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Multiply accumulate operation (a) conventional implementation and (b) distributed Arithmetic implementation 3.2.1. Internal configuration
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The discrete wavelet transform has gained the reputation of being a very effective sig-nal analysis tool for many practical applications. However, due to its computation-intensive na-ture, current implementations of the transform fall short of meeting real-time processing re-quirements of most applications. This paper describes a parallel implement...
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... the input samples are represented with B bits of preci- sion, B clock cycles are required to complete an inner-product calculation. An example of a distributed arithmetic implementation of a 4- element inner product operation is shown in Figure 1 along with the conventional imple- mentation of the same product operation. ...
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... is noted from the results obtained above, and further illustrated in Figure 10, that the throughput of the distributed arithmetic im- plementation is higher than the throughput of the conventional arithmetic implementation. This is expected since the distributed arith- metic implementation replaced the time-con- suming conventional multiply accumulate op- erations with fast look-up tables and shift op- erations. ...
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... partial products of all multiply accumulate operations were pre- computed offline and stored in the LUTs, thus saving a great a mount of real-time computa- tion. As for Virtex slice utilization, distributed arithmetic, uses less hardware resources than the conventional arithmetic, as illustrated in Figure 11. Conventional Arithmetic Implementation ...
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... DWT Inverse DWT Figure 11. Comparison between the utilization of two DWT implementations This is also expected since the conventional arithmetic multiplier requires much more logic resources than the distributed arithmetic multiplier which requires small LUTs, sim- ples adders and shift registers. ...
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Citations
... The MAC method of FIR filter implementation is expensive to implement in a fieldprogrammable gate array (FPGA) owing to logic complexity and resource usage [6]. To resolve this problem, many researchers have used the distributed arithmetic (DA) algorithm in the FIR filter design process [9,15]. In the MAC method, any arithmetic operation is implemented by first multiplying and then adding; however, the DA algorithm converts this by shifting and adding. ...
... It has a basic-to-advanced converter at the front end, followed by a chip and several peripheral components, such as memory, to store data and channel coefficients [8]. Mechanical advancements have improved the various zones of DSP, one of which is the structure of all-around arranged calculations to ascertain the discrete Fourier transform [9]. The introduction of programmable digital signal processors (PDSPs) in the late 1970s was another advancement in this field that provided the option to perform multiplication and addition in one clock cycle. ...
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... One can then insert neural layers between the two parts. The whole model is trained and then fine-tuned with the channels considered [1,13,155,114]. ...
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... Three different architectures of DWT named as direct approach, recursive pyramidal approach and a new modified RPA, based on flexible filter and control unit structure, has been implemented in [5]. A parallel implementation of DWT and its inverse DWT reformulated using distributed arithmetic architecture has been implemented on high-density FPGA in [3]. Yazhini et al. [10] implemented DWT using modified DA with partial tables. ...
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... Implementations based on DA get better performance than that based on convolution approach. [4] This paper is organized as following: Section II: digital FIR filters, Section III FIR implementation, Section IV simulation and results, and V conclusion. ...
... Distributed Arithmetic (DA) algorithm is the most suitable alternative for convolution approach in case of constant coefficients [1, 11, and 12]. DA algorithm is suitable for portable applications, because in DA algorithm the costly MACs units are replaced with Look-Up-Tables (LUTs) and shifts which reduce the power consumption [4]. ...
... In Fig. 6, the m-bit LUT used in Fig. 4 have been divided into two ml2-bit LUTs. Then the output of the two LUTs are added before fed into the scaling accumulator [4,13]. ...
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... Implementations based on DA get better performance than that based on convolution approach. [4] This paper is organized as following: Section II: digital FIR filters, Section III FIR implementation, Section IV simulation and results, and V conclusion. ...
... Distributed Arithmetic (DA) algorithm is the most suitable alternative for convolution approach in case of constant coefficients [1, 11, and 12]. DA algorithm is suitable for portable applications, because in DA algorithm the costly MACs units are replaced with Look-Up-Tables (LUTs) and shifts which reduce the power consumption [4]. ...
