The Zak transform and some counterexamples in time-frequency analysis
نویسندگان
چکیده
منابع مشابه
The Zak transform and some counterexamples in time- frequency analysis
It is shown how the Zak transform can be used to find nontrivial examples of functions f, g E L 2 ( 2 ) with f . g = 0 = F . C, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, keL2(T1), h # k, such that I h I = 1 k 1 , I H I = I K 1 . A similar construction is used to find an abundance of nontrivial pairs of functions h...
متن کاملThe Zak transform and some counterexamples in time-frequency analysis
It is shown how the Zak transform can be used to find nontrivial examples of functions f, g E L 2 ( 2 ) with f . g = 0 = F . C, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, keL2(T1), h # k, such that I h I = 1 k 1 , I H I = I K 1 . A similar construction is used to find an abundance of nontrivial pairs of functions h...
متن کاملThe Zak transform and some counterexamples in time- frequency analysis
It is shown how the Zak transform can be used to find nontrivial examples of functions f, g E L 2 ( 2 ) with f . g = 0 = F . C, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, keL2(T1), h # k, such that I h I = 1 k 1 , I H I = I K 1 . A similar construction is used to find an abundance of nontrivial pairs of functions h...
متن کاملTime and frequency split Zak transform for finite Gabor expansion
The relationship between finite discrete Zak transform and finite Gabor expansion are well discussed in this paper. In this paper, we present two DFT-based algorithms for computing Gabor coefficients. One is based upon the time-split Zak transform, the other is based upon the frequency-split Zak transform. These two methods are time and frequency dual pairs. With the help of Zak transform, the ...
متن کاملThe Zak Transform ( s )
We introduce the operator Z that is often called the Zak transform. Our definition is a bit different from the one that usually appears in the literature. We will discuss this difference and will also give a historical account that the reader may find particularly interesting. In order to do this, however, we need to present our treatment of the operator Z (and Z̃) which shows that the Fourier t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 1992
ISSN: 0018-9448
DOI: 10.1109/18.108265