Reply by Fred Marshall August 12, 20102010-08-12
Eric Jacobsen wrote:
> On Thu, 12 Aug 2010 12:43:08 -0700, Fred Marshall > <fmarshall_xremove_the_xs@xacm.org> wrote: > >> Jerry Avins wrote: >> >>> The window used in windowed sinc filter design and for applying to data >>> to be DFTed obey the same underlying math. It isn't very useful to apply >>> that math to the window used to soften the edges of square pulses -- >>> think keyed CW -- thus controlling adjacent-channel interference. >>> >>> Jerry >> Jerry, >> >> I still think it does. To soften the edges of a square pulse, one way >> to think of doing that (about as simple a way as possible) is to >> convolve the square pulse with another, shorter square pulse - giving >> ramped edges. >> >> The Fourier Transform of the shorter square pulse is a broad sinc >> relative to the narrower sinc of the original square pulse. It has the >> effect of reducing adjacent-cahnnel interference. >> >> Obviously we use better window functions than a square pulse but I hope >> this conveys the idea as clearly as possible. >> >> Windowing in filter design is the Fourier Transform dual of the pulse >> shaping process: >> - A perfect lowpass or bandpass filter is the dual of the original >> rectangular pulse and >> - removing the "unrealistic" time response or making it FIR through >> multiplication of a temporal window is the dual of controlling >> adjacent-channel interference. >> >> So, maybe the perspective is in *how* the pulse shaping is done? >> >> Fred > > I'm not sure if this is what you're thinking about, but as I mentioned > to the OP, "Raised Cosine" as applied to FFT and frequency analysis > windowing (or even filter design) is not the same thing as "Raised > Cosine" as applied to pulse-shaping for Nyquist filters (i.e., matched > filters) for communication systems. > > Wikipedia is useful to illustrate the difference. For window > functions, the most relevant windows are the Hann and Hamming: > > http://en.wikipedia.org/wiki/Window_function > > Note that the idea is just to take a cycle of a cosine function and > adjust the amplitude and DC offset. That becomes the "Raised Cosine" > window function. > > For a comm system pulse-shaping application the function, and > interpretation, is not the same: > > http://en.wikipedia.org/wiki/Raised-cosine_filter > > Note that the argument of the cosine function is very different, and > contains beta, the so-called "rolloff factor" or "excess bandwidth" > metric. This beta function takes the center passband of the filter > and stretches it out so that there is a flat portion in the middle. > This most resembles the Tukey window in the first Wiki link on window > functions, but it's still not quite the same thing. > > In the pulse-shaping example the "Raised Cosine" function is directly > describing the spectrum of the signal and has nothing to do with > resolution or sidelobe control. So the basic use of the function > also differs from the spectral windowing application. > > The idea of the spectral and time-domain dualities still holds for > both cases, and there is some conceptual overlap, but that's > fundamental for pretty much anything. > > It's clear that in both applications "Raised Cosine" is not an > inappropriate name for the functions. It is just unfortunate that > the same name being applied for two different things (gosh, that never > happens otherwise in DSP ;) ) causes regular confusion. > > > Eric Jacobsen > Minister of Algorithms > Abineau Communications > http://www.abineau.com
Eric, Yes. I understood that once you'd mentioned it. It's a good point that I'd never particularly focused on. Fred
Reply by Eric Jacobsen August 12, 20102010-08-12
On Thu, 12 Aug 2010 12:43:08 -0700, Fred Marshall
<fmarshall_xremove_the_xs@xacm.org> wrote:

>Jerry Avins wrote: > >> >> The window used in windowed sinc filter design and for applying to data >> to be DFTed obey the same underlying math. It isn't very useful to apply >> that math to the window used to soften the edges of square pulses -- >> think keyed CW -- thus controlling adjacent-channel interference. >> >> Jerry > >Jerry, > >I still think it does. To soften the edges of a square pulse, one way >to think of doing that (about as simple a way as possible) is to >convolve the square pulse with another, shorter square pulse - giving >ramped edges. > >The Fourier Transform of the shorter square pulse is a broad sinc >relative to the narrower sinc of the original square pulse. It has the >effect of reducing adjacent-cahnnel interference. > >Obviously we use better window functions than a square pulse but I hope >this conveys the idea as clearly as possible. > >Windowing in filter design is the Fourier Transform dual of the pulse >shaping process: >- A perfect lowpass or bandpass filter is the dual of the original >rectangular pulse and >- removing the "unrealistic" time response or making it FIR through >multiplication of a temporal window is the dual of controlling >adjacent-channel interference. > >So, maybe the perspective is in *how* the pulse shaping is done? > >Fred
