Adaptive Filter | ADPCM | ADSP | ADSP-2181 | Aliasing | AMR | Anti-Aliasing | ARMA | Autocorrelation | AutoCovariance | Beamforming | Bessel | Blackfin | Butterworth | C6713 | CCS | Chebyshev | CIC Filter | Circular Convolution | Code Composer Studio | Comb Filter | Compression | Convolution | Cross Correlation | DCT | Decimation | Deconvolution | Demodulation | DM642 | DSP Boards | DSP/BIOS | DTMF | Echo Cancellation | Equalization | Equalizer | ETSI | EZLITE (Ez-kit Lite) | FFT | FFTW | FIR Filter | Fixed Point | FSK | G.711 | G.723 | G.729 | Gaussian Noise | Goertzel | GPIO | Hilbert Transform | IFFT | IIR Filter | Interpolation | Invariance | JTAG | Kalman | Laplace Transform | Levinson | LPC | McBSP | MIPS | Modulation | MPEG | Multirate | Notch Filter | Nyquist | OFDM | Oversampling | Pink Noise | Pitch | PLL | Polyphase | QAM | QDMA | Quantization | Quantizer | Radar | Random Noise | Reed Solomon | Remez | Resampling | RTDX | Sampling | Sharc | TI C6711 | Undersampling | Viterbi | Wavelets | White Noise | Wiener Filter | Windowing | XDS510PP | Z Transform

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?

______________________________
DSPRelated.com's 50,000th member announced! Details Here.

On Fri, 20 Nov 2009 12:50:34 -0600, Richard Owlett <r...@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

______________________________
DSPRelated.com's 50,000th member announced! Details Here.

Greg Berchin wrote:
> On Fri, 20 Nov 2009 12:50:34 -0600, Richard Owlett <r...@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

______________________________
DSPRelated.com's 50,000th member announced! Details Here.

On 20 Nov, 19:50, Richard Owlett <rowl...@pcnetinc.com> wrote:
> In an *UNRELATED* post Chris Bore said:
> "
> The way I sometimes think of it, you choose =A0a 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" =A0 =A0 =A0one 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] =3D 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

______________________________
DSPRelated.com's 50,000th member announced! Details Here.

Rune Allnor wrote:
> On 20 Nov, 19:50, Richard Owlett <rowl...@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.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

______________________________
DSPRelated.com's 50,000th member announced! Details Here.

Richard Owlett 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"?
> 
> 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?
> 

Is there any essential difference between a window and a filter?  Yes. 
Unless you want to call them both "functions" and leave it at that.

A window function refers first to a time-limited or bandwidth-limited or 
space-limited situation.  An antenna or a lens is a pretty good example 
that's easy to visualize and leads one immediately to the notion of 
"window".  Think of a window in a building... same thing. The latter are 
all spatially limited in extent.

So, the simplest window is one that doesn't weigh what comes through it.
Thus the gate function, uniform window that we use all the time. 

Antennas again are a good example of more complicated window functions 
where the aperture (the physical extent of the window) is weighted in 
order to reduce sidelobes.
In signal processing window functions are used for the same thing - to 
reduce spectral sidelobes *AS APPLIED TO OR RELATIVE TO SPECTRAL LINES* 
(because of the convolution in frequency).
So, just about all window functions are nonzero except maybe at the 
edges and perhaps with a rather longish taper at the edges and extend 
for the entire limited extent.

A filter refers first to what one wants to do with a function such as 
spectral content which may be of infinite extent (but not need be). 
Except for equalizers, most filters have stop bands and lowpass filters 
attempt to be as close to zero as possible above a certain frequency. 
In this sense they are very different from windows.  In fact, maybe 
you'd call them "black out screens" if taken in the same context.

You can take any function and multiply with it in one domain and see the 
result as a convolution in the Fourier Transformed domain and vice 
versa.  So, this mathematical assertion has nothing to do with the type 
of functions being used.  In general though:
- we design a window function according to its convolution kernel and 
most often implement a window function by multiplying in the opposite 
domain.  The objective is reduction of sidelobes or spectral leakage.
- we design a filter function according to its multiplicative effect and 
very often implement a filter by convolving in the opposite domain and 
sometimes by multiplying in the design domain.  The objective is band 
pass and band stop.
And, we use the two terms because they have specific meaning as above.

If you look at the windowing method of filter design then it should be 
clear how the two fit together in distinct ways.
An idealized filter function is first defined - likely with sharp / 
brick wall band transsitions
Then a window function is used to conceptually convolve the ideal filter 
function to achieve a real filter function with realizable band 
transitions and with acceptable band edge trillies and often to 
time-limit the filter unit sample response as the original filter spec 
likely doesn't represent a FIR filter.

