Two Classes of Cosine-Modulated IIR/IIR and IIR/FIR NPR Filter Banks

Abstract

This paper introduces two classes of cosine-modulated causal and stable filter banks (FBs) with near perfect reconstruction (NPR) and low implementation complexity. Both classes have the same infinite-length impulse response (IIR) analysis FB but different synthesis FBs utilizing IIR and finite-length impulse response (FIR) filters, respectively. The two classes are preferable for different types of specifications. The IIR/FIR FBs are preferred if small phase errors relative to the magnitude error are desired, and vice versa. The paper provides systematic design procedures so that PR can be approximated as closely as desired. It is demonstrated through several examples that the proposed FB classes, depending on the specification, can have a lower implementation complexity compared to existing FIR and IIR cosinemodulated FBs (CMFBs). The price to pay for the reduced complexity is generally an increased delay. Furthermore, two additional attractive features of the proposed FBs are that they are asymmetric in the sense that one of the analysis and synthesis banks has a lower computational complexity compared to the other, which can be beneficial in some applications, and that the number of distinct coefficients is small, which facilitates the design of FBs with large numbers of channels.

Adaptive window method of FIR filter design

“…Linnea Rosenbaum et al are introduced two classes of cosine modulated causal and stable filter banks with near perfect reconstruction (NPR) and low implementation complexity. These classes are preferable for different type of specifications [10]. 2 III.…”

Study the Characteristics of FIR filter Based on Modified Kaiser Window

“…An optimized filter design technique is achieved [15]. A filter bank structure based on low complexity is implemented [16]. A programmable architecture applied programmable logic device (PLD) and FFT [17], then introduced PLD and digital signal processor [18].…”

Efficient design of very large‐scale DFT modulated filter banks using M th band condition

“…Other alternative approaches are the frequency sampling algorithms [17,21], while the designed filter bank cannot allow low delay and discretisation of frequency domain in design is not rigorous from a mathematical viewpoint. Also, the frequency-response masking (FRM) algorithms [19,22,23] probably play an important role in large-scale filter bank design, the FRM algorithm can efficiently reduce the complexity and lead to filter bank with good overall performance, whereas the complexity reduction is at the expense of increasing system delay. In our previous work [9], the modified Newton's method with exact line search was utilised to design large-scale DFT modulated filter banks.…”

“…Furthermore, the matrix inverse lemma [25] is utilised to dramatically reduce the size of inversed matrix at each Newton's iteration, which indicates that the proposed algorithm is much more suitable for designing very large-scale filter bank than the algorithm in [9]. Compared with the FRM methods [19,22,23], the proposed algorithm also possesses much lower complexity. The reason is that the PF is solved by the proposed method with closed-from equations rather than optimised with constrained problem in the FRM method.…”