Signal Processing for Communication Systems
Antennas are radiation sources of finite physical dimension. To a distant observer, the radiation waves from the antenna source appears more like a spherical wave and the antenna appears to be a point source regardless of its true shape. The terms far-field and near-field are associated with such observations/antenna measurement. The terms imply that there … Read more
Key focus: Understand retarded potentials – the basic building block for understanding antenna array patterns. Retarded potentials are potentials at an observation point when the quantities at the source are non-static (varies in both space and time) The static case : potentials The fundamental premise of understanding antenna radiation is to understand how a radiation … Read more
Key focus: Briefly look at the building blocks of antenna array theory starting from the fundamental Maxwell’s equations in electromagnetism. Maxwell’s equations Maxwell’s equations are a collection of equations that describe the behavior of electromagnetic fields. The equations relate the electric fields () and magnetic fields () to their respective sources – charge density () … Read more
Key focus: Briefly look at linear antennas and various dipole antennas and plot the normalized power gain pattern in polar plot and three dimensional plot. Linear antennas Linear antennas are electrically thin antennas whose conductor diameter is very small compared to the wavelength of the radiation λ. Viewed in a spherical coordinate system (Figure 1), … Read more
Key focus: Bayes’ theorem is a method for revising the prior probability for specific event, taking into account the evidence available about the event. Introduction In statistics, the process of drawing conclusions from data subject to random variations – is called “statistical inference”. Usually, in any random experiment, the observations are recorded and conclusions have … Read more
Line code is the signaling scheme used to represent data on a communication line. There are several possible mapping schemes available for this purpose. Lets understand and demonstrate line code and PSD (power spectral density) in Matlab & Python. Line codes – requirements When transmitting binary data over long distances encoding the binary data using … Read more
Key focus: Euclidean & Hamming distances are used to measure similarity or dissimilarity between two sequences. Used in Soft & Hard decision decoding. Distance is a measure that indicates either similarity or dissimilarity between two words. Given a pair of words a=(a0,a1, … ,an-1) and b=(b0,b1,…,bn-1) , there are variety of ways one can characterize … Read more
Key focus: Window function smooths the observed signal over the edges. Analysis of some important parameters to help select the window for an application. Spectral leakage As we know, the DFT operation can be viewed as processing a signal through a set of filter banks with bandwidth Δf centered on the bin (frequency) of interest … Read more
Key focus: Equivalent noise bandwidth (ENBW), is the bandwidth of a fictitious brick-wall filter that allows same amount of noise as a window function. Learn how to calculate ENBW in applications involving window functions and FFT operation. FFT and spectral leakage As we know, the DFT operation can be viewed as processing a signal through … Read more
The Parseval’s theorem (a.k.a Plancherel theorem) expresses the energy of a signal in time-domain in terms of the average energy in its frequency components. Suppose if the x[n] is a discrete-time sequence of complex numbers of length N : xn={x0,x1,…,xN-1}, its N-point discrete Fourier transform (DFT)[1] : Xk={X0,X1,…,XN-1} is given by The inverse discrete Fourier … Read more