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Fixed Point Arithmetic

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Fixed Point Arithmetic is a numerical representation method where numbers are expressed with a fixed number of digits before and after the decimal point. This approach allows for efficient computation in digital systems, particularly in environments with limited processing power, by avoiding the complexities of floating-point arithmetic.
lightbulbAbout this topic
Fixed Point Arithmetic is a numerical representation method where numbers are expressed with a fixed number of digits before and after the decimal point. This approach allows for efficient computation in digital systems, particularly in environments with limited processing power, by avoiding the complexities of floating-point arithmetic.
The physical limits being reached in silicon-based computing, new ways have to be found to overcome the predicted end of Moore's law. Many applications can tolerate approximations in their computations at several levels without... more
Transforms like Discrete Fourier Transform (DFT) are a major block in communication systems such as OFDM, etc. This paper reports architecture of a DFT core using new distributed arithmetic (NEDA) algorithm. The advantage of the proposed... more
Often embedded programmers and application specific integrated circuit (ASIC) designers are frustrated by the inability to realize near floating-point accuracy in a fixedpoint application. The problem is not limited to function... more
Often embedded programmers and application specific integrated circuit (ASIC) designers are frustrated by the inability to realize near floating-point accuracy. in a fixed-point application. The problem is not limited to function... more
This paper presents an efficient orthogonal sparse 8×8 transform matrix for color image compression particularly at lower bit rate applications. The transform matrix is made sufficiently sparse by appropriately inserting additional zeros... more
The realisation of signal processing algorithms in fixed-point offers performance advantages over floating-point realisations. However, the task is widely acknowledged to be tedious, error prone, and time consuming. In this paper, we... more
In this paper, an encoder and decoder system is proposed using Bose-Chaudhuri-Hocquenghem (BCH) doubleerror-correcting and triple-error detecting (DEC-TED) with emerging memories of low power and high decoding efficiency. An adaptive... more
Neuromorphic chips are used to model biologically inspired Spiking-Neural-Networks(SNNs) where most models are based on differential equations. Equations for most SNN algorithms usually contain variables with one or more e x components.... more
Digital images have an inherent amount Deepika Sharma of noise introduced either by the imaging process or manual creation. Singular value decomposition (SVD) is one of the most important and useful factorizations in linear algebra. We... more
Understanding and predicting electromagnetic behavior is needed more and more in modern technology. The Finite-Difference Time-Domain (FDTD) method is a powerful computational electromagnetic technique for modelling the electromagnetic... more
Complex signal processing algorithms are specified in floating point precision. When their hardware implementation requires fixed point precision, type refinement is needed. The paper presents a methodology and design environment for this... more
This correspondence presents an analysis of the finite register length influence on the accuracy of results obtained by the time-frequency distributions (TFD's). In order to measure quality of the obtained results, the variance of the... more
A flexible system for timefrequency signal analysis is presented. It is based on the S-method, which has a significant advantage in implementation since it can involve, as a key intermediate step, the Shorttime Fourier transform or the... more
FPGA implementations of floating-point operators have historically been designed to use binary floating-point representations. The general computing world settled on binary floating-point representations over three decades ago, and more... more
We review some of the classical methods used for quickly obtaining low-precision approximations to the elementary functions. Then, for each of the three main classes of elementary function algorithms (shift-and-add algorithms, polynomial... more
Neural network quantization is a promising compression technique to reduce memory footprint and save energy consumption, potentially leading to real-time inference. However, there is a performance gap between quantized and full-precision... more
Computational energy versus computational precision represents a critical implementation-level tradeoff facing embedded DSP systems. Focusing on multiply-accumulate (MAC) hardware, which is used extensively in DSP implementations (e.g.,... more
the real and imaginary components of the input sequence is easier to implement. Let the real and imaginary components of the input sequence satisfy IRe[x] < a and imIx,I < a . (2) These bounds result in IXkl < v'Na, k = 0,1 N -1. With... more
This paper discusses common fixed-point theorem in fuzzy metric space for three self-mappings by using the conditions of compatible mappings of type (K). This theorem generalizes the results of K.B. Manandhar et al. (2014), and also the... more
This work examines the numerical fixed-point performance of a new multichannel lattice RLS filtering algorithm using data from two underwater acoustic communication experiments. The algorithm may be an appealing choice for underwater... more
One of the most important goals of current and future sensor networks is energy-efficient communication of images. This paper presents a quantitative comparison between the energy costs associated with 1) direct transmission of... more
A statistical model is used to predict the output signal-tonoise ratio (SNR) when a two-pass fast Fourier transform (FFT) is computed using fixed-point arithmetic. Theresultsshow that the ratio varies essentially as the square root of the... more
Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.... more
Over the last few years, neural networks have started penetrating safety critical systems to make decisions as for example in robots, rockets and autonomous driving car. Neural networks based on floating-point arithmetic are very time and... more
Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.... more
A lower-error and lower-variance n X ?Z multiplier is suitably proposed for VLSI design. Considering next lower significant stage in P,-' column and useful error-compensation model in the least significant part, and utilizing a near... more
In the digital signal processing (DSP) area, one of the most important tasks is digital filter design. Currently, this procedure is performed with the aid of computational tools, which generally assume filter coefficients represented with... more
The study describes an innovative adaptive beamforming system that improves wireless communication performance through the utilization of field-programmable gate arrays (FPGAs). Field-Programmable Gate Array (FPGA) technology is utilized... more
This correspondence presents an analysis of the finite register length influence on the accuracy of results obtained by the time-frequency distributions (TFD's). In order to measure quality of the obtained results, the variance of the... more
Arithmetic circuit plays a key role in digital signal processing (DSP). A datapath is used to implement the specification usually represented as a polynomial. The two most important problems are verification and optimization of the... more
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