Yates wrote:
>>> Les Cargill <lcargill99@comcast.com> writes:
>>>> [...]
>>>> Tim Wescott wrote:
>>>>> Note that what I gave you was a 2-tap boxcar with a pole at z = 0;
>>>>
>>>> Yeah, it compares quite closely with a classic moving average.
>>>
>>> Boxcar, moving average - same damn thing.
>>>
>>
>>
>> Very similar - but not exactly the same.
>
> Les,
>
> What difference do you think exists?
>

Huh. Are they mathematically equivalent?

Using the york.uk generated code for a first order* Butterworth it is
(paraphrased):

*higher order; just add buckets an constants.

// alpha is the cutoff frequency:
CONST1 = (alpha/Fs);
foreach k in range {
     xv[0] = xv[1];
     xv[1] = in[k] / DCGAIN;
     yv[0] = yv[1];
     yv[1] =   (xv[0] + xv[1])
                  + ( CONST1  * yv[0]);
     out[k] = yv[1];
}

so CONST1 simply acts as a weight. I am not fully convinced I
understand how the "delay" part of the 0 and 1 index use works.

Naively, I would think a first-order, weighted, moving average would
have one less  "bucket". xv[0] and yv[0] are buckets; so are
xv[1] and yv[1].

I'm being persnickety about "equivalent" and "very similar". They
may well be functionally so similar as to be indistinguishable.

-- 
Les Cargill