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No I would not suggest using symbollic math at all... Matlab internally uses 64-bit IEEE binary64 (CPU hardware supported) numerical data format for all arithmetic operations including FFT function. Even at 64-bits there is a limit of precision and accumulation of errors. You can consider the followings to increase (if possible) the precison of your ...


If you can relax on pure orthogonality, there exist Integer Discrete Fourier transforms, like the Integer fast Fourier transform (INTFFT) (Integer FFT(Fast Fourier Transform) in Python).


An FFT using symbolic math might be possible, but would be many orders of magnitude slower. (I'm guessing at least 10,000 times slower, except for a set of exact equation input signals). You would have to use a symbolic math package instead of Matlab. (Perhaps Mathematica, Maxima, or Maple?) Instead you might be able pre- and post-process certain inputs ...


Dr. Manuel Kuehner, You are close. You need to take the square root of the linear values squared. $$P_{\mbox{total_linear}}=\sqrt{p_1^2+p_2^2+...}$$ $$P_{\mbox{total_dB}}=20 log_{10}\left( P_{\mbox{total_linear/20E-6}} \right)$$ FYI: I wrote a MATLAB function to do exactly as you request. It is here Looking to read? See page 16 of this book: https://...

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