At the beginning, the history of wireless communication revolved around analog communication systems for several decades. Amplitude Modulation (AM) and Frequency Modulation (FM) were the most widely used techniques during this time. Gradually, however, a transition towards digital transmission occurred in wireless systems as well, a phenomenon that was in sync with digital revolution in the society as a whole. So what are the main benefits of digital technology that made it much superior to its analog counterpart? Let us analyze some of them below [1]. Performance Analog signals suffer from distortion and noise, even if they are small. Although

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## A Unit Impulse in Continuous-Time

This post treats the signals in continuous time which is different than the approach I adopted in my book which deals exclusively in discrete time. A unit impulse is defined as \begin{equation*} \delta (t) = \displaystyle{\lim_{\Delta \to 0}} \begin{cases} \frac{1}{\Delta} & -\frac{\Delta}{2} < t < +\frac{\Delta}{2} \\ 0 & \text{elsewhere} \end{cases} \end{equation*} The result is an impulse with zero width and infinite height, but a consequence of defining it in this way is that the area under the curve is unity. \begin{equation*} \text{Area under a rectangle} = \Delta \cdot \frac{1}{\Delta} = 1 \end{equation*} This is shown in Figure below. Stated

Continue reading## The Concept of Frequency

A wireless signal from one device to another travels through the use of electromagnetic waves propagated by an antenna. Electromagnetic waves have different frequencies and one can pick up a specific signal by tuning a radio Rx to a specific frequency. But what is a frequency anyway? Watch the video below for an interesting description of actual time domain samples and how to interpret their frequency domain representation. A Complex Sinusoid Consider a complex number $V$ in an $IQ$-plane. A complex number is defined as a pair of real numbers in $(x,y)$-plane similar to the vectors but with different arithmetic

Continue reading## A Simple Communication System

"The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point." Claude Shannon – A Mathematical Theory of Communication Our main purpose is to transfer digital information – which is a sequence of bits 0’s and 1’s – from one system to another through a communication channel. Let us return for a moment to the concept behind simple digital logic where logic 0 can be assigned to one voltage level while logic 1 to another. Provided the static discipline is followed, all our system electronics has to do is

Continue reading## System Characterization

In wireless communications and other applications of digital signal processing, we often want to modify a generated or acquired signal. A device or algorithm that performs some prescribed operations on an input signal to generate an output signal is called a system. In another article about transforming a signal, we saw how a signal can be scaled and time shifted, or added and multiplied with another signal. These are all examples of a system. Amplifiers in communication receivers and filters in image processing applications are some systems that we interact with in daily lives. A communication channel is also a

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