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From: Richard Owlett on 20 Nov 2009 13:50
In an *UNRELATED* post Chris Bore said:
"
The way I sometimes think of it, you choose a window function
whose kernel best matches the shape that either you think the
signal's spectrum has, or that you want the signal's spectrum
to have.
"

My question --- Is there any ESSENTIAL difference between a
"window" and a "filter"?

I suspect that the answer is "No."

Explanation:
If in "time domain" one refers to a "window".
If in "frequency domain" one refers to a "filter".

Am I close?

From: Greg Berchin on 20 Nov 2009 15:36
On Fri, 20 Nov 2009 12:50:34 -0600, Richard Owlett <rowlett(a)pcnetinc.com> wrote:

>My question --- Is there any ESSENTIAL difference between a
>"window" and a "filter"?
>
>I suspect that the answer is "No."
>
>Explanation:
>If in "time domain" one refers to a "window".
>If in "frequency domain" one refers to a "filter".
>
>Am I close?

Typically a signal is convolved with a filter in the time domain or multiplied
by a filter in the frequency domain (both suitably transformed).

Typically a signal is multiplied by a window in the time domain or convolved
with a window in the frequency domain (as above).

At least, that is the most general usage of the terms, in my experience. So
under those definitions, they are duals of each other.

Greg
From: Richard Owlett on 21 Nov 2009 08:03
Greg Berchin wrote:
> On Fri, 20 Nov 2009 12:50:34 -0600, Richard Owlett <rowlett(a)pcnetinc.com> wrote:
>
>> My question --- Is there any ESSENTIAL difference between a
>> "window" and a "filter"?
>>
>> I suspect that the answer is "No."
>>
>> Explanation:
>> If in "time domain" one refers to a "window".
>> If in "frequency domain" one refers to a "filter".
>>
>> Am I close?
>
> Typically a signal is convolved with a filter in the time domain or multiplied
> by a filter in the frequency domain (both suitably transformed).
>
> Typically a signal is multiplied by a window in the time domain or convolved
> with a window in the frequency domain (as above).
>
> At least, that is the most general usage of the terms, in my experience. So
> under those definitions, they are duals of each other.
>
> Greg

Thanks

From: Rune Allnor on 21 Nov 2009 09:01
On 20 Nov, 19:50, Richard Owlett <rowl...(a)pcnetinc.com> wrote:
> In an *UNRELATED* post Chris Bore said:
> "
> The way I sometimes think of it, you choose  a window function
> whose kernel best matches the shape that either you think the
> signal's spectrum has, or that you want the signal's spectrum
> to have.
> "
>
> My question --- Is there any ESSENTIAL difference between a
> "window" and a "filter"?

Well, the statement by Cris seems to be about spectrum
estmation. Which is an application of windows that is
unrelated to filters.

> I suspect that the answer is "No."
>
> Explanation:
> If in "time domain"      one refers to a "window".
> If in "frequency domain" one refers to a "filter".
>
> Am I close?

Well... both windows and filters can be discussed in
time or frequency domain, so in that sense you are
close. But you missed the main argument:

A "filter" is the desired product of a filter design
procedure or algorithm. The ideal filter response in
frequency domain, the rectangular response, results in
the infitely long sinc in time domain.

Since we can not work with infinitely long signals,
we truncate the sinc. Formally, this is equivalent to
element-wise multiplication between the infinitely
long sinc and an infinitely long window function
w such that

w[n] = 1, |n| < N; 0 otherwise.

This truncation, that formally but not always
semantically is a window operation, results in certain
problems with high side lobes in the filter's frequency
response.

To mitigate these problems, the coeffcients in the
filter are multiplied with cefficients in a window
function, one might call them 'explicit window functions'
to make them distinct from the rectangular window that was
implicitly applied through truncating the sinc.

These explict window functions have one explicit task
in the window design procedure: To reduce the side lobes
introduced by the implicitly applied rectangular window.

Rune
From: Jerry Avins on 21 Nov 2009 11:40
Rune Allnor wrote:
> On 20 Nov, 19:50, Richard Owlett <rowl...(a)pcnetinc.com> wrote:
>> In an *UNRELATED* post Chris Bore said:
>> "
>> The way I sometimes think of it, you choose a window function
>> whose kernel best matches the shape that either you think the
>> signal's spectrum has, or that you want the signal's spectrum
>> to have.
>> "
>>
>> My question --- Is there any ESSENTIAL difference between a
>> "window" and a "filter"?
>
> Well, the statement by Cris seems to be about spectrum
> estmation. Which is an application of windows that is
> unrelated to filters.
>
>> I suspect that the answer is "No."
>>
>> Explanation:
>> If in "time domain" one refers to a "window".
>> If in "frequency domain" one refers to a "filter".
>>
>> Am I close?
>
> Well... both windows and filters can be discussed in
> time or frequency domain, so in that sense you are
> close. But you missed the main argument:
>
> A "filter" is the desired product of a filter design
> procedure or algorithm. The ideal filter response in
> frequency domain, the rectangular response, results in
> the infitely long sinc in time domain.
>
> Since we can not work with infinitely long signals,
> we truncate the sinc. Formally, this is equivalent to
> element-wise multiplication between the infinitely
> long sinc and an infinitely long window function
> w such that
>
> w[n] = 1, |n| < N; 0 otherwise.
>
> This truncation, that formally but not always
> semantically is a window operation, results in certain
> problems with high side lobes in the filter's frequency
> response.
>
> To mitigate these problems, the coeffcients in the
> filter are multiplied with cefficients in a window
> function, one might call them 'explicit window functions'
> to make them distinct from the rectangular window that was
> implicitly applied through truncating the sinc.
>
> These explict window functions have one explicit task
> in the window design procedure: To reduce the side lobes
> introduced by the implicitly applied rectangular window.

That's good, but it boiks down to "It depends on what it is used for."
Many objects and concepts depend on use and scale. Where is the
transition between a wire and a rod? A rod and a bar? A bar and a bolt?

Jerry
--
Engineering is the art of making what you want from things you can get.
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