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Estimate magnitude/phase on single frequency

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I excite a system with a sine wave at a fixed frequency and I have the signals of excitation and response.

What is the best way to calculate the magnitude and phase of the system at this frequency? (Similarly to a frequency response estimation, but with only one chosen frequency).

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I would use a lockin amplifier with some sort of comms interface:-) Failing that you could simply implement the same algorithm - multiply your signal by sine and cosine waveforms at the refetence frequency, low pass filter, calculate the mean and feed into x,y to polar co-ordinate convertor. Altetnatively, up-sample the signal, feed into an FFT, index out the right (complex) element and covert to r,theta.

Edited by gb119
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