International Journal of Scientific & Engineering Research Volume 2, Issue 5, May-2011 1 ISSN 2229-5518 IJSER © 2011 http://www.ijser.org Speedy Deconvolution using Vedic Mathematics Rashmi K. Lomte (Mrs.Rashmi R. Kulkarni), Prof.Bhaskar P.C Abstract— Deconvolution is a computationally intensive digital signal processing (DSP) function widely used in applications such as imaging, wireless communication, and seismology. In this paper deconvolution of two finite length sequences (NXM) , is implemented using direct method to reduce deconvolution processing time. Vedic multiplier is used to achieve high speed. Urdhava Triyakbhyam algorithm of ancient Indian Vedic Mathematics is utilized to improve its efficiency. For division operation non-restoring algorithm is modified and used. The efficiency of the proposed convolution circuit is tested by embedding it on Spartan 3E FPGA. Simulation shows that ,the circuit has a delay of 79.595 ns from input to output using 90nm process library. It also provides the necessary modularity, expandability, and regularity to form different deconvolutions for any number of bits. Index Terms— Deconvolution, Non-Restoring algorithm, Urdhva Tiryagbhyam ——————————  —————————— 1 INTRODUCTION HE concept of deconvolution is widely used in the techniques of signal processing and image processing. The concept of deconvolution has appli- cations in reflection seismology, in reversing the optical distortion, to sharpen images etc. Faster additions, multip- lications and divisions are of extreme importance in DSP for deconvolution. Speeding up deconvolution using a Hardware Description Language for design entry not only increases (improves) the level of abstraction, but also opens new possibilities for using programmable devices. In this paper, a novel method for computing the linear deconvolution of two finite length sequences is used. Me- thod is explained in detail in [1]. This method is similar to computing long-hand division and polynomial division. As a need of project, all required possible adders are studied. All these adders are synthesized using Xilinx9.2i. There delays and areas are compared. Adders which have highest speed and comparatively less area occupied, are selected for implementing deconvolution. Since 4×4 bit multiplier is need of this project, different 4×4 bit multip- liers are studied and Urdhava Triyakbhyam algorithm which gives lowest delay among remaining all multipliers is used here. For division, different division algorithms are studied, by comparing drawbacks and advantages of each algorithm, Non restoring algorithm is modified ac- cording to need and then used. This paper can be considered as extension of [2]. where discrete linear convolution of two finite length se- quences(4 ×4) is implemented. That convolved output of [2]. is input to this proposed design, impulse response of system is known is another input, this paper proposes design that carry out high speed deconvolution and ex- tracts input samples. Paper is organized as follows: section 2 gives brief in- troduction of novel method for deconvolution. Section 3 describes division algorithm. Section 4 discusses the Ved- ic mathematics and Urdhva Tiryagbhyam algorithm for multiplication. Section 5 presents selection of speedy ad- der. In section 6 design verification is given. Finally, the conclusion is obtained. 2NOVEL METHOD FOR CALCULATING DECONVOLUTION In general, the object of deconvolution is to find the solution of a convolution equation of the form: f *g = h (1) Usually, h is some recorded signal, and ƒ is some signal that wish to recover, but has been convolved with some other signal g before get recorded. The function g might represent the transfer function of an instrument or a driv- ing force that was applied to a physical system.If one know g or at least form of g,then one can perform deter- ministic deconvolution. If the two sequences f(n) and g ( n ) are causal, then the con- volution sum is: h(n) = k), n  0 (2) Therefore, solving for f(n) given g(n) and y(n) results in f(n) = , n ǃ 1 (3) where f(0) = (4) where solution requires that g(0) ƾ 0 This recursion can be carried out in a manner similar to long division. Lets take example ,let h[n] = [16 36 56 17 28 12 ] and g[n] = [ 4 4 3 2 ] , solving for f(n) given g(n) and h(n). The sequences are set up in a fashion similar to long division, as shown below, but where no carries are performed out of a column. T