I'm not sure if this is what you're thinking about, but as I mentioned to the OP, "Raised Cosine" as applied to FFT and frequency analysis windowing (or even filter design) is not the same thing as "Raised Cosine" as applied to pulse-shaping for Nyquist filters (i.e., matched filters) for communication systems. Wikipedia is useful to illustrate the difference. For window functions, the most relevant windows are the Hann and Hamming: http://en.wikipedia.org/wiki/Window_function Note that the idea is just to take a cycle of a cosine function and adjust the amplitude and DC offset. That becomes the "Raised Cosine" window function. For a comm system pulse-shaping application the function, and interpretation, is not the same: http://en.wikipedia.org/wiki/Raised-cosine_filter Note that the argument of the cosine function is very different, and contains beta, the so-called "rolloff factor" or "excess bandwidth" metric. This beta function takes the center passband of the filter and stretches it out so that there is a flat portion in the middle. This most resembles the Tukey window in the first Wiki link on window functions, but it's still not quite the same thing. In the pulse-shaping example the "Raised Cosine" function is directly describing the spectrum of the signal and has nothing to do with resolution or sidelobe control. So the basic use of the function also differs from the spectral windowing application. The idea of the spectral and time-domain dualities still holds for both cases, and there is some conceptual overlap, but that's fundamental for pretty much anything. It's clear that in both applications "Raised Cosine" is not an inappropriate name for the functions. It is just unfortunate that the same name being applied for two different things (gosh, that never happens otherwise in DSP ;) ) causes regular confusion. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
Reply by Fred Marshall August 12, 20102010-08-12
Jerry Avins wrote:

> > The window used in windowed sinc filter design and for applying to data > to be DFTed obey the same underlying math. It isn't very useful to apply > that math to the window used to soften the edges of square pulses -- > think keyed CW -- thus controlling adjacent-channel interference. > > Jerry
Jerry, I still think it does. To soften the edges of a square pulse, one way to think of doing that (about as simple a way as possible) is to convolve the square pulse with another, shorter square pulse - giving ramped edges. The Fourier Transform of the shorter square pulse is a broad sinc relative to the narrower sinc of the original square pulse. It has the effect of reducing adjacent-cahnnel interference. Obviously we use better window functions than a square pulse but I hope this conveys the idea as clearly as possible. Windowing in filter design is the Fourier Transform dual of the pulse shaping process: - A perfect lowpass or bandpass filter is the dual of the original rectangular pulse and - removing the "unrealistic" time response or making it FIR through multiplication of a temporal window is the dual of controlling adjacent-channel interference. So, maybe the perspective is in *how* the pulse shaping is done? Fred
Reply by Jerry Avins August 11, 20102010-08-11
On 8/11/2010 9:54 PM, Steve Pope wrote:
> Fred Marshall<fmarshall_xremove_the_xs@xacm.org> wrote: > >> Jerry Avins wrote: > >>> A pulse shaped like a raised cosine in the time domain has >>> much less "splatter" -- broadband energy -- than a rectangular pulse of >>> the same width. What has that to do with windowing the data fed to a DFT >>> routine? > >> Jerry, > >> Oh, I'd say "everything"! :-) > > I'd tend to agree. And it depends upon why you are applying a DFT. > > If you are trying to estimate the relative amplitudes and phases > of expected components within the passband of a signal, often there is > no windowing applied first. > > If instead you are trying to find out how much unwanted energy there > is in the stopband, outside of the signal of interest, you pretty much > have to apply a window. > > (The above is of course a very broad generalization, to which there > are many exceptions, but I think it holds up pretty often.)
The window used in windowed sinc filter design and for applying to data to be DFTed obey the same underlying math. It isn't very useful to apply that math to the window used to soften the edges of square pulses -- think keyed CW -- thus controlling adjacent-channel interference. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Reply by Steve Pope August 11, 20102010-08-11
Fred Marshall  <fmarshall_xremove_the_xs@xacm.org> wrote:

>Jerry Avins wrote:
>> A pulse shaped like a raised cosine in the time domain has >> much less "splatter" -- broadband energy -- than a rectangular pulse of >> the same width. What has that to do with windowing the data fed to a DFT >> routine?
