QR decomposition is another powerful technique to solve linear equations. In QR decomposition, the co-efficient matrix need not to be a symmetric matrix. In special cases where the input signal is compressible or sparse, QR decomposition can directly operate on matrix if less than . This way an underdetermined linear system is solved. Matrix is …
Gaussian Elimination (GE) is one of the most popular methods to solve an linear equation. GE algorithm is the only direct method which is of much interest to the researchers. This method considers that the co-efficient matrix is square. If the matrix is not square then it can be made square and symmetric as shown …
Solving Linear Equations using Gaussian Elimination Read More »
In our previous tutorial, we have discussed about Cholesky decomposition which is a very important matrix factorization to solve a linear equation. But this technique has some drawbacks which are also discussed in the same tutorial. In this tutorial, we will discuss about modified Cholesky Decomposition which is an alternative version of Cholesky decomposition. This …
Solving Linear Equations with Modified Cholesky Decomposition Read More »
Cholesky decomposition is a very important matrix factorization technique which is used to solve a linear equation. This technique originally derives from very popular LU decomposition and very suitable for higher order matrices. In Cholesky decomposition, the co-efficient matrix has to be a symmetric positive definite matrix. But in general, the co-efficient matrix can be …
Solving Linear Equations using Cholesky Decomposition Read More »
Singular Value Decomposition (SVD) is one of the matrix factorization techniques which can be used to solve linear equations. But this is not the primary objective of SVD. SVD can provide singular values of matrix. Singular values reveal unique information about a matrix. SVD has many uses in machine learning, image processing etc. Linear equations …
QR decomposition is one of the powerful matrix factorization techniques that is used to solve a linear equation, to find matrix inverse or to find pseudo-inverse. In this factorization technique, a matrix (A) is factorized into two matrices Q and R such that A = QR. Here, Q is an ortho-normal matrix and R is …
FPGA Implementation QR Decomposition Based on CORDIC Read More »
Pulse Width Modulation (PWM) signal is used in place of a Digital to Analog Converter (DAC) to simplify the digital-to-analog conversion process. PWM is used when we need to generate analog voltage corresponding to some digital value. PWM is a technique where the width of a pulse is varied. This means the duty cycle of …
Ultrasonic sensor is one of the most important sensors which are used for IoT applications. There are plenty of tutorials available in the internet which tells us how to interface an ultrasonic sensor with Arduino and other popular controllers. In this tutorial, we will talk about interfacing ultrasonic sensor with FPGA and for that we …
Almost every FPGA boards are having seven segment display elements. These displays are very useful for displaying data in he form of BCD. Suppose, one design is implemented on FPGA and display of the result is required. Then the result of the design can be displayed on these seven segment displays. Seven segment displays are …
A numerically controlled oscillator (NCO) is used for on-chip generation of major signals like cosine, sine, linear frequency modulated (LFM), Gaussian etc. in system on chips (SoCs). These signals can be generated by two ways, either by analog circuitry or by digital circuitry. In a digital system, these signals are generated using numerically controlled oscillator …
Signal processing algorithms sometimes involve computation of exponential as well as logarithm. Thus it is important to implement both the functions on digital hardware. In our previous tutorials, we have discussed implementation of exponential function. In this work, design of digital hardware to find logarithm of a number is discussed. The logarithm function is computed …
In the previous post, we have discussed the theory for computation of exponential and discussed about its hardware architecture. In this post, we will discuss an alternative architecture to compute the exponential. If we examine the equations which evaluate the exponential function, then we can see that is multiplied by or . In the previous …
Signal processing algorithms sometimes involve computation of exponential. Thus it is important to implement the exponential function. In this work, design of digital hardware for exponential function is discussed. Like other elementary functions, exponential function is also computed using the iterative formulas. In this work, computation of the exponential function is shown for three cases. …
I. Introduction Fast Fourier transform (FFT), an efficient technique to perform discrete Fourier transform (DFT), is the most important block in the signal processing domain. FFT is used to convert a signal in time domain to its frequency domain. On the other hand, inverse FFT (IFFT) block is used to convert the signal in frequency …
FPGA Implementation of 1024-point FFT/IFFT Processor Read More »
Fast Fourier Transform (FFT) is an efficient technique to implement Discrete Fourier Transform (DFT). FFT is used to observe the frequency domain characteristics of a signal or an image. Similarly Inverse FFT (IFFT) is used to convert a frequency domain signal to its time domain. Thus FFT and IFFT are very important functions in the …
MATLAB Realization of FFT/IFFT w/o Direct Function Read More »
