From: "Yi Cao" <y.cao@cranfield.ac.uk>
Path: news.mathworks.com!newsfeed-00.mathworks.com!webcrossing
Newsgroups: comp.soft-sys.matlab
Subject: Re: How to zoom into a certain part of FFT?
Message-ID: <ef5bd15.15@webcrossing.raydaftYaTP>
Date: Fri, 29 Jun 2007 04:05:31 -0400
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Vista wrote:
>
>
>
> "Yi Cao" <y.cao@cranfield.ac.uk> wrote in message
> news:ef5bd15.13@webcrossing.raydaftYaTP...
>> Vista wrote:
>>>
>>>
>>> Hi folks,
>>>
>>> This is not a joke post. I really have this question in my
mind
> for
>>> long
>>> time.
>>>
>>> When I truncate/extract out F(w) for w in [-B, B] and use
step
> size
>>> deltaB
>>> to sample it and then do IFFT, what is the portion of f(t)
I
> see?
>>> Say f(t)
>>> for t in [a, b]. What are a and b?
>>>
>>> Now suppose I find there is some fine structure in [c, d],
which
> is
>>> shown
>>> from the visual display of f_hat(t), t in [a, b]. And
>> a<c<d<b.
>>>
>>> How to do IFFT targeting at f(t) on [c, d] with higher
> resolution?
>>>
>>> And so on and so forth?
>>>
>>> Thanks!
>>>
>>>
>> If you want to know relations between F(w) and f(t), here it
is:
>>
>> The bandwidth of F(w), [0, B] determines the sample rate in
f(t),
>> i.e. 2B (in Hz) = 1/T (in second); The numer of samples of F(w)
> in [0
>> B] equals the number of samples of f(t) in [0 tf] after IFFT;
> Then,
>> tf, the time range of f(t) can be determined from T and number
of
>> samples.
>>
>> hth
>> Yi
>
> Thanks. If you want [c, d] in the time domain, not [0, tf], how to
> do it?
>
> Btw, I am not sure how the "0" (the left boundary) is determined?
>
>
>
>

Depend on how you get F(w). If you get it from experiment, then c is
determined by your record starting time, but reference it as 0. If
you get F(w) from FFT of a time series f(t), then c is determined by
the original f(t) when you pick of a section [c, d] of f(t) to
perform FFT. Again, you can reference the starting time as 0. No way
you can determine c purly from F(w) without any extra information.

hth
Yi