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If you have a finite-sized window of data whose center is reference to some known time stamp, position, or event (e.g. the center of an image, known delay after some positive zero-crossing of some stimulus, etc.), the phase in the time domain makes sense, and is an easy calculator. If you decompose your time-domain signal into an even part (symmetric ...

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No, this doesn't make much sense. What you can do in the time domain is compute the analytic signal and derive the signal's instantaneous amplitude (envelope) and its instantaneous phase from it. Take as an example $$x[n]=A\sin(\omega_0n+\theta)\tag{1}$$ The corresponding analytic signal is $$x_a[n]=-jAe^{j(\omega_0n+\theta)}\tag{1}$$ Its instantaneous ...

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Assuming that your microphones and speaker set up is such that you don't have echos or noise from external sources, you could use the cross FFT. Its output gives you the comparison of two signals. If the two are identical, you get a flat line. Multiply that line with the known response of the reference microphone, and you have the response of your unknown ...

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Say $\mathbf{h}_1$ and $\mathbf{h}_2$ are the impulse response coefficients of mic1 and mic2, respectively, where $\mathbf{h}_1$ is known. Let $\mathbf{x}$ represent the input signal. Then, we can write the output of mic1 as \begin{align} \mathbf{b} = \mathbf{X} \mathbf{h}_1 \end{align} where $\mathbf{X}$ is a Toeplitz matrix. If you want to find the ...

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