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You are not logged in. #1 20090424 21:55:17
Discrete Fourier TransformCan somebody tell me what is the process to calculate the eigenvalues of the discrete fourier transform matrix? Or a reference would be good also. thanks!! #2 20090425 10:17:13
Re: Discrete Fourier TransformHi dannyv; Last edited by bobbym (20090425 10:18:20) In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20090425 13:13:13
Re: Discrete Fourier TransformI found this wikipedia page http://en.wikipedia.org/wiki/Discrete_Fourier_transform that gives a really good and correct definitions and properties of the DFT. It also gives the eigenvalues but doesn't tell exactly how to find them. This is a quote from the page: This can be seen from the inverse properties above: operating twice gives the original data in reverse order, so operating four times gives back the original data and is thus the identity matrix. This means that the eigenvalues satisfy a characteristic equation: Therefore, the eigenvalues of are the four roots of unity: is +1, 1, +i, i What is not clear form me is why is the characteristic equation . How can I derive this algebraically? Also, how do I calculate the multiplicity of these eigenvalues? The calculation of the multiplicities is given in this paper "J. H. McClellan and T. W. Parks (1972). "Eigenvalues and eigenvectors of the discrete Fourier transformation". IEEE Trans. Audio Electroacoust. 20 (1): 66–74" (http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1162342), but my university doesn't have access to this paper, so I haven't read this yet. In summary my questions are as follows: 1) How to derive algebraically the characteristic equation 2) How to calculate the multiplicity of the eigenvalues 3) What is a good alternate reference for this paper Thanks in advanced!!! #4 20090425 18:06:07
Re: Discrete Fourier TransformHi dannyv; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 