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1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 09 | Sep 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1204 Implementation of Reversible Radix-2 FFT VLSI Architecture using Programmable Reversible Gate Sourabh Sharma1, Prof. Gurpreet Singh2 1Research scholar, Electronics & Communication Department, Trinity Institute of Technology & Research, Bhopal 2Professor, Electronics & Communication Department, Trinity Institute of Technology & Research, Bhopal ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - The Discrete Fourier Transform (DFT) is a critical procedure in the field of Digital Signal Processing (DSP) and Telecommunications, particularly for applications in Orthogonal Frequency Division Multiplexing (OFDM) frameworks. The Fast Fourier Transform (FFT) is an effective calculation to process the DFT and its reverse. The FFT processor assumes a key job in the field of correspondence frameworks, for example, DigitalVideoorAudioBroadcasting, Wireless LAN with Standards of IEEE 802.11, High Speed Digital Subscriber Lines and so forth. Inthispaperincludes the execution of a zone proficient 8-point, 16-point and 32-point radix-2 DIT FFT calculation with the assistance of DKG reversible Gate. Two strategies areutilizedtoplanradix-2FFT calculation. In firest strategy is plan radix-2 FFT with the help of reversible Peres gate and TR gate. Second method is design radix-2 FFT with the help of reversible DKG Gate. The all structure are usage vertex-4 gadget family Xilinx programming and looked at past calculation. Key Words: FFT, Reversible Gate, DKG Gate, Peres Gate, TR Gate 1. INTRODUCTION The Fourier Transform isaninescapablemethodologyinflag handling, especially for applications in OFDM frameworks [1]. The Discrete Fourier Transform decays a lot of qualities into various segments of recurrence. The FFT is a fitting strategy to do control of DFT. The calculation of FFT was concocted by Cooley and Tukey so as to diminish the measure of multifaceted nature as for time and calculations [2]. The equipment of FFT can be executed by two sorts of groupings memory design and pipeline engineering. The memory engineeringcontainsa solitaryhandlingcomponent and different units of memory [3]. The benefits of memory design incorporate low power and minimal effort when contrasted with that of different styles. The explicit bad marks are more noteworthy idleness and lower throughput. The above bad marks of the memory engineering are completely killed by pipeline design to the detriment of additional equipment in a satisfactory way. The different sorts of pipeline engineering incorporate Single defer criticism (SDF), Single postpone commutator (SDC) and various postpone commutator (MDC). The pipeline engineering is an ordinary structure which canbeembraced by utilizing equipment portrayal dialect in a simple way. In the ongoing years, the correspondence frameworks need to transmit voice and video signs of high caliberina productive way. In present day the effective module is a rapid, solid innovation of correspondence [4]. Symmetrical OFDM is such a solid choice to achieve the above necessity. The calculationsofFFTcanbegatheredinto settled radix, blended radix and split radix calculations inan unpleasant way [5]. The essential classes of calculations of FFT incorporate - Decimation in-frequency (DIF) and the Decimation-in-time (DIT) as appeared in Figure 1. Both of these calculations rely upon crumbling of change of a N- point groupingintonumerous subsequencesina progressive way. There is no real distinction between them to the extent intricacy of calculation is concerned. For the most part DIT manages the info and yield backward arrangement and ordinary grouping separately, while DIF manages information and yield in typical succession and turn around arrangement individually. Just DIT calculation will be contemplated. Fig -1: Time and frequency signal 2. FAST FOURIER TRANSFORM There are two sorts concerning FFT calculation formulated by Cooley and Tukey - Decimation-in-Time calculation (DIT) and Decimation-in-Frequency calculation (DIF). The calculation of an arrangement of N-point can be acquired by methods for a double methodology. The info succession x(n) of size 'N' is disintegrated into tests of odd and even and the comparing sub-groupings f1(n) and f2(n) are given by:
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 09 | Sep 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1205 Fig -2: 8-point DIT-FFT Radix-2 Butterfly Fig -3: 8-point DIF-FFT Radix-2 Butterfly In figure 2, demonstrate the butterfly of radix-2 DIT FFT calculation. In this figure we utilized eight sources of info and eight yields. If there should be an occurrence of DIT the info test is utilized piece inversion arrange while the yield of DIT FFT coefficients is produced innormal request.InFigure 3, demonstrate the butterfly of radix-2 DIF FFT calculation. In the event of DIF the information testisutilizedincommon request while the yield of DIF FFT coefficient is produced in bit turned around request. 3. REVERSIBLE GATE Several reversible logic gate (RLG) are utilized in past structure. Figure 4 demonstrates the Peres door (PG). A bit of the 3x3 entryways are planned for executing some basic combinational limits despite the basic limits. Fig -4: Block Diagram of PG Fig -5: Block Diagram of TRG Figure 5, shows the TRG with 3×3 system. TRG gate as working of half sub-tractor, when thirdinputassume‘0’. The RDKG is presented by figure 6. RDKG is 4×4 system representation. RDKG is working on full adder and full sub- tractor when first input assumes ‘0’ and ‘1’. Fig -6: DKG Gate Fig -7: Block Diagram of 1-bit Full Adder Fig -8: Block Diagram of n-bit Full Adder