I hope this helps.

Fred

______________________________
DSPRelated.com's 50,000th member announced! Details Here.

Fred Marshall wrote:
> Richard Owlett 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"?
>>
>> 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?
>>
> 
> Is there any essential difference between a window and a filter?  Yes. 
> Unless you want to call them both "functions" and leave it at that.
> 
> A window function refers first to a time-limited or bandwidth-limited or 
> space-limited situation.  An antenna or a lens is a pretty good example 
> that's easy to visualize and leads one immediately to the notion of 
> "window".  Think of a window in a building... same thing. The latter are 
> all spatially limited in extent.
> 
> So, the simplest window is one that doesn't weigh what comes through it.
> Thus the gate function, uniform window that we use all the time.
> Antennas again are a good example of more complicated window functions 
> where the aperture (the physical extent of the window) is weighted in 
> order to reduce sidelobes.
> In signal processing window functions are used for the same thing - to 
> reduce spectral sidelobes *AS APPLIED TO OR RELATIVE TO SPECTRAL LINES* 
> (because of the convolution in frequency).
> So, just about all window functions are nonzero except maybe at the 
> edges and perhaps with a rather longish taper at the edges and extend 
> for the entire limited extent.
> 
> A filter refers first to what one wants to do with a function such as 
> spectral content which may be of infinite extent (but not need be). 
> Except for equalizers, most filters have stop bands and lowpass filters 
> attempt to be as close to zero as possible above a certain frequency. In 
> this sense they are very different from windows.  In fact, maybe you'd 
> call them "black out screens" if taken in the same context.
> 
> You can take any function and multiply with it in one domain and see the 
> result as a convolution in the Fourier Transformed domain and vice 
> versa.  So, this mathematical assertion has nothing to do with the type 
> of functions being used.  In general though:
> - we design a window function according to its convolution kernel and 
> most often implement a window function by multiplying in the opposite 
> domain.  The objective is reduction of sidelobes or spectral leakage.
> - we design a filter function according to its multiplicative effect and 
> very often implement a filter by convolving in the opposite domain and 
> sometimes by multiplying in the design domain.  The objective is band 
> pass and band stop.
> And, we use the two terms because they have specific meaning as above.
> 
> If you look at the windowing method of filter design then it should be 
> clear how the two fit together in distinct ways.
> An idealized filter function is first defined - likely with sharp / 
> brick wall band transsitions
> Then a window function is used to conceptually convolve the ideal filter 
> function to achieve a real filter function with realizable band 
> transitions and with acceptable band edge trillies and often to 
> time-limit the filter unit sample response as the original filter spec 
> likely doesn't represent a FIR filter.
> 
> I hope this helps.

I'm sure it did. Perhaps I will unhelp a bit. Consider a telescope's 
circular aperture. It is the hard-edged window through which light 
passes to form the final image, and like all hard-edged windows, causes 
oscillations in intensity at sharp transitions in the image. (Example: a 
point becomes an Airy disk, complete with sidelobes. The bigger the 
aperture, the more compact the Airy disk, but the form remains the same. 
The sidelobe rings can be suppressed if one is willing to pay the price 
of a larger disk. This is done by modifying the window so that it grays 
out toward the edges instead of going opaque abruptly. Except for the 
circular symmetry, this is the same as as a window applied to FFT data 
or FIR coefficients. In optics, it is called "apodizing". 
http://tinyurl.com/ybxw2o6 shows a picture of a device to perform that 
windowing. I think most people would call it a filter. The maker does.

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

______________________________
DSPRelated.com's 50,000th member announced! Details Here.

On Nov 20, 1:50=A0pm, Richard Owlett <rowl...@pcnetinc.com> wrote:
> In an *UNRELATED* post Chris Bore said:
> "
> The way I sometimes think of it, you choose =A0a 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" =A0 =A0 =A0one refers to a "window".
> If in "frequency domain" one refers to a "filter".
>
> Am I close?

There are four flash tutorials here on the DFT.  The last one goes
over why windowing is used:

http://www.fourier-series.com/fourierseries2/DFT_tutorial.html

There is a flash tutorial on digital convolution here:

http://www.fourier-series.com/fourierseries2/convolution.html

This gives background to how an FIR filter coefficients are calculated
to get the proper answer at each point in time

This page points to two flash tutorials on how to generate low pass
FIR filters and FIR BP filters.  It allows you to either apply
windowing or not applt windowing.


http://www.fourier-series.com/fourierseries2/FIR-filter.html

______________________________
DSPRelated.com's 50,000th member announced! Details Here.