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### Impulse response, amplitude, phase, inverse Fourier

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```I have measured the threshold amplitude (A) of a low-pass filter as a function of sinusoidal frequency between 0.5 Hz and 50 Hz (the amplitude varies between 0 and 1 as a fraction of the mean of the sinusoid). I need to find the impulse response of the filter (i.e. convert the data from the frequency to the time domain). I have to do the following and I am not sure how:

i) derive the phase by taking the derivative (i.e. slope) of the amplitude-frequency curve in dB/decade (do I use (20*log10(A/A0))=Amplitude in dB and if so then what do I put for A0? is A0=1 for all values of A? if I use 2*pi"Hz=frequency in radians and then plot the radians vs amplitude in dB then how do I make sure that I calculate the slope (derivative) in dB/decade instead of dB/octave or otherwise?)

ii) combine the amplitude and phase together to produce a transfer function (what units should I use and what formula?)

iii) find the inverse Fourier transform of the transfer function to get the impulse response (after I use the ifft command what other commands should I use e.g. should I find the complex conjugate? what should my units be for an impulse response?...)

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