An integrator is a very important filter that proves useful in implementation of many blocks of a communication receiver such as symbol timing synchronization and Phase-Locked Loop (PLL). It is an inverse operation to a differentiator that is also used in many signal processing applications such as FM demodulation and image processing. In continuous-time case, an integrator finds the area under the curve of a signal amplitude. A discrete-time system deals with just the signal samples and hence a discrete-time integrator serves the purpose of collecting a running sum of past samples for an input signal. Looking at an infinitesimally

Continue reading# Tag: Phase Recovery

## Phase Locked Loop (PLL) in a Software Defined Radio (SDR)

IBM Watson and Google DeepMind are the most complex computers that, some believe, will try to run the world in a distant future. A PLL on the other hand is the simplest computer that actually runs so much of the world as a fundamental component of intelligent electronic circuits. The PLL was invented by the French engineer Henri de Bellescize in 1932 when he published his first implementation in the French journal L’Onde Electrique. A Phase Locked Loop (PLL) is a device used to synchronize a periodic waveform with a reference periodic waveform. In essence, it is an automatic control

Continue reading## Basics of Synchronization

In every digital communication system, the Tx has the easier role of signal generation while the Rx has the tougher job of figuring out the intended message. Just like solving a puzzle told by someone. Estimating and compensating for the frequency, phase and timing offsets between Tx and Rx oscillators is one such challenge. The solution can be designed depending on many factors such as some part of data is known (called a ‘training sequence’) or not, the synchronizer needs to be one-shot or continuously updating, and so on. Known Data Availability Depending on the availability of known data, synchronization

Continue reading## The Master Algorithm

Recently, I was reading the book The Master Algorithm by Pedro Domingos — a Professor at the University of Washington in machine learning. According to the description of his book, The Master Algorithm in Machine Learning A spell-binding quest for the one algorithm capable of deriving all knowledge from data, including a cure for cancer. Society is changing, one learning algorithm at a time, from search engines to online dating, personalized medicine to predicting the stock market. But learning algorithms are not just about Big Data – these algorithms take raw data and make it useful by creating more algorithms.

Continue reading## What is Carrier Phase Offset and How It Affects the Symbol Detection

In case of Quadrature Amplitude Modulation (QAM) and other passband modulation schemes, Rx has no information about carrier phase of the Tx oscillator. Let us explore what impact this has on the demodulation process. Constellation Rotation To see the effect of the carrier phase offset, consider that a transmitted passband signal consists of two PAM waveforms in $I$ and $Q$ arms denoted by $v_I(t)$ and $v_Q(t)$ respectively and combined as \begin{equation}\label{eqRealWorldQAMPhaseOffset} s(t) = v_I(t) \sqrt{2} \cos 2\pi F_C t – v_Q(t) \sqrt{2}\sin 2\pi F_C t \end{equation} Here, $F_C$ is the carrier frequency and $v_I(t)$ and $v_Q(t)$ are the continuous versions

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