Thread: short time Fourier transform

Hey, I have a question about localization a signal in time domain by windowing.
would anyone explain to me these phrases:
1) The basis functions sin(ωt) and cos(ωt) are not localized in time!(support region in frequency = 0)
2) The δ(t) is not localized in frequency! (support region in time = 0)
cheers.

1) The basis functions are nonzero for arbitrarily large times. For example, for arbitrarily large .
2) The delta distribution is nonzero for artitrarily large frequencies. Note that , and hence in the freqency domain, is the constant function 1 which does not have compact support (take nonzero values over an infinite range).

Originally Posted by vincisonfire

1) The basis functions are nonzero for arbitrarily large times. For example, for arbitrarily large .
2) The delta distribution is nonzero for artitrarily large frequencies. Note that , and hence in the freqency domain, is the constant function 1 which does not have compact support (take nonzero values over an infinite range).

Thanks for reply, but I don't get the point of view
what it means: support region in frequency = 0 for sin & cos?

The support is the set of times such that the function takes nonzero values . For a -function, the support is .
So what the statement above is saying is: note that even though a -function's support is a single number, its Fourier transform is completely unbounded.