... In Fig. 6, the m-bit LUT used in Fig. 4 have been divided into two ml2-bit LUTs. Then the output of the two LUTs are added before fed into the scaling accumulator [4,13]. ...
Finite impulse response (FIR) digital filters are extensively used due to their key role in various digital signal processing (DSP) applications. Several attempts have been made to develop hardware realization of FIR filters characterized by implementation complexity, precision and high speed. Field Programmable Gate Array is a reconfigurable realization of FIR filters. Field-programmable gate arrays (FPGAs) are on the verge of revolutionizing digital signal processing. Many front-end digital signal processing (DSP) algorithms, such as FFTs, FIR or IIR filters, are now most often realized by FPGAs. Modern FPGA families provide DSP arithmetic support with fast-carry chains that are used to implement multiply-accumulates (MACs) at high speed, with low overhead and low costs. In this paper, distributed arithmetic (DA) realization of FIR filter as serial and parallel are discussed in terms of hardware cost and resource utilization.
... Another research reveal, DA exploits parallelism (at the vector level) and pipelining (at the bit level) and is highly suitable for FPGA implementation due to their fine grained device fabric, massive parallelism capabilities, register rich architecture that enables efficient implementation of ROM structures in lookup tables (LUTs) [13]. The superior performance and hardware efficient nature of DA when compared to conventional arithmetic has been suitably demonstrated in the implementation of various algorithms such as algorithms based on matrix-vector multiplication, [14], [15]. ...
This paper describes the design and implementation of three-dimensional (3-D) Haar with transpose-based computation and distributed arithmetic (DA). As a results of the separately property of the multidimensional Haar wavelet transform (HWT), the proposed architecture has been implemented using a cascade of
three N-point one-dimensional (1-D) Haar and two transpose memories for a 3-D volume of N × N × N, suitable for 3-D medical image compression. The 3-D HWT architecture were implemented on SubRIO-9632 board National Instrument. Experimental result and analysis of area, power consumption and maximum frequency are discussed in this paper.
... This modified architecture uses parallel FIR filter structure to compute DWT for n resolution levels. [4]represents computation of fast discrete wavelet transform using FIR filter implementation using Distributed Arithmetic .This paper proposes a parallel implementation of DWT and its inverse DWT ,here, wavelet transform is reformulated according to distributed arithmetic and is implemented on high density field programmable gate array. [5] gives exact technique and implementation of distributed arithmetic with the use of partial tables. ...
... Generally, for the implementation of DWT, FIR filter is implemented using direct from structure as show in fig 2. In fig2, each filter tap consists of a delay element, an adder, and a multiplier [4]. But, this structure faces major drawback that filter throughput is inversely proportional to the number of filter taps. ...
... Distributed arithmetic is originated from a simple equation of Boolean algebra where, variable Y indicates the result of product between an input data vector x and a coefficient vector a for i values. The conventional representation of product of distributed arithmetic is given as follows [4]: ...
... Where W L (n, j) and W H (n, j) are the n th scaling and wavelet coefficient at the j th stages, h 0 (n) and h 1 (n) are dilation coefficients [18] corresponding to scaling and wavelet functions. The forward DWT has been implemented using Decimator block, which consists of a PDA FIR filter and down sampling operator. ...
Development of modern integrated circuit technologies makes it feasible to
develop cheaper, faster and smaller special purpose signal processing function
circuits. Digital Signal processing functions are generally implemented either
on ASICs with inflexibility, or on FPGAs with bottlenecks of relatively smaller
utilization factor or lower speed compared to ASIC. Field Programmable DSP
Array (FPDA) is the proposed DSP dedicated device, redolent to FPGA, but with
basic fixed common modules (CMs) (like adders, subtractors, multipliers,
scaling units, shifters) instead of CLBs. This paper introduces the development
of reconfigurable system architecture with a focus on FPDA that integrates
different DSP functions like DFT, FFT, DCT, FIR, IIR, and DWT etc. The
switching between DSP functions is occurred by reconfiguring the
interconnection between CMs. Validation of the proposed architecture has been
achieved on Virtex5 FPGA. The architecture provides sufficient amount of
flexibility, parallelism and scalability.
