An efficient implementation for db4 wavelet and scaling filters are presented here that employs a specifically designed ReMB. It is shown that addition of multiplexers into shift-add networks provides reconfigurability to the well known constant multiplication blocks. By taking the advantage of the recent FPGA technologies having 6-input LUTs, 3:1/4:1 muxes are employed in the design of ReMBs at no additional hardware cost which updates the concepts proposed in the open literature. In order to evaluate the re- source and power efficiency of the proposed structure, the proposed ReMB is employed in time-multiplexed FIR filters and conventional DWT FBs which are implemented on a Kintex-7 FPGA platform and are compared to the reference designs employing parallel multipliers and to the designs present in the open-literature. Although there is a sub- stantially diverse literature on efficient FPGA and Very-Large-Scale Integration (VLSI) implementations of the wavelet transform, to the best of author’s knowledge, applica- tion of reconfigurable multiplier blocks with optimized structure for FPGA platforms has not been investigated in the field of biomedical signal processing. The replacement of multipliers in DWT with shift-add networks has been subject to research in image processing and image compression applications, however reconfigurable constant multi- plications are not studied. As the results demonstrate, the proposed ReMB massively reduces the resource utilization when compared to the parallel multipliers. The ra- tio of the savings increase with the increasing input word-length, as the number of adders in the parallel multiplier increases while the number of adders in the ReMB remains the same. When employed in a time-multiplexed FIR filter architecture, the
structure however, the proposed design still utilizes 39% less logic elements against the reference design. Furthermore, the 1-level analysis filter bank cost assessment results also demonstrated that the proposed system massively improves the resource utiliz- ation and power consumption compared to the open-literature and the conventional reference design.
4.8
Conclusions
In this chapter an alternative implementation method is investigated in order to reduce the hardware complexity and power consumption of the DWT filter banks. A practical approach referred to as ‘ReMB’, which replaces the conventional GP parallel multipliers is presented. In this approach, the advantage of having constant coefficients is taken and each multiplication operation is replaced with simpler shift and add operations. From the work presented in this chapter, it can be concluded that the proposed ReMB approach provides simplicity to the implementation of the DWT wavelet filter banks and the designer can easily achieve massive hardware and power reduction up to 50%. The performance of the ReMB approach is also compared to the state-of-the-art mul- tiplierless implementation solutions for the presented wavelet family and it can be observed that the presented approach achieves the highest savings with no other archi- tectural or algorithmic optimization. These savings are simply related to the reduction in the number of addition operations with the aid of large (3:1/4:1) multiplexers for no additional cost for FPGA implementations. The FPGA implementation results provided an insight that the proposed approach is low-cost and power efficient com- pared to other FPGA implementations. Therefore, it can be concluded that the ReMB
structures are suitable for DWT filter banks and can be used for ASIC implementa- tions and employed in low-cost embedded platforms for ambulatory physiological signal monitoring and analysis.
Chapter 5
IIR Wavelet Filter Banks for
Biomedical Signal Processing
5.1
Introduction
As mentioned in Chapter 2, DWT can be realised as a two-channel PR quadrature mirror (QMF) filter banks in which the input data is decomposed by iterating the lowpass branch of the analysis filter bank, and reconstructed through the synthesis filter bank. Although the most commonly used wavelets are realised with non-recursive filters that have finite impulse response, recursive filters with infinite impulse response can also be used for implementing wavelet filter banks. In DSP applications, the IIR filters has an advantage over their FIR counterparts, as they can achieve comparable filter specifications such as passband ripples, stopband attenuation and transition bandwidth with much lower filter orders which leads to reduced arithmetic operations, memory constraints and hence lower system delay. Furthermore, the advantage of realizing
IIR filters with polyphase networks composed of allpass filters, further reduces the computational burden and makes the filter more robust to coefficient quantization. Thus, IIR filters are more desirable for low-power and low complexity applications
where coefficient precision is a significant factor to consider. In the literature for
wavelet transform , a vast amount of research employed FIR filter banks for many application areas such as biomedical, communication, audio signal and image and video processing [76, 79, 80, 148, 152, 162], meanwhile the IIR wavelet filter banks are studied relatively less and limited to image processing and compression applications [163–166]. The use of non-linear phase IIR filters in the analysis filter bank generally leads to unstable but causal or non-causal but stable synthesis filters. Therefore, the design of IIR based filter banks with PR property becomes more challenging than the FIR based counterparts, which is the main reason for the limited application area and interest. However, the computational simplicity of the IIR filter based analysis filter banks are appealing alternatives to FIR filter based ones which motivated the study presented in this chapter.
The rest of this chapter presents the desired properties and design procedure of ortho- gonal IIR wavelet analysis filter banks which are realised as parallel connections of real allpass filters. Therefore, the IIR wavelet analysis filter design problem is reduced to the allpass filter design, where Remez exchange algorithm [167] based on eigenvalue decomposition is used. Furthermore, the problem of non-causal IIR synthesis filters is investigated and a novel hybrid solution is proposed where the analysis and syn- thesis filter banks employ IIR and FIR filters, respectively. To the best knowledge of the author, this hybrid solution is the first in the area of biomedical signal processing
and wavelet literature which offers reduced hardware complexity solutions for DWT implementation to be employed in portable, limited size and power, health monitor- ing systems. Validation and cost assessment studies are carried out and comparative results are also presented.