Analysis and Evaluation of MAC Operators for Fast Fourier Transformation

Arithmetic tasks are broadly utilized in Digital Signal Processing (DSP) applications. In this paper, a streamlined plan of the melded Add-Multiply (FAM) administrators is being investigated for the expanding execution. The direct plan of an AM unit is executed by apportioning a snake and afterward driving its yield to the contribution of a multiplier, increments essentially both region and basic way postponement of the circuit. The immediate recoding of the entirety of two numbers in its MB structure prompts a progressively effective execution of the intertwined Add-Multiply unit contrasted with the regular one, earlier recoding plans depend on complex controls in bit-level, which are actualized by committed circuits in entryway level. This new recoding plan and Modified CSA Tree, diminishes the basic way delay and decreases power utilization. This paper focuses on the extra decrease of dormancy and force utilization of CSA tree multiplier. This is cultivated by the utilization of Modified stall ADD-Multiply administrator and 4:2 compressor adders. Three elective plans of the proposed S-MB approach utilizing regular and marked piece Full Adders (FAs) and Half Adders (HAs) are being investigated as building squares

DESIGN OF THE OPTIMIZED FUSED-ADD MULTIPLY (FAM) OPERATOR BY USING MODIFIED BOOTH

Complex arithmetic operations are widely used in Digital Signal Processing (DSP) applications. In this work, we focus on optimizing the design of the fused Add-Multiply (FAM) Operator for increasing performance. We investigate techniques to implement the direct recoding of the sum of two numbers in its Modified Booth (MB) form. We introduce a structured and efficient recoding technique and explore three different schemes by incorporating them in FAM designs. Comparing them with the FAM designs which use existing recoding schemes, the propose technique yields considerable reductions in terms of critical delay, hardware complexity of the FAM unit. The FAM Architecture is implemented by Verilog Hardware Description Language and it is synthesized by Xilinx ISE tool. In proposed, we focus on AM units which implement the operation. The conventional design of the AM operator requires that its inputs and are first driven to an adder and then the input and the sum are driven to a multiplier in order to get. The drawback of using an adder is that it inserts a significant delay in the critical path of the AM. As there are carry signals to be propagated inside the adder, the critical path depends on the bit-width of the inputs. In order to decrease this delay, a SPST adder can be used which, however, the increases the area occupation and the power dissipation. An optimized design of the AM operator is based on the fusion of the adder and the MB encoding unit into a single data path block by direct recoding of the sum to its MB representation. The fused Add-Multiply (FAM) component contains only one adder at the end (final adder of the parallel multiplier). As a result, significant area savings are observed and the critical path delay of the recoding process is reduced and decoupled from the bit-width of its inputs. In this work, we present a new technique for direct recoding of two numbers in the MB representation of their sum

Multiplierless CSD techniques for high performance FPGA implementation of digital filters.

I leverage FastCSD to develop a new, high performance iterative multiplierless structure based on a novel real-time CSD recoding, so that more zero partial products are introduced. Up to 66.7% zero partial products occur compared to 50% in the traditional modified Booth's recoding. Also, this structure reduces the non-zero partial products to a minimum. As a result, the number of arithmetic operations in the carry-save structure is reduced. Thus, an overall speed-up, as well as low-power consumption can be achieved. Furthermore, because the proposed structure involves real time CSD recoding and does not require a fixed value for the multiplier input to be known a priori, the proposed multiplier can be applied to implement digital filters with non-fixed filter coefficients, such as adaptive filters.My work is based on a dramatic new technique for converting between 2's complement and CSD number systems, and results in high-performance structures that are particularly effective for implementing adaptive systems in reconfigurable logic.My research focus is on two key ideas for improving DSP performance: (1) Develop new high performance, efficient shift-add techniques ("multiplierless") to implement the multiply-add operations without the need for a traditional multiplier structure. (2) There is a growing trend toward design prototyping and even production in FPGAs as opposed to dedicated DSP processors or ASICs; leverage this trend synergistically with the new multiplierless structures to improve performance.Implementation of digital signal processing (DSP) algorithms in hardware, such as field programmable gate arrays (FPGAs), requires a large number of multipliers. Fast, low area multiply-adds have become critical in modern commercial and military DSP applications. In many contemporary real-time DSP and multimedia applications, system performance is severely impacted by the limitations of currently available speed, energy efficiency, and area requirement of an onboard silicon multiplier.I also introduce a new multi-input Canonical Signed Digit (CSD) multiplier unit, which requires fewer shift/add/subtract operations and reduced CSD number conversion overhead compared to existing techniques. This results in reduced power consumption and area requirements in the hardware implementation of DSP algorithms. Furthermore, because all the products are produced simultaneously, the multiplication speed and thus the throughput are improved. The multi-input multiplier unit is applied to implement digital filters with non-fixed filter coefficients, such as adaptive filters. The implementation cost of these digital filters can be further reduced by limiting the wordlength of the input signal with little or no sacrifice to the filter performance, which is confirmed by my simulation results. The proposed multiplier unit can also be applied to other DSP algorithms, such as digital filter banks or matrix and vector multiplications.Finally, the tradeoff between filter order and coefficient length in the design and implementation of high-performance filters in Field Programmable Gate Arrays (FPGAs) is discussed. Non-minimum order FIR filters are designed for implementation using Canonical Signed Digit (CSD) multiplierless implementation techniques. By increasing the filter order, the length of the coefficients can be decreased without reducing the filter performance. Thus, an overall hardware savings can be achieved.Adaptive system implementations require real-time conversion of coefficients to Canonical Signed Digit (CSD) or similar representations to benefit from multiplierless techniques for implementing filters. Multiplierless approaches are used to reduce the hardware and increase the throughput. This dissertation introduces the first non-iterative hardware algorithm to convert 2's complement numbers to their CSD representations (FastCSD) using a fixed number of shift and logic operations. As a result, the power consumption and area requirements required for hardware implementation of DSP algorithms in which the coefficients are not known a priori can be greatly reduced. Because all CSD digits are produced simultaneously, the conversion speed and thus the throughput are improved when compared to overlap-and-scan techniques such as Booth's recoding

