What phase rotation occurs when you take the derivative of an audio signal? If you take the derivative of an audio signal, it provides a 6 dB/oct upward sloping filter (increasing high frequencies / cutting low frequencies) all the way across the spectrum.
What is the result in terms of the phase? Is there phase rotation? Is it uniform across the spectrum or does it vary with frequency? What would the plot of this phase rotation look like?
Thanks
Simple Fourier Transform propery for differentiation is
$$\mathcal{F}\{\frac{\partial}{\partial t}x(t)\}=j\omega \cdot\mathcal{F}\{x(t)\}$$
Differentiation in time corresponds to multiplication with $j\omega$ in frequency. Hence the +6dB/octave slope. The phase shift is a constant 90 degrees for all frequencies.