>Jerry,
>Oh, I'd say "everything"! :-)
I'd tend to agree. And it depends upon why you are applying a DFT. If you are trying to estimate the relative amplitudes and phases of expected components within the passband of a signal, often there is no windowing applied first. If instead you are trying to find out how much unwanted energy there is in the stopband, outside of the signal of interest, you pretty much have to apply a window. (The above is of course a very broad generalization, to which there are many exceptions, but I think it holds up pretty often.) Steve
Reply by Fred Marshall August 11, 20102010-08-11
Jerry Avins wrote:
> On 8/11/2010 4:38 PM, Zeph80 wrote: >>> On 8/11/2010 3:55 PM, Zeph80 wrote: >>>> So I'm pretty confused about something.While studying DFT windowing, I >> saw >>>> how rectangular window has lowest bandwidth compared to Hanning window( >>>> which is basically raised cosine), but higher side-lobes. >>>> But in all pulse shaping filter tutorials, apart from minimizing ISI >> they >>>> describe how the bandwidth of the rectangular pulse is almost twice the >>>> raised cosine pulse ( for alpha=0). >>>> What am I doing wrong? This seems very contradictory to me. In both >> cases >>>> windowing and pulse shaping we are looking are the frequency response >>>> aren't we??Im obviously making some very basic mistake, please >> enlighten >>>> me. >>> >>> English is evidently not your first language. Basically, you are >>> confusing the bandwidth of a pulse with the selectivity of a filter. > >> Could you please elaborate? In both cases aren't we considering the >> DFT of >> the same time domain waveform? > > What cases? A pulse shaped like a raised cosine in the time domain has > much less "splatter" -- broadband energy -- than a rectangular pulse of > the same width. What has that to do with windowing the data fed to a DFT > routine? > > Jerry
Jerry, Oh, I'd say "everything"! :-) Rectangular window vs. raised cosine window..... Fred
Reply by Zeph80 August 11, 20102010-08-11
>On Wed, 11 Aug 2010 16:01:45 -0500, "Zeph80" ><surabhi_talwar@n_o_s_p_a_m.hotmail.com> wrote: > >>>On 8/11/2010 4:38 PM, Zeph80 wrote: >>>>> On 8/11/2010 3:55 PM, Zeph80 wrote: >>>>>> So I'm pretty confused about something.While studying DFT
windowing,
>>I >>>> saw >>>>>> how rectangular window has lowest bandwidth compared to Hanning >>window( >>>>>> which is basically raised cosine), but higher side-lobes. >>>>>> But in all pulse shaping filter tutorials, apart from minimizing
ISI
>>>> they >>>>>> describe how the bandwidth of the rectangular pulse is almost twice >>the >>>>>> raised cosine pulse ( for alpha=0). >>>>>> What am I doing wrong? This seems very contradictory to me. In >>both >>>> cases >>>>>> windowing and pulse shaping we are looking are the frequency
response
>>>>>> aren't we??Im obviously making some very basic mistake, please >>>> enlighten >>>>>> me. >>>>> >>>>> English is evidently not your first language. Basically, you are >>>>> confusing the bandwidth of a pulse with the selectivity of a filter. >>> >>>> Could you please elaborate? In both cases aren't we considering the
DFT
>>of >>>> the same time domain waveform? >>> >>>What cases? A pulse shaped like a raised cosine in the time domain has >>>much less "splatter" -- broadband energy -- than a rectangular pulse of
>>>the same width. What has that to do with windowing the data fed to a DFT
>>>routine? >>> >>>Jerry >>>-- >>>Engineering is the art of making what you want from things you can get. > >>>Ok, I think you did not understand my question. However I think I
realize
>>my mistake. >>Case 1: I'm comparing the DFT of a rectangular window and a hanning
(raised
>>cosine window). >>Case 2: Then I'm comparing the frequency domain of a rectangular pulse
to
>>a raised cosine shaped pulse . >>I thought that case 1 and case 2 should have the same results >>I think the mistake is that even though the Hanning window is called
raised
>>cosine, its really a truncated raised cosine compared to the shaped
raised
>>cosine pulses used to transmit data. > >A Raised Cosine window for a DFT is not the same as a Raised Cosine >response for a pulse shape. This is an unfortunate overloading of >the terminology "Raised Cosine", as the raising of the cosine is used >differently and does different things in each case. > >So they are not expected to be the same. > > >Eric Jacobsen >Minister of Algorithms >Abineau Communications
Thanks, I guess I was not communicating my question well. You're the only one who understood my question and mistake. Thanks, again!
>http://www.abineau.com >
Reply by Eric Jacobsen August 11, 20102010-08-11
On Wed, 11 Aug 2010 16:01:45 -0500, "Zeph80"
<surabhi_talwar@n_o_s_p_a_m.hotmail.com> wrote:

>>On 8/11/2010 4:38 PM, Zeph80 wrote: >>>> On 8/11/2010 3:55 PM, Zeph80 wrote: >>>>> So I'm pretty confused about something.While studying DFT windowing, >I >>> saw >>>>> how rectangular window has lowest bandwidth compared to Hanning >window( >>>>> which is basically raised cosine), but higher side-lobes. >>>>> But in all pulse shaping filter tutorials, apart from minimizing ISI >>> they >>>>> describe how the bandwidth of the rectangular pulse is almost twice >the >>>>> raised cosine pulse ( for alpha=0). >>>>> What am I doing wrong? This seems very contradictory to me. In >both >>> cases >>>>> windowing and pulse shaping we are looking are the frequency response >>>>> aren't we??Im obviously making some very basic mistake, please >>> enlighten >>>>> me. >>>> >>>> English is evidently not your first language. Basically, you are >>>> confusing the bandwidth of a pulse with the selectivity of a filter. >> >>> Could you please elaborate? In both cases aren't we considering the DFT >of >>> the same time domain waveform? >> >>What cases? A pulse shaped like a raised cosine in the time domain has >>much less "splatter" -- broadband energy -- than a rectangular pulse of >>the same width. What has that to do with windowing the data fed to a DFT >>routine? >> >>Jerry >>-- >>Engineering is the art of making what you want from things you can get.
>>Ok, I think you did not understand my question. However I think I realize >my mistake. >Case 1: I'm comparing the DFT of a rectangular window and a hanning (raised >cosine window). >Case 2: Then I'm comparing the frequency domain of a rectangular pulse to >a raised cosine shaped pulse . >I thought that case 1 and case 2 should have the same results >I think the mistake is that even though the Hanning window is called raised >cosine, its really a truncated raised cosine compared to the shaped raised >cosine pulses used to transmit data.
A Raised Cosine window for a DFT is not the same as a Raised Cosine response for a pulse shape. This is an unfortunate overloading of the terminology "Raised Cosine", as the raising of the cosine is used differently and does different things in each case. So they are not expected to be the same. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
Reply by dbd August 11, 20102010-08-11
On Aug 11, 12:55=A0pm, "Zeph80" <surabhi_talwar@n_o_s_p_a_m.hotmail.com>
wrote:
> So I'm pretty confused about something.While studying DFT windowing, I sa=
w
> how rectangular window has lowest bandwidth compared to Hanning window( > which is basically raised cosine), but higher side-lobes.
These windows are applied in the time domain.
> But in all pulse shaping filter tutorials, apart from minimizing ISI they > describe how the bandwidth of the rectangular pulse is almost twice the > raised cosine pulse ( for alpha=3D0).
Shaping filter specifications are in the frequency domain.
> =A0What am I doing wrong? This seems very contradictory to me. In both ca=
ses
> windowing and pulse shaping we are looking are the frequency response > aren't we??
No.
>...
Dale B. Dalrymple
Reply by Zeph80 August 11, 20102010-08-11
>On 8/11/2010 4:38 PM, Zeph80 wrote: >>> On 8/11/2010 3:55 PM, Zeph80 wrote: >>>> So I'm pretty confused about something.While studying DFT windowing,
I
>> saw >>>> how rectangular window has lowest bandwidth compared to Hanning
window(
>>>> which is basically raised cosine), but higher side-lobes. >>>> But in all pulse shaping filter tutorials, apart from minimizing ISI >> they >>>> describe how the bandwidth of the rectangular pulse is almost twice
the
>>>> raised cosine pulse ( for alpha=0). >>>> What am I doing wrong? This seems very contradictory to me. In
both
>> cases >>>> windowing and pulse shaping we are looking are the frequency response >>>> aren't we??Im obviously making some very basic mistake, please >> enlighten >>>> me. >>> >>> English is evidently not your first language. Basically, you are >>> confusing the bandwidth of a pulse with the selectivity of a filter. > >> Could you please elaborate? In both cases aren't we considering the DFT
of
>> the same time domain waveform? > >What cases? A pulse shaped like a raised cosine in the time domain has >much less "splatter" -- broadband energy -- than a rectangular pulse of >the same width. What has that to do with windowing the data fed to a DFT >routine? > >Jerry >-- >Engineering is the art of making what you want from things you can get. >&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533; >Ok, I think you did not understand my question. However I think I realize
my mistake. Case 1: I'm comparing the DFT of a rectangular window and a hanning (raised cosine window). Case 2: Then I'm comparing the frequency domain of a rectangular pulse to a raised cosine shaped pulse . I thought that case 1 and case 2 should have the same results I think the mistake is that even though the Hanning window is called raised cosine, its really a truncated raised cosine compared to the shaped raised cosine pulses used to transmit data.