Okay, this gets a bit technical, let me explain the background. In doing loudspeaker measurements for its direct sound in normal rooms that have reflections, what we do is measure the whole impulse response of the system, including room reflections. Then we use time windowing, using some standard window function like Hanning as multiplier in time domain that filters out to zero any signals that are due to room reflections after the direct impulse from the loudspeaker. Then to get the frequency response, we do FFT for the limited time impulse signal.

The question I'm asking now: Obviously the limited time windowed sample of the real full length impulse response can't give frequency response data for any low frequencies that don't at least have half a period fit into that time, due to simple fact how Fourier series works. My question thou: If the window length is only the length of the impulse sample, then the frequency resolution is very limited since 2nd frequency term in the Fourier series is actually double that of the first frequency. There are tons of frequencies in-between that have no spectral data from the windowed impulse, although the impulse is of length long enough for representing the response of those frequencies. Or is it? Shouldn't it be?

My question is: What if we add a long chain of zeros in front of the windowed impulse and then do FFT. This new FFT obviously has way better frequency resolution. It also does include lower frequencies that don't have at least half a period within that impulse so spectral results at those frequencies are wrong and have no meaning. But starting from the frequency that has half a period within the impulse upwards, is this added frequency resolution some real data? Something that this limited sampled impulse can really represent as the frequency response of the system.

(And to make it clear, I'm just a hobbyist with university background measuring my own designed loudspeakers for fun. No business)


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