You can use the command sound(x,fs) to listen to the entire audio file. The time scale in the data is compressed by a factor of 10 to raise the pitch and make the call more clearly audible. Because blue whale calls are low-frequency sounds, they are barely audible to humans. Start by forming a time vector running from 0 to. A function with half-wave symmetry obeys f (t + 1 2 ) -f (t), that is, the graph of the function in the second half of the period is the same as the graph of the function in the first half turned upside down. Load and format a subset of the data in, which contains a Pacific blue whale vocalization. This example shows how the Fourier series expansion for a square wave is made up of a sum of odd harmonics. There is another sort of symmetry that has an important effect on the Fourier series representation. This data can be found in a library maintained by the Cornell University Bioacoustics Research Program. Many specialized implementations of the fast Fourier transform algorithm are even more efficient when n has small prime factors, such as n is a power of 2.Ĭonsider audio data collected from underwater microphones off the coast of California. This computational efficiency is a big advantage when processing data that has millions of data points. The fast Fourier transform algorithm requires only on the order of n log n operations to compute. Using the Fourier transform formula directly to compute each of the n elements of y requires on the order of n 2 floating-point operations.
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