Inter-symbol interference & pulse shaping

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Key focus: Inter-symbol interference: symbols sent through a dispersive channel, arrive at different time intervals and interfere due to non-constant group delay. Introduction Communication systems have progressed from analog to digital implementation due to the latter’s advantages of bandwidth efficiency and exceptional immunity to noise. The greatest challenge to a communication systems engineer lies in … Read more

Maximum-length sequence (m-sequence) generator

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Key focus: Model and simulate m-sequence generator using Galois linear feedback shift registers (LFSR) that implement linear recursion. Plot correlation properties. Maximum-length sequences (also called as m-sequences or pseudo random (PN) sequences) are constructed based on Galois field theory which is an extensive topic in itself. A detailed treatment on the subject of Galois field theory … Read more

Differentially encoded BPSK: coherent detection

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In coherent detection, the receiver derives its demodulation frequency and phase references using a carrier synchronization loop. Such synchronization circuits may introduce phase ambiguity in the detected