Musical Intelligence Analysis
Based on the temperament and physical properties of melody, we exploit splines, Gaussian function and trigonometric functions to construct two sets of stable bases and give the proof of stability. For both constructed function and real music signal,we can obtain the approximation using these bases. Meanwhile, frequency information can be detected exactly by FFT and the approximation is the sum of amplitudes of all frequencies. So, we can get the exact time-frequency music analysis theoretically and our numerical results also prove that well for both kinds of signals.
KeywordsShort Time Fourier Transform Stable Basis Fundamental Tone Pitch Estimation Amplitude Graph
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