HIGH-LEVEL OPTIMIZATION TECHNIQUES FOR LOW-POWER MODIFIED BOOTH MULTIPLIER DESIGN OF FPGA

Complex arithmetic operations are widely used in Digital Signal Processing (DSP) applications. In this work, we focus on optimizing the design of the fused Add-Multiply (FAM) Operator for increasing performance. We investigate techniques to implement the direct recoding of the sum of two numbers in its Modified Booth (MB) form. We introduce a structured and efficient recoding technique and explore three different schemes by incorporating them in FAM designs. Comparing them with the FAM designs which use existing recoding schemes, the propose technique yields considerable reductions in terms of critical delay, hardware complexity of the FAM unit. The FAM Architecture is implemented by Verilog Hardware Description Language and it is synthesized by Xilinx ISE tool. In proposed, we focus on AM units which implement the operation. The conventional design of the AM operator requires that its inputs and are first driven to an adder and then the input and the sum are driven to a multiplier in order to get. The drawback of using an adder is that it inserts a significant delay in the critical path of the AM. As there are carry signals to be propagated inside the adder, the critical path depends on the bit-width of the inputs. In order to decrease this delay, a SPST adder can be used which, however, the increases the area occupation and the power dissipation. An optimized design of the AM operator is based on the fusion of the adder and the MB encoding unit into a single data path block by direct recoding of the sum to its MB representation. The fused Add-Multiply (FAM) component contains only one adder at the end (final adder of the parallel multiplier). As a result, significant area savings are observed and the critical path delay of the recoding process is reduced and decoupled from the bit-width of its inputs. In this work, we present a new technique for direct recoding of two numbers in the MB representation of their sum

Implementation of RISC Processor for DSPAcceleratorArchitectureExploiting Carry Save Arithmetic

