On the clifford short-time fourier transform and its properties
نویسندگان
چکیده
In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of main properties such as orthogonality relation, reconstruction property and reproducing kernel formula. Moreover, show effects modulating translating signal window function, respectively. Finally, demonstrate Lieb’s uncertainty principle for transform.
منابع مشابه
Windowing and the Short-Time Fourier Transform
With efficient tools for computing the Fourier transform in hand, in this lecture we briefly describe issues that arise when we try to use this tool to analyze signals. We will discuss two major issues. The first is the effect of only collecting a finite number of samples x[0], . . . , x[L − 1], rather than observing x[n] for all n. The second is what happens when the signal of interest has fre...
متن کاملReal Clifford Windowed Fourier Transform
We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to ...
متن کاملThe Clifford Fourier transform in real Clifford algebras
We use the recent comprehensive research [17, 19] on the manifolds of square roots of −1 in real Clifford’s geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the imaginary unit j ∈ C is replaced by a square root of−1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known ...
متن کاملWindowing Effects of Short Time Fourier Transform on Wideband Array Signal Processing Using Maximum Likelihood Estimation
During the last two decades, Maximum Likelihood estimation (ML) has been used to determine Direction Of Arrival (DOA) and signals propagated by the sources, using narrowband array signals. The algorithm fails in the case of wideband signals. As an attempt by the present study to overcome the problem, the array outputs are transformed into narrowband frequency bins, using short time Fourier tran...
متن کاملWindowing Effects of Short Time Fourier Transform on Wideband Array Signal Processing Using Maximum Likelihood Estimation
During the last two decades, Maximum Likelihood estimation (ML) has been used to determine Direction Of Arrival (DOA) and signals propagated by the sources, using narrowband array signals. The algorithm fails in the case of wideband signals. As an attempt by the present study to overcome the problem, the array outputs are transformed into narrowband frequency bins, using short time Fourier tran...
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: Applied Mathematics and Computation
سال: 2022
ISSN: ['1873-5649', '0096-3003']
DOI: https://doi.org/10.1016/j.amc.2021.126812