Optimal cosine modulated nonuniform linear phase FIR filter bank design via stretching and shifting frequency response of prototype filter

This paper proposes an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank design. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of the prototype filter. The total aliasing error of the filter bank is minimized subject to a specification on the maximum amplitude distortion of the filter bank as well as specifications on both the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter. This filter bank design problem is actually a functional inequality constrained optimization problem. Our recently developed integration approach is employed for solving the problem. Computer numerical simulation results show that our proposed design method outperforms existing design methods

Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction

We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2π/M rather than π/M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband. The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system

On the theory and design of a class of PR uniform and recombination nonuniform causal-Stable IIR cosine modulated filter banks

This paper studies the theory and design of a class of perfect reconstruction (PR) uniform causal-stable infinite-impulse response (IIR) cosine modulated filter banks (CMFBs). The design approach is also applicable to the design of PR recombination nonuniform (RN) IIR CMFBs. The polyphase components of the prototype filters of these IIR CMFBs are assumed to have the same denominator so as to simplify the PR condition. In designing the proposed IIR CMFB, a PR FIR CMFB with similar specifications is first designed. The finite-impulse response prototype filter is then converted to a nearly PR (NPR) IIR CMFB using a modified model reduction technique. The NPR IIR CMFB so obtained has a reasonably low reconstruction error. Its denominator is designed to be a polynomial in z M, where M is the number of channels, to simplify the PR condition. Finally, it is employed as the initial guess to constrained nonlinear optimization software for the design of the PR IIR CMFB. Design results show that both NPR and PR IIR CMFBs with good frequency characteristics and different system delays can be obtained by the proposed method. By using these IIR CMFBs in the RN CMFBs, new RN NPR and PR IIR CMFBs can be obtained similarly. © 2008 IEEE.published_or_final_versio

An Iterative Design with Variable Step Prototype Filter for Cosine Modulated Filter Bank

A systematic and self controlled prototype filter design approach for multichannel Cosine Modulated Near Perfect Reconstruction (NPR) filter bank is proposed in this paper. The primary goal is to design a prototype filter with enhanced performance i.e., minimum amplitude distortion and aliasing error. This algorithm approximates 3dB cutoff frequency very close to π/2M. This is achieved by selecting suitable step size which is a function of transition width. If the selection of step size is too fine, the objective function oscillates. Whereas, if step size is coarse, 3dB cutoff frequency will not be close to π/2M. This will degrade the overall performance of the prototype filter. Thus by choosing the step size as a function of transition width and varying the step size from coarser to finer level, the minimum amplitude distortion and aliasing error can be definitely achieved. The proposed filter is designed using two input parameters: number of subbands M and attenuation A and all other system parameters are derived from it to avoid heuristic inputs. Simulation results indicate better performance with reference to algorithms existing in literature. In addition, the design approach is systematic and self controlled

Alias-free, real coefficient m-band QMF banks for arbitrary m

Based on a generalized framework for alias free QMF banks, a theory is developed for the design of uniform QMF banks with real-coefficient analysis filters, such that aliasing can be completely canceled by appropriate choice of real-coefficient synthesis filters. These results are then applied for the derivation of closed-form expressions for the synthesis filters (both FIR and IIR), that ensure cancelation of aliasing for a given set of analysis filters. The results do not involve the inversion of the alias-component (AC) matrix

Low-delay nonuniform pseudo-QMF banks with application to speech enhancement

Journal ArticleAbstract-This paper presents a method for designing low-delay nonuniform pseudo quadrature mirror filter (QMF) banks. This method is motivated by the work of Li, Nguyen, and Tantaratana, in which the nonuniform filter bank is realized by combining an appropriate number of adjacent sub-bands of a uniform pseudo-QMF bank. In prior work, the prototype filter of the uniform pseudo-QMF bank was constrained to have linear phase and the overall delay associated with the filter bank was often unacceptably large for filter banks with a large number of sub-bands. This paper proposes a pseudo-QMF filter bank design technique that significantly reduces the delay by relaxing the linear phase constraints. An example in which an oversampled critical-band nonuniform filter bank is designed and applied to a two-state modeling speech enhancement system is presented in this paper. Comparison of the performance of this system to competing methods employing tree-structured, linear phase multiresolution analysis indicates that the approach described in this paper strikes a good balance between system performance and low delay

Channel estimation techniques for filter bank multicarrier based transceivers for next generation of wireless networks

