Time-Frequency Analysis And Automatic Transcription Of Music

This thesis introduce several method about the time-frequency analysis of music and make a comparison, analysis their strongpoint and disadvantage.We can make our choose according our need and the character of every method.Given a music passage s(t),according to the method introduced in this thesis,we can make an analysis of the instant information,that is to transform the data to the time-frequency plane. In this way,we can see clearly which one or which several notes is happening in every moment, then make feature extraction,after these,we can make the music onset detection and polyphonic pitch estimation and so on.The earliest analysis method is fourier series,it just can extract the feature in either time domain or frequency domain,can not joint them together.But it also give us many illumination.The expression of the fourier series is:As a conventional and efficient analysis method,the short time fourier transform (STFT) have a broad application in music analysis.As said in the thesis,STFT have a uniform resolution in time-frequency plane,this conflicts with the requirement that music signal analysis need a better time resolution at high frequency and better frequency resolution at low frequency.The expression of STFT is:Another time-frequency analysis tool,wavelet analysis,can provide a constant-Q frequency resolution that almost matches the requirement of music signal analy- sis.The expression of wavelet transform is:As mentioned before,the Wigner-Distribution has a good time-frequency energy concentration,but it is the cross-term interference and high computation cost that prevent Wigner-Distribution from applying as a general time-frequency analysis tool in practical music analysis.The expression of Wigner-Distribution is:As mentioned in the previous section,the auditory filter bank is commonly used to model the human ear as a frequency analyzer,so the auditory filter bank is often designed to match as far as possible with the human ear's frequency analysis function based on the existing data from the psychoacoustics and physiology research.If a practical music processing task needs relatively high frequency resolution,the audio-model-based time-frequency analysis often includes two phases:first the input signal is separated into the different frequency bands by auditory filter bank,and then more detail frequency information need to be obtained in every frequency band in some other ways.The expression of the impulse response in time domain of the Gammatone filter is:Resonator time-frequency image(RTFI) is a frequency-based time-frequency analysis tool ,it is specially designed for the process of music signal. As practical applications,it is improved that RTFI is a efficient time-frequency analysis tool by music onsets detection and polyphonic pitch estimation.Using the RTFI,one can select different time-frequency resolution, such as uniform analysis,constant-Q analysis, or ear-like analysis by simply setting several parameter.RTFI generalize all these analysis in one framework.The expression of RTFI is:RTFI(t,ω) = s{t) * I_R(t,ω) =r(ω)intrgral from n=0 to t s((?))e^{(?)(ω)((?)-t)e-jω((?)-t)}d(?)I_R(t,ω) =(?)(ω)e((-(?)(ω)+jω)t,r(ω)=map(ω)>0,t>0And introduced two applications based in this method:1)Music onset detection.It includes two detection algorithms:Energy-based detection algorithm and Pitch-based dctection algorithm.The Energy-based detection algorithm performs well on the detection of hard onsets. The Pitch-based detection algorithm is the first one,which successfully exploits the pitch change clue for the onset detection in real polyphonic music,and achieves a much better performance than the other existing detection algorithms for the detection of soft onsets.2)Polyphonic pitch estimation. It also includes two algorithms:The first estimation method mainly makes best of the harmonic relation and spectral smoothing principle,consequently achieves an excellent performance on the real polyphonic music signals;The second polyphonic pitch estimation method is based on the combination of signal processing and machine learning,The basic idea behind this method is to transform the polyphonic pitch estimation as a pattern recognition problem.The estimation method is mainly composed by a signal processing block followed by a learning machine.Support vector machine(SVM)is selected as learning machine.In the third part of the chapter three,I briefly introduced several commonly used onset detection algorithm.These algorithm are often divided into three steps,that is:preprocessing,reduction and peak-picking.The detection can be classified into two kinds,they are detection algorithm based on signal feature based and probability models.And make a comparison between them.The aim of this thesis is to introduce several methods for music time-frequency analysis,it is the first step in the music signal's analysis.And then one can do music onset detection and polyphonic pitch estimation.The music signal is often considered as the succession of the discrete acoustic events..The term "music onset detection" refers to the detection of the instant when a discrete event begins in acoustic signal.The term" polyphonic pitch estimation" refers to the estimation of possible pitches in the polyphonic music signal that several music notes may occur simultaneously.The time-frequency analysis of music is an establishment in the multi-disciplinary foundation comprehensive technology. Along with many new theories,the new method,the new technology unceasing appearances,the content in this field will grow richer and get the development.