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 09 | Sep 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1206 4. PROPOSED METHODOLOGY The expense and defer figurings are indistinguishable to the 4-bitb snake/sub tractor in figure 9. We have design 4-bit full sub-tractor/adder with the help of DKG Gate. If the fourth input of the DKG Gate is ‘0’ then output of the DKG Gate as a adder and fourth input of the DKG Gate is ‘1’ then output of the DKG Gate as a sub-tractor. Fig -9: Reversible 4-bit Adder/ Sub tractor using DKG Gate Fig -10: Proposed DIT Radix-2 FFT algorithm using Radix- 2 Butterfly Example of 8-point FFT Then the 8-point FFT can be rewritten as 10)0( WhhX 10)1( WhhX 32)2( WhhX 32)3( WhhX 54)4( WhhX 54)5( WhhX 76)6( WhhX 76)7( WhhX Where 100 Wggh 101 Wggh 322 Wggh 323 Wggh 544 Wggh 545 Wggh 766 Wggh 767 Wggh Where )4()0(0 Wxxg )4()0(1 Wxxg )6()2(2 Wxxg )6()2(3 Wxxg )5()1(4 Wxxg )5()1(5 Wxxg )7()3(6 Wxxg )7()3(7 Wxxg In the modified equation in second stage 12 nforWggk nnn 221 nforWggk nnn 3422 nforWggk nnn 4423 nforWggk nnn And third stage 14 nforWkkX nnn
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 09 | Sep 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1207 24 nforWkkX nnn 34 nforWkkX nnn 44 nforWkkX nnn A fast Fouriertransform (FFT)isan algorithm thatcomputes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and viceversa.TheDFTisobtained by decomposing a sequence of values into components of different frequencies. This operation isuseful inmanyfields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformationsby factorizing the DFT matrix intoa product of sparse (mostly zero) factors. The difference in speed can be enormous, especially for longdata setswhere N maybein the thousands or millions. In thepresenceof round-offerror, many FFT algorithms are much more accurate than evaluating the DFT definition directly. 4. SIMULATION RESULT The reproduction results for different FFT calculations have been tried basically by executing in the Vertex-4 Xilinx programming. Additionally these product yields can be confirmed with reproduction results got utilizing MODELSIM. A portion of the previews of results in the Xilinx programming and reenactment are as per the following Fig -11: View Technology Schematic of 8-point DIT-FFT algorithm Fig -12: RTL View of DIT 8-point DIT-FFT algorithm Fig -13: RTL View of 16-point DIT-FFT algorithm 5. CONCLUSIONS FFT is an often utilized DSP calculation for the utilizations of OFDM. The blend of OFDM with Multiple Input Multiple Output (MIMO) flag handling is a distinct methodology of upgrading the information ratesofdifferentcorrespondence frameworks, for example, Wireless LAN, e Mobile, 4G and so forth. The discrete Fourier transform (DFT) is one of the most powerful tools in digital signal processing. The DFT enables us to conveniently analyze and design systems in frequency domain; however, part of the versatility of the DFT arises from the fact that there are efficient algorithms to calculate the DFT of a sequence. A class of these algorithms are called the Fast Fourier Transform (FFT). This article will, first, review the computational complexity of directly calculating the DFT and, then, it will discuss how a class of FFT algorithms, i.e., decimation in time FFT algorithms, significantly reduces the number of calculations. REFERENCES [1] Shashidhara. K. S and H.C. Srinivasaiah, “LowPowerand Area efficient FFT architecture through decomposition technique”, International Conference on Computer
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 09 | Sep 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1208 Communication and Informatics (ICCCI -2017),Jan.05– 07, 2017, Coimbatore, INDIA. [2] Fahad Qureshi, Jarmo Takala, Anastasia Volkova, Thibault Hilaire, “Multiplierless UnifiedArchitecturefor Mixed Radix-2/3/4 FFTs”, 2017 25th European Signal Processing Conference (EUSIPCO), IEEE 2017. [3] Fahad Qureshi, Muazam Ali, and Jarmo Takala, “Multiplierless Reconfigurable Processing Element for Mixed Radix-2/3/4/5 FFTs”, 978-1-5386-0446- 5/17/$31.00 ©2017 IEEE. [4] Ms. A. Anjana and Mrs. A.V Ananthalakshmi, “Design of Reversible 32-Bit BCD Add-Subtract Unit using Parallel Pipelined Method”, International Conference on Advances in Electrical, Electronics, Information, CommunicationandBio-Informatics(AEEICB16)978-1- 4673-9745-2 ©2016 IEEE. [5] Matthew Morrison andNagarajanRanganathan,“Design of a Reversible ALU based on Novel Programmable Reversible Logic Gate Structures”, 2015 IEEE Computer Society Annual Symposium on VLSI. [6] Lekshmi Viswanath and Ponni.M, “Design and Analysis of 16 Bit Reversible ALU”, ISSN: 2278-0661 Volume 1, Issue 1 (May-June 2014), PP 46-53. [7] Akanksha Dixit and VinodKapse, “Arithmetic & Logic Unit (ALU) Design using Reversible Control Unit”, International Journal of Engineering and Innovative Technology (IJEIT) Volume 1, Issue 6, June 2014. [8] Mr. Abhishek Gupta, Mr. UtsavMalviya and Prof. VinodKapse, “Design of Speed, Energy and Power Efficient Reversible Logic Based Vedic ALU for Digital Processors”, 2012 IEEE Computer Society Annual Symposium on VLSI. [9] H. Thapliyal and N. Ranganathan, "Design of Efficient Reversible Binary Subtractors Based on A New Reversible Gate," Proc. of the I ComputerSociety Annual Symposium on VLSI, 2009. [10] M. Morrison and N. Ranganathan, "Design of a Reversible ALU Based on Novel Programmable Reversible Logic Gate Structures," IEEE International Symposium on VLSI, 2011, pp. 126-131.
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