| Summarizing the development & application of the theory of Time-Frequency Analysis, this paper researches on several kinds of classic methods of Time-Frequency Analysis such as Time-Frequency Analysis based on Instantaneous Frequency, Wavelet Transform based on Time-Scale Analysis and Cohen's class Time-Frequency Distribution. Analyzes the advantages and disadvantages of them. When affirming the advantages of Short-Time Fourier Transform in the problems of that such as cross-items, physical meaning, computation etc, this paper also points out the limitation of Short-Time Fourier Transform due to its fixed time duration of the window function applied to analyze the nonstationary signal with great-different-scale components together. But its advantages are remarkable. In order to overcome its limitation, this paper puts forward a new means of Time-Frequency Analysis by introducing the thoughts of Multi-Resolution Analysis to Short-Time Fourier Transform, which called MRTFA. Basing on the thoughts of Multi-Resolution Analysis, MRTFA advocates applying STFT to the different scale components of the signal with corresponding scale size of the window function and so overcomes the limitation caused for fixing the scale size of the window function. In order to realize the theory, this paper researches thoroughly on the means to realize MRA of the signal—Dyadic orthonormal Wavelet Transform. In realizing Dyadic orthonormal Wavelet Transform of the signal with limited time zone, this paper puts forward a model with 4 steps to decompose the signal into series through Dyadic orthonormal Wavelet Transform of the signal. With this model, this paper explains why the series are with Zero-Phase Distortion. With this model, this paper explains the problem of Edge Distortion caused by phase delay when applying Dyadic orthonormal Wavelet Transform to the signal with limited time zone. And with this model, this paper solves the problem of Edge Distortion through enlarging the time zone of the signal. When researching the edge problem of the signal with limited time zone, this paper puts forward a new way for expanding the limited time zone—Edge Value Padding. Compared with the traditional means such as Zero-Value Padding, Symmetric-Value Padding and Smooth-Value Padding, it seems more advantageous.MRA of the signal can be realized through Dyadic orthonormal Wavelet Transform. But the property of such a kind of MRA is fixed and lacks of enough adaptability to different kinds of signals because of the fixed Dyadic regular. The Wavelet PacketTransform can be more flexible to adapt to the multi-scale property of the signal. However, there exists a question that the series got through the Wavelet Packet Transform of the signal are in Natural Order but are disordered in frequency domain. This paper proves that the Harr Wavelet Packet in Natural Order is exactly the same as the Walsh-Paley Function in zone and so the Frequency Order of the Walsh-Kaczmarz Function tells the Frequency Order of the Harr Wavelet Packet. Moreover, it can be known from relational analysis in theory that the relation between the Frequency Order and the Natural Order of the Wavelet Packet is fixed and is independent of the Wavelet Packet Function. And so the Frequency Order of the Harr Wavelet Packet tells the Frequency Order of any Wavelet Packet. The research work on the arrangement of the Frequency Order of Wavelet Packet is a creative work.This paper applies MRTFA to the signal with great-different-scale components and compares the result with that of Wigner Distribution, Choi-Williams Distribution, STFT and CWT. Declares the advantage of MRTFA.This paper also puts forward the means of digital filtering with Zero-Phase Distortion. Thereinto the means to directly construct the digital filter with Zero-Phase Distortion is simple but practical.In practice, this paper introduces a virtual system of TFA with multi-functions—QLVJTF-1 developed by the author. It is the first analyzer of TFA in China. It has powerful functions to analyze or pro...
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