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Coprime DFT filter banks (coprime DFTFB) achieve the effect of an MN-DFTFB by using two DFTFBs of size only M and N, where M and N are coprime integers. However, coprime DFTFBs need to be designed properly, to avoid unwanted bumps in stopbands or unsatisfactory total spectrum coverage, quantified by overall amplitude responses. In this paper, a detailed theoretical analysis will be made on the tradeoffs...
The analog harmonic oscillators are well-studied in quantum physics, including their energy states, wavefunctions, orthogonal properties, and eigenfunctions of the Fourier transform. In addition, the continuous solutions in different dimension and coordinate systems are known. Some discrete equivalents of the 1D wavefunctions were also studied. However, in the 3D spherical coordinate system, the discrete...
In this paper, the general form of the two-dimensional Fourier transform (2D FT) eigenfunctions is discussed. It is obtained from the linear combination of the 2D separable Hermite Gaussian functions (SHGFs). For example, the rotated Hermite Gaussian functions (RHGFs) for the rotated coordinate and the Laguerre Gaussian functions (LGFs) for the polar coordinate are two special cases of the general...
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