Hardware acceleration has been proved an extremely promisingimplementation strategyforthedigitalsignal processing(DSP) domain.Ratherthanadoptingamonolithicapplication-specificintegrated circuit designapproach,  in thisbrief, we present a  novel accelerator architecture comprising flexiblecomputational  units that support the executionofalargesetofoperationtemplatesfoundinDSPkernels. Wedifferentiatefrompreviousworksonflexibleacceleratorsbyenabling computations tobeaggressivelyperformedwithcarry-save(CS)formatteddata.Advancedarithmeticdesignconcepts, i.e.,recodingtechniques, areutilizedenabling CSoptimizationstobeperformedinalargerscope thaninpreviousapproaches.Extensiveexperimentalevaluationsshow thattheproposedacceleratorarchitecturedeliversaveragegainsofup to 61.91%in area-delay productand54.43%in energy consumption comparedwiththestate-of-artflexibledatapaths. In this paper, their concentration is on 16 bit operations but here in the proposed scheme, the focus is on 32 bit operations.Hardware Acceleration basically refers to the usage of computer hardware to perform some functions faster than they are actually possible within the software running on general purpose CPU. TheRISCor ReducedInstructionSetComputerisadesignphilosophythathasbecomeamainstreaminScientificandengineeringapplications.Themainobjectiveofthispaperis to design and implement of 32 – bit RISC(ReducedInstruction Set Computer) processor forflexible DSP Accelerator Architecture.Thedesignwillhelp to improve the speed of the processor, and to give thehigherperformance of the processor. The most important featureofthe RISC processor is that this processor is very simpleandsupport load/store architecture. The important componentsofthis processor include the Arithmetic Logic Unit,Shifter,Rotator and Control unit. The module functionalityandperformance issues like area, power dissipationandpropagation delay are analyzed. Therefore, here we meet some of the main constraints likeComplexity of the instruction set, which will reduce the amount of space, time, cost, power, heat and other things that it takes to implement the instruction set part of a processor. As the Time of execution decreases, the Speed of execution automatically increases.Hardware acceleration has been proved an extremely promisingimplementation strategyforthedigitalsignal processing(DSP) domain.Ratherthanadoptingamonolithicapplication-specificintegrated circuit designapproach,  in thisbrief, we present a  novel accelerator architecture comprising flexiblecomputational  units that support the executionofalargesetofoperationtemplatesfoundinDSPkernels. Wedifferentiatefrompreviousworksonflexibleacceleratorsbyenabling computations tobeaggressivelyperformedwithcarry-save(CS)formatteddata.Advancedarithmeticdesignconcepts, i.e.,recodingtechniques, areutilizedenabling CSoptimizationstobeperformedinalargerscope thaninpreviousapproaches.Extensiveexperimentalevaluationsshow thattheproposedacceleratorarchitecturedeliversaveragegainsofup to 61.91%in area-delay productand54.43%in energy consumption comparedwiththestate-of-artflexibledatapaths. In this paper, their concentration is on 16 bit operations but here in the proposed scheme, the focus is on 32 bit operations.Hardware Acceleration basically refers to the usage of computer hardware to perform some functions faster than they are actually possible within the software running on general purpose CPU. TheRISCor ReducedInstructionSetComputerisadesignphilosophythathasbecomeamainstreaminScientificandengineeringapplications.Themainobjectiveofthispaperis to design and implement of 32 – bit RISC(ReducedInstruction Set Computer) processor forflexible DSP Accelerator Architecture.Thedesignwillhelp to improve the speed of the processor, and to give thehigherperformance of the processor. The most important featureofthe RISC processor is that this processor is very simpleandsupport load/store architecture. The important componentsofthis processor include the Arithmetic Logic Unit,Shifter,Rotator and Control unit. The module functionalityandperformance issues like area, power dissipationandpropagation delay are analyzed. Therefore, here we meet some of the main constraints likeComplexity of the instruction set, which will reduce the amount of space, time, cost, power, heat and other things that it takes to implement the instruction set part of a processor. As the Time of execution decreases, the Speed of execution automatically increases

Carry-Propagate Free Combinational Multiplier

Multipliers are the heart of most digital systems, however, they are quite complex devices. Standard multiplier designs in digital systems use three basic parts to compute a product, which mainly involve creating and adding partial products. Unfortunately, a significant amount of the worst-case delay attributed to larger multipliers stem from carry-propagate adders to compute the final product. This research involves modifying basic parallel multipliers, so that it can compute the final product using a redundant number notation. Using multipliers that use redundant numbers can increase the complexity of multiplication units, however, it can present designs that avoid the final carry-propagate addition. In this thesis, a design is presented that utilizes the Signed Digit notation, which is used to allow redundancy within the numbers, and subsequently avoid the final carry-propagate adder. Results using silicon standard-cell libraries indicate that for multipliers larger than 32 bits, a significant savings using the proposed architecture is shown. Comparisons versus traditional multipliers are presented and compared for analysis.School of Electrical & Computer Engineerin

Improved 64-bit Radix-16 Booth Multiplier Based on Partial Product Array Height Reduction

In this paper we describe an optimization for binary radix-16 (modified) Booth recoded multipliers to reduce the maximum height of the partial product columns to ceil(n/4) for n = 64-bit unsigned operands. This is in contrast to the conventional maximum height of ceil((n + 1)/4). Therefore a reduction of one unit in the maximum height is achieved. This reduction may add flexibility during the design of the pipelined multiplier to meet the design goals, it may allow further optimizations of the partial product array reduction stage in terms of area/delay/power and/or may allow additional addends to be included in the partial product array without increasing the delay. The method can be extended to Booth recoded radix-8 multipliers, signed multi- pliers, combined signed/unsigned multipliers, and other values of n

