When assessing impulse response measurement test signals for numerical error, why do exponentially swept sinusoids always feature poorer signal-to-noise ratio at lower frequencies?
I'm making a lot of assumptions here, so I might or might not be answering your question.
I'm assuming that you are taking the FFT of a signal of the form exp((a+jw)*t)). As the frequency is lowered, are you increasing the number of points over which you are calculating the FFT?
Are you first multiplying the time series data with a window function? If not, you will have significant 1/f component in your output spectrum. Remember that the Fourier transform assumes that your signal is periodic. If you take your input data and imagine the portion over which the FFT is calculated as repeating indefinitely, it becomes clear that there is a step at the start of each sample.
A window function tapers your data to zero at the start and end of the window, eliminating the step between the Nth sample and N+1 sample, removing the 1/f spectrum.
From the frequency domain, consider that by taking a finite section of your data you are effectively multiplying the input data with a pulse that is as long as the number of points in your FFT. In the frequency domain, this pulse has a sin(x)/x envelope that is convolved with the single frequency point you are expecting (plus the exponential envelope as well).
Windowing is just one of many ways to make a periodic approximation of an aperiodic signal, but is certainly the most common.
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