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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 ...


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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).


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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 ...


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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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