Fred Marshall wrote:
> "Richard Owlett" <
[email protected]> wrote in message
> news:
[email protected]...
while having had 5 hours sleep in previous 40+
response below is being composed after >12 hrs sleep ;}
>
>>I am neophyte [ perhaps read ignorant ;]
>>
>>I've been told that a poorly chosen window can cause problems .}
>>
>>For my application the ratio of "maximumly flat" to transition region is
>>
>>>1000:1.
>>
>>What should I be considering?
>>where should I be looking?
>>
>>Thanks
>
>
> Well, you might be a bit more explicit with your terms.
Yes and I should have stated what I wanted to window and for what purpose.
I have data in time domain on which I would like to examine how its
spectrum changes in time.
> I'll just use
> conjecture here:
>
> The transition region might be defined as a fraction of fs, as a fraction of
> fs/2 or maybe as a fraction of the passband. You seem to imply as a
> fraction of the passband of a lowpass. It's a lot easier to talk about if
> it's a fraction of fs or fs/2.
I associate your terms with the frequency domain.
I'm thinking about the time domain.
I know the math is the same but natural language makes a distinction
whose underlying presuppositions can snare. Or, "words are slippery".
>
> Here's a rule of thumb:
> The transition band width (or the narrowest transition band width) will be
> no narrower than the reciprocal of the length of the filter.
> So, if you're going to window data then that same length requirement
> applies.
>
> Next, it's important to state the purpose of the window because:
>
> - you might be windowing data for the purpose of reducing spectral spreading
> (which is related to ripple in a filter).
This is what I was thinking of.
> - you might be doing filter design using the windowing method.
No. I'm not even sure of what that is. Let's leave that portion of my
education for another time.
>
> Either way, the Fourier Transform of the window function will convolve
> either:
> - the signal spectrum
> or
> - the filter frequency response.
>
> Think about this:
> A window in time will look something like a sinc in the frequency domain -
> with more or less ripple decay and with more or less main lobe width.
> The affect of multiplying in time by one of these windows is convolution in
> frequency. So, you are convolving in frequency with something very similar
> to a sinc. As the sinc gets wider, the ripples on the edges get smaller for
> good windows.
> For sharp response, the sinc-like function needs to be narrow / so the
> filter needs to be long in time.
> For a narrow sinc-like function, the convolution with a typical perfect
> rectangular lowpass or bandpass filter will appear much like the integral of
> the sinc-like function centered on the transitions.
> So, a very ripply sinc-like function - integrated - will be ripply.
> A wider sinc-like function will make the transitions wide.
> and so forth .....
>
> Unless you care about fine detail,
But just what is "fine detail". I'm operating intuitively here thinking
that a "fine detail" might just come back to bite me.
> the details of the window don't matter
> all that much. Each decent window gets you close to the same result. To
> see this do the following:
>
> 1) Compute the Fourier Transform of a triangle and of a raised cosine both
> of the same length.
> How much different are the results?
I had been working along those lines. But I kept having the problem how
to determine that two different windows had comparable width. eg are the
first two windows on http://astronomy.swin.edu.au/~pbourke/other/windows/
really comparable?
>
> 2) Apply each of these windows to a temporal sinc to get a windowed design
> of a lowpass filter.
> How much different are the Fourier Transforms / the filter responses?
>
> More control of the window gets better results but as the windows get
> better, the results vary not all that much.
>
> Fred
>
>