ΒΕΛΤΙΣΤΟΠΟΙΗΣΗ ΜΟΝΑΔΑΣ ΥΠΟΛΟΓΙΣΜΟΥ BUTTERFLY ΓΙΑ ΤΟΝ ΑΛΓΟΡΙΘΜΟ FFT

Ο σκοπός της διπλωματικής εργασίας αυτής είναι η διερεύνηση της λειτουργίας της μονάδας υπολογισμού πεταλούδας, Butterfly Computation Unit (BCU), και η παρουσίαση δύο εναλλακτικών αρχιτεκτονικών για την υλοποίηση της μονάδας αυτής. Η μονάδα υπολογισμού Butterfly είναι η βασική μονάδα για την υλοποίηση μονάδων Fast Fourier Transform (FFT) για αποδεκατισμό στο πεδίο του χρόνου, η οποία χρησιμοποιείται ευρέως σε εφαρμογές Ψηφιακής Επεξεργασίας Σημάτων όπως η Ανάλυση Φάσματος σημάτων, η Συμπίεση Δεδομένων, η σχεδίαση φίλτρων, η λύση Μερικών Διαφορικών Εξισώσεων, ο Πολλαπλασιασμός Πολυωνύμων, και ο υπολογισμός Συνέλιξης. Σκοπός της παρούσας εργασίας είναι η διερεύνηση μίας συμβατικής υλοποίησης της μονάδας υπολογισμού πεταλούδας, αλλά και τριών εναλλακτικών μονάδων οι οποίες έχουν σχεδιαστεί με σκοπό την αποδοτικότερη υλοποίησή της. Συγκεκριμένα, προτείνεται η χρήση του αλγορίθμου του Gauss, για τον πολλαπλασιασμό δύο μιγαδικών αριθμών καθώς η πράξη αυτή περιέχει το μεγαλύτερο υπολογιστικό φόρτο στην μονάδα υπολογισμού πεταλούδας. Επίσης, προτείνεται η χρήση προ-κωδικοποιημένων πολλαπλασιαστών για την υλοποίηση της Μονάδας Μιγαδικού Πολλαπλασιασμού, με σκοπό την περαιτέρω βελτίωση της λειτουργίας της, σε αντιπαράθεση με την συμβατική της υλοποίηση, που κάνει χρήση πολλαπλασιαστών κωδικοποίησης Modified Booth. Οι παραπάνω μονάδες περιγράφηκαν με χρήση της γλώσσας περιγραφής υλικού Verilog, στην συνέχεια επαληθεύσαμε την ορθότητα λειτουργίας τους και συνθέσαμε τα κυκλώματα αυτά, με σκοπό να τα συγκρίνουμε ως προς την καθυστέρηση, την επιφάνεια που καταλαμβάνει το κύκλωμά τους, αλλά και την κατανάλωση ενέργειάς τους, με χρήση των εργαλείων σύνθεσης και προσομοίωσης της Synopsys. Τέλος, έγινε παρουσίαση των αποτελεσμάτων που προέκυψαν, καθώς και μία συγκριτική μελέτη τους για τα διάφορα μήκη λέξης εισόδου. Έτσι προέκυψαν τα απαραίτητα συμπεράσματα για την λειτουργία των διαφορετικών σχημάτων που υλοποιήθηκαν, καθώς, κάθε ένα από τα σχήματα που σχεδιάστηκαν, έδωσε αποτελέσματα που τα καθιστά κατάλληλα για διαφορετικές εφαρμογές, ανάλογα με το που εμφανίζουν την βέλτιστη συμπεριφορά τους.The scope of the thesis is the exploration of the Butterfly Computation Unit, and the introduction of two alternative architectures for the implementation of the said unit. The Butterfly Computation Unit is the most essential unit for the implementation of the algorithm of the Fast Fourier Transform, for Decimation in Time, that is used widely in applications for Digital Signals Processing like Spectral Analysis, Data Compression, and in solving Partial Differential equations, Filtering algorithms, Polynomial Multiplication and Convolution. The purpose of this thesis is the exploration of a conventional implementation of the Butterfly Computation Unit, but also three more alternative schemes that have been designed in order to be more efficient than the conventional one. Specifically, we propose the use of the Gauss algorithm for multiplying two complex numbers as this operation contains the largest computational effort in the Butterfly Computation Unit. Also, we proposed the use of pre-encoded multipliers to implement the complex number multiplication unit, in order to further improve its functioning, in juxtaposition with the conventional implementation, which uses Modified Booth multipliers. The units described above have been implemented, using Verilog hardware description language, next, their functionality has been behaviorally verified and we synthesized the circuits in order to experimentally compare them in delay, area and power consumption, using the Synopsys tools. Lastly, we presented the results that arose, and we also presented a comparative study for various input bit-widths. This way, we reached the necessary conclusions for the operation of the different proposed schemes that we designed and implemented, and according to the findings each proposed scheme showed its advantages, depending on the application that they are targeted for, where they appear to perform optimally