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I’m experiencing some strange behaviour, and I wonder if someone could explain it to me.

1) Take a signal with only real values (the ultrasonic burst used in “The first document”, for example)
2) Create a formula FFT(Burst)
3) Evaluate the formula – you now have a complex signal
4) Do an inverse FFT on that signal IFFT(Formula)

This should return the original signal, but does not! Due to rounding errors in the calculations I would expect a small imaginary component to the results, but the magnitude of the imaginary component is not small at all!

What am I missing here?

Paul Warshawsky