A dissertation submitted to Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science in Engineering (Electrical and Information Engineering), August 2017The fourth generation (4G) of wireless communication system is designed based on the principles of cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) where the cyclic prefix (CP) is used to combat inter-symbol interference (ISI) and inter-carrier interference (ICI) in order to achieve higher data rates in comparison to the previous generations of wireless networks. Various filter bank multicarrier systems have been considered as potential waveforms for the fast emerging next generation (xG) of wireless networks (especially the fifth generation (5G) networks). Some examples of the considered waveforms are orthogonal frequency division multiplexing with offset quadrature amplitude modulation based filter bank, universal filtered multicarrier (UFMC), bi-orthogonal frequency division multiplexing (BFDM) and generalized frequency division multiplexing (GFDM). In perfect reconstruction (PR) or near perfect reconstruction (NPR) filter bank designs, these aforementioned FBMC waveforms adopt the use of well-designed prototype filters (which are used for designing the synthesis and analysis filter banks) so as to either replace or minimize the CP usage of the 4G networks in order to provide higher spectral efficiencies for the overall increment in data rates. The accurate designing of the FIR low-pass prototype filter in NPR filter banks results in minimal signal distortions thus, making the analysis filter bank a time-reversed version of the corresponding synthesis filter bank. However, in non-perfect reconstruction (Non-PR) the analysis filter bank is not directly a time-reversed version of the corresponding synthesis filter bank as the prototype filter impulse response for this system is formulated (in this dissertation) by the introduction of randomly generated errors. Hence, aliasing and amplitude distortions are more prominent for Non-PR. Channel estimation (CE) is used to predict the behaviour of the frequency selective channel and is usually adopted to ensure excellent reconstruction of the transmitted symbols. These techniques can be broadly classified as pilot based, semi-blind and blind channel estimation schemes. In this dissertation, two linear pilot based CE techniques namely the least square (LS) and linear minimum mean square error (LMMSE), and three adaptive channel estimation schemes namely least mean square (LMS), normalized least mean square (NLMS) and recursive least square (RLS) are presented, analyzed and documented. These are implemented while exploiting the near orthogonality properties of offset quadrature amplitude modulation (OQAM) to mitigate the effects of interference for two filter bank waveforms (i.e. OFDM/OQAM and GFDM/OQAM) for the next generation of wireless networks assuming conditions of both NPR and Non-PR in slow and fast frequency selective Rayleigh fading channel. Results obtained from the computer simulations carried out showed that the channel estimation schemes performed better in an NPR filter bank system as compared with Non-PR filter banks. The low performance of Non-PR system is due to the amplitude distortion and aliasing introduced from the random errors generated in the system that is used to design its prototype filters. It can be concluded that RLS, NLMS, LMS, LMMSE and LS channel estimation schemes offered the best normalized mean square error (NMSE) and bit error rate (BER) performances (in decreasing order) for both waveforms assuming both NPR and Non-PR filter banks. Keywords: Channel estimation, Filter bank, OFDM/OQAM, GFDM/OQAM, NPR, Non-PR, 5G, Frequency selective channel.CK201

On the theory and design of a class of PR causal-stable IIR non-uniform recombination cosine modulated filter banks

This paper studies the theory and design of a class of perfect reconstruction (PR) causal-stable nonuniform recombination cosine modulated filter banks (RN CMFBs) with IIR filters. It is based on the RN CMFB previously proposed by one of the author. A PR FIR RN CMFB of similar specification is first designed. The prototype filters of the CMFBs are then model reduced to obtain a nearly PR (NPR) IIR RN CMFB by modifying a model reduction technique proposed by Brandenstein and Unbehauen. With these NPR IIR RN CMFBs as initial guess, PR IIR RN CMFB with very good frequency characteristics can be obtained readily by solving a constrained nonlinear optimisation problem using for example the function fmincom from MATLAB. Design results show that the proposed method is very effective in designing PR RN IIR CMFBs with good frequency characteristics and different system delays. © 2005 IEEE.published_or_final_versio

Design of low-delay nonuniform pseudo QMF banks

Journal ArticleABSTRACT This paper presents a method for designing low-delay nonuniform pseudo QMF banks. The method is motivated by the work of Li, Nguyen and Tantaratana, in which the nonuniform filter bank is realized by combining an appropriate number of adjacent subbands of a uniform pseudo QMF filter bank. In prior work, the prototype filter of the uniform pseudo QMF is constrained to have linear phase and the overall delay associated with the filter bank was often unacceptably large for filter banks with a large number of subbands. By relaxing the linear phase constraints, this paper proposes a pseudo QMF filter bank design technique that significantly reduces the delay. An example that experimentally verifies the capabilities of the design technique is presented