FFT Windowing and Transmit Pulse Shaping

Started by August 11, 2010
```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.
```
```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.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```>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.
>
>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;
>

Could you please elaborate? In both cases aren't we considering the DFT of
the same time domain waveform?
```
```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.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```>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.
```
```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

```
```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
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
```
```>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
>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
>
```
```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
```
```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
```