Hi all,
I'm currently working on a soundscape ecology study in which the entire acoustic community is of interest. I have been reading up about the Fast Fourier Transform (FFT), and the trade-off between the time and frequency resolution, which is determined by the choice of window length.
I have however failed to find any resources which explain which temporal/frequency resolution is required for the sounds of interest.
I understand that if only one/a few species with known vocalizations are of interest, this choice can be justified easily, but what if you're dealing with an unknown acoustic community? Studies of the acoustic community which use only the audible spectrum (with a sampling rate of 44.1 kHz) often use a frequency resolution of 172 Hz, but don't offer a justification why they chose this. And what if you're also looking at the ultrasonic part of the acoustic community - how would the required frequency resolution change to capture both sonic and ultrasonic signals?
I appreciate any insights you might have.
Hi Thomas Luypaert , The window size in a FFT analysis represents a number of samples, and a duration. To set the size you would need to look at the fundamental frequency in your system, its intensity and any changes it may experience in time. The window size expressed in samples along with your sampling rate (samples/second) would give you information to calculate the window duration.
Also, from the spectraplus page: " The frequency resolution of each spectral line is equal to the Sampling Rate divided by the FFT size. For instance, if the FFT size is 1024 and the Sampling Rate is 8192, the resolution of each spectral line will be: 8192 / 1024 = 8 Hz. Larger FFT sizes provide higher spectral resolution but take longer to compute."
Hope this helps!
Hi Martin E. Baltazar-Lopez , thank you for your clarification. I understand how the sampling rate and blocklength (the number of samples, also referred to as FFT size or window length) determine the bandwidth, temperal resolution and frequency resolution. As the sampling rate is fixed for the data I have collected, the choice of the blocklength will determine the obtained temporal and frequency resolution.
My question pertains more to the justification for the choice of this parameter for an unknown acoustic community. How do I know which temporal/frequency resolution I require, and thus which blocklength I should go with, if the acoustic community is unknown to me. Where lies the optimal choice for the blocklength, considering the trad-off between the temporal and frequency resolution.
Hi Thomas Luypaert , If I'm understanding well, then you have a a case of transient signal, then it may be possible that a wavelet analysis is more suitable for this application. The Wavelet Analysis is a multiresolution technique; which as implied by its name, analyzes the signal at different frequencies with multiple resolutions through wavelets of different scales and positions. Not every spectral component is resolved equally, as for example, in the Short Time Fourier Transform STFT, where the exact time-frequency representation of a signal cannot be known. What can be known are the time intervals in which certain band of frequencies exists, which is a resolution problem. This is directly related to the width of the window function that is used within the STFT. If a window of infinite length is used, the Fourier Transform is obtained, which gives perfect frequency resolution, but no time information. On the other hand, the narrower the window (short enough for the portion of the signal to be considered stationary, that is not time dependent), the better the time resolution, and the better the assumption of stationarity but frequency resolution is poor.
Hope this helps!
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