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I am working with a finite signal response from an experiment. Basically, I feed in a uniform amplitude sine wave which ramps from 20Hz to 20kHz over the course of 50 seconds, and I read the output, which has the same frequency but with varying amplitudes. The ramp is logarithmic, so I know exactly the conversion which tells me the frequency at a given time in my sweep.

I have two ways which I can think of to analyze this response signal. The first is a discrete Fourier transform, and the second is a Hilbert transform to find the analytic signal of the response, which I can use to get an envelope of my response signal.

My assumption with the second is that it gives me the most accurate results, since I can take the envelope, which is basically a measure of amplitude as a function of time, and convert the time coordinates to frequency to get amplitude as a measure of frequency.

I don't believe the Fourier transform is a good representation, since the discrete transform of the input signal is not a straight line, but rather grows with frequency. I imagine this is because it takes larger high-frequency signals to cancel out low frequency waves in the later part of the signal, but honestly I don't know if I properly understand the Fourier transform well enough to know if this is true.

My question is, essentially, which of these methods is more suited to understanding the frequency response? I believe the wave envelope seems to make the most sense, but some of the people I'm working with say the Fourier transform should be sufficient. I think the Fourier transform is giving a recipe to generate the signal with additive sine waves rather than the actual amplitude of a given frequency. In other words, if I fed in single frequencies and plotted them, they won't line up with a Fourier transform. Is this a correct way to understand this? If I am right, is there any way to prove it analytically?

P.S. I don't post much on this board, and I realize I haven't included any equations, so if I need to add something to my question to make it more understandable, please let me know. If I'm wrong, why am I wrong, and why do these methods give different results?

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Plot 20*log10(output/input) vs the frequency. If the y-axis is linear and the x-axis is semi-log, the plot is called a Bode plot. When I was in Engineering school, we use to call such plots the frequency response.

You don't need need to do Fourier Transform or any else to your data.

Such plots usually include the phase too.

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