Design Method Of Digital FIR Filters Based On Nonuniform Samples Of Z-Transform

This thesis is focused on the design methods of digital finite length impulse response (FIR) filters based on nonuniform samples of z-transform.Chater 1 is a overview of research background, development and status of nonuniform sampling, and the main research works .Chapter 2 introduces the nonuniform discrete Fourier transform (NDFT). We apply the Newton polynomial interpolation formula to express the filter system function H(z) to show the existence of the inverse of NDFT (INDFT). The research we have done shows that it is no feasibility of calculating the expression of INDFT by using polynomial interpolation formula, the only use of this expression is offering the proof for the existence of INDFT. In accordance with the reconstruction of X(z) from its nonuniform samples, using the spline interpolation function, we got a numerical algorithm to evaluate X(z).Chapter 3 discuses the nonuniform frequency sampling design methods of FIR filters. Attention is the design by solving simultaneous equations based on the discrete least squared error criterion. For linear phase FIR lowpass, highpass and bandpass filters, the derivation of design algorithm of desired frequency response and its samples are presented in detail.Chapter 4 illustrates and analyses the necessity for sampling in the transition band. The design algorithms derived in Chapter 3 are revised. Design examples are presented to demonstrate the effectiveness of the proposed algorithm, as compared with the Parks-McClellan algorithm.Finally, provides the conclusion of this thesis: A design algorithm for finite length impulse response digital filter is proposed: for the designing specifications of linear phase FIR filter, according the discrete least squared error criterion, using the nonuniform frequency samples, the impulse response of FIR filter can be obtained by solving simultaneous equations. In the case of holding the length of filter and the samples in the passband and stopband, the number of samples in the transition band can be varying. For the design of bandpass filter with unequal width of transition band, the proposed algorithm result is better than the result of Parks-McClellan algorithm.