Signal Processing for Communication Systems
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
Parseval’s theorem, also known as Plancherel’s theorem or Rayleigh’s energy theorem, is a fundamental result in Fourier analysis and signal processing. It relates the energy (or power) of a function (or signal) to the energy (or power) of its Fourier transform. In essence, it states that the total energy remains the same whether you calculate … Read more
In wireless environments, transmitted signal may be subjected to multiple scatterings before arriving at the receiver. This gives rise to random fluctuations in the received signal and this phenomenon is called fading. The scattered version of the signal is designated as non line of sight (NLOS) component. If the number of NLOS components are sufficiently … Read more
Key focus: Discuss statistical measures for stochastic signals : mean, variance, skewness, kurtosis, histogram, scatterplot, cross-correlation and auto-correlation. Deterministic and stochastic signals A deterministic signal is exactly predictable for the given time span of interest. It could be expressed using analytic form (example: x(t) = sin (2 π fc t) ). Many of the signals … Read more
Key focus: Simulate bit error rate performance of Binary Phase Shift Keying (BPSK) modulation over AWGN channel using complex baseband equivalent model in Python & Matlab. Why complex baseband equivalent model The passband model and equivalent baseband model are fundamental models for simulating a communication system. In the passband model, also called as waveform simulation … Read more
The phase transition properties of the different variants of QPSK schemes and MSK, are easily investigated using constellation diagram. Let’s demonstrate how to plot the signal space constellations, for the various modulations used in the transmitter. Typically, in practical applications, the baseband modulated waveforms are passed through a pulse shaping filter for combating the phenomenon … Read more
Articles in this series Phased Array Antenna – an introduction Electronic Scanning Arrays Grating lobes in electronic scanning Array pattern multiplication (this article) Array pattern multiplication If the element pattern of an array is very broad (as in an Omni directional antenna element) the pattern of the array is mostly the Array Factor since it … Read more
The array is a periodic structure in space with elements placed at equidistant. d/λ acts as the frequency term and λ/d as the time period. The incremental phase shift between adjacent elements is (2π/λ)×d×[sin(θ)-sin(θ0)]. d is the inter-element distance in unit of λ, θ-any position during the scanning of the array and θ0 – the … Read more