| Summary: | 碩士 === 國立高雄第一科技大學 === 電腦與通訊工程所 === 92 === ABSTRACT
In many applications of signal processing, there is a need for a delay which is a fraction of the sampling period. These applications include beam steering of antenna array, modeling of music instruments, sampling rate conversion, speech code and sound synthesis, time delay estimation, comb design and AD converter etc. Generally speaking, the design methods can be classified into two categories. One is the fixed fractional delay (FFD); the other is variable fractional delay (VFD) filter design.
In this thesis, two design methods for variable fractional delay (VFD) filters are proposed. One is the design of VFD filter using differentiator bank approach; the other is the sinusoid-based VFD filter design. The details of these two methods are presented in chapter 2 and chapter 3.
In chapter 2, a new VFD filter design method using differentiator bank is presented. First, the Taylor series expansion is used to transform the specification of VFD filter into the one of differentiator bank. This transform makes the design problem of VDF reduce to the design of differentiator with different orders. Then, the error analysis and implementation structure are provided to discuss the design accuracy and implementation complexity. Finally, we extend the differentiator bank method to design 2-D VFD filters and several examples are demonstrated to illustrate the proposed differentiator bank method is more general than the maximally flat method.
In chapter 3, the design of sinusoid-based variable fractional delay FIR and all pass filters are presented. First, the coefficients of filters are expressed as the linear combination of sinusoidal basis by using Fourier series expansion. Then, the weighted least squares method is applied to find the optimal linear combination coefficients by solving a set of linear simultaneous equations. Finally, the design examples are use to demonstrate that the design error of proposed sinusoidal-basis method is smaller than the one of conventional polynomial-based method for the same truncation order.
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