![]() Note that if you use the asymmetric scaling, then you will still have an orthogonal transform, but not unitary (orthonormal). $$\left[\begin$$ Such matrices are called unitary matrices (aka orthonormal) and such transforms are called unitary transforms.įor DFT being a unitary transform, you need to have the symmetric scaling as in Eqs 1 and 2. The standard unscaled version does multiply the input vector by: The eigenvalue problem is to determine the solution to the equation Av v, where A is an n -by- n matrix, v is a column vector of length n, and is a scalar. ![]() It should be noted that, depending on the software used, scaling can be different, and ought to be checked. Eigenvalues in MATLAB Ask Question Asked 13 years ago Modified 8 years, 7 months ago Viewed 20k times 9 In MATLAB, when I run the command V,D eig (a) for a symmetric matrix, the largest eigenvalue (and its associated vector) is located in last column. Now I would like to show with formulas why this convention gives me the right amplitude? I have already searched online and here on the forum, but I did not find any good answer that explain every passage. I have already demonstrated (in my report) that if I scale the fft by a factor 1/N, I obtain the right amplitude, since the first value of my fft is equal to the time average of my function.But the vectors returned in V are not an orthogonal set. It is fast, well supported by MathWorks, has a great user community, has a student license, and is far, far, far, far, easier to manage, license-wise, than any PTC product. They assume that all matrices have an eigenvalue decomposition where they can recover the original matrix. In addition, programming is more intuitive in MATLAB for me (extensive background w 3G, 4G programming languages) than Mathcad. Why, doing the fft, I cannot have both: amplitude checked and energy checked? In fact, the matrix Lsr is a defective matrix. ![]() If I use the factor 1/N the amplitude is checked, if I use the factor dt then the parseval identity is preserved. As I have read online, there are not right convention or wrong convention. Unfortunately I had discussion with one of my advisors, because, since this convention does not give you the right amplitude, he thinks it is wrong. I used to use the scaling convention of multipling the fft by the time increment (dt), this convention was good for me, because it ensures the check of the Parseval theorem. I am writing a report, and my advisor asked me to explain why I scale the fft by a factor 1/N (where N is the length of the array). This section describes how Mathcad interprets equations and explains Mathcad’s computational features: units of measurement, complex numbers, matrices, built- in functions, solving equations, programming, and so on. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |