Methods to compute linear convolution

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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

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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

Compute signal power in Matlab

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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

Uniform random variable

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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 AWGN, plot PSD, check variance

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Simulate white / Gaussian noise in Matlab: generate with randn, verify variance and flat PSD, then reuse the noise model in BER simulations.

Breaking the Bandwidth Barrier – Li-Fi turns LED bulbs into High Speed Internet Hotspots

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Researchers, working on Ultra-Parallel Visible Light Communications (UP-VLC) project, have demonstrated 3.5Gpbs free space data transmission via three separate micro-LEDs that emit red, blue and green colours.  In effect, combining the three colours (that makes up for white colour), researchers say that achieving data rates over 10Gbps is feasible. The technology enabler here is called … Read more

Symbol Timing Recovery for QPSK (digital modulations)

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Digital Modulations Lab path:BPSK → QPSK → M-PSK simulation → QPSK symbol timing → π/2-BPSK (5G NR)Tools: BER vs Eb/N0 · EVM → SNR · OFDM CP overhead The goal of timing recovery is to estimate and correct the sampling instants and phase at the receiver, such that it allows the receiver to decode the … Read more

Minimum-variance unbiased estimator (MVUE)

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As discussed in the introduction to estimation theory, the goal of an estimation algorithm is to give an estimate of random variable(s) that is unbiased and has minimum variance. This criteria is reproduced here for reference $latex E\left\{\hat{f}_0 \right\} = f_0 $ $latex \sigma^{2}_{\hat{f}_0}= E \left\{ ( \hat{f}_0 – E [ \hat{f}_0 ] )^2 \right\} … Read more