Cramér-Rao Lower Bound (CRLB)-Vector Parameter Estimation
Key focus: Applying Cramér-Rao Lower Bound (CRLB) for vector parameter estimation. Know about covariance matrix, Fisher information matrix & CRLB matrix.
Introducing The Kalman Filter
Introducing The Kalman Filter – Ramsey Faragher PDF Text: click here PDF Text: click here Note: Click the playlist icon (located at the top left corner of the video frame) to watch all lectures Video Lectures: Watch, Listen and Learn !!! † Link will take you to external sites Disclaimer: All the materials posted in … Read more
Non-central Chi square distribution
This post contains interactive python code which you can execute in the browser itself. If squares of k independent standard normal random variables are added, it gives rise to central Chi-squared distribution with ‘k’ degrees of freedom. Instead, if squares of k independent normal random variables with non-zero means are added, it gives rise to … Read more
Methods to compute linear convolution
Mathematical details of convolution, its relationship to polynomial multiplication and the application of Toeplitz matrices in computing linear convolution are discussed in the previous article. A short survey of different techniques to compute discrete linear convolution (with Matlab code) is given here. Definition Given an LTI (Linear Time Invariant) system with impulse response \(h[n]\) and … Read more
Convolution: understand the mathematics
Convolution operation is ubiquitous in signal processing applications. The mathematics of convolution is strongly rooted in operation on polynomials. The intent of this text is to enhance the understanding on mathematical details of convolution. Polynomial functions: Polynomial functions are expressions consisting of sum of terms, where each term includes one or more variables raised to … Read more
Chi square distribution – demystified
A random variable is always associated with a probability distribution. When the random variable undergoes mathematical transformation the underlying probability distribution no longer remains the same. Consider a random variable $latex Z $ whose probability distribution function (PDF) is a standard normal distribution ($latex \mu=0 $ and $latex \sigma^2=1 $). Now, if the random variable … Read more
Compute signal power in Matlab
Calculating the energy and power of a signal was discussed in one of the previous posts. Here, we will verify the calculation of signal power using Discrete Fourier Transform (DFT) in Matlab. Check here to know more on the concept of power and energy. The total power of a signal can be computed using the … Read more
Power and energy of a signal — formulas, classification, and examples
Energy Ex = Σ|x|² vs power Px as a long-window average of |x|²; energy signals vs power signals; physical scaling by load Z; Python examples and links to Matlab verification.
Uniform random variable
Uniform random variables are used to model scenarios where the expected outcomes are equi-probable. For example, in a communication system design, the set of all possible source symbols are considered equally probable and therefore modeled as a uniform random variable. The uniform distribution is the underlying distribution for an uniform random variable. A continuous uniform … Read more
White noise in Matlab — generate, analyze, and measure power
How to simulate white noise in Matlab, check spectrum and power, and relate AWGN variance to SNR — with links to AWGN generation and BER tools.