A HIGH-RESOLUTION TIME-FREQUENCY REPRESENTATION FOR MUSICAL-INSTRUMENT SIGNALS

Analyzing musical signals to obtain the time-varying magnitudes and fr equencies of instruments' partial frequency components is important fo r resynthesis, transcription, and instrument physics. Windowing techni ques, including Fourier series extensions, short-time Fourier transfor ms, and constant-Q transforms, generate bias in time and frequency dic tated by the uncertainty principle. This is significant to analysis re quirements of such properties as attack, which involve changes over mi llisecond time ranges and require frequency accuracy on the order of c ents. Alternatives such as the Wigner distribution avoid the uncertain ty principle restriction and associated bias, but nonlinear cross prod ucts of magnitude and frequency computations are not smoothed as with windowing methods, increasing those sources of bias. All these techniq ues belong to Cohen's class, a framework where this paper develops the modal distribution, exhibiting decreased total bias. Computation of t he modal distribution and a constant-Q version are detailed. Comparati ve examples to windowing methods are provided. Further research on mod al distribution magnitude and phase estimation verifies the advantage of this distribution over others. (C) 1996 Acoustical Society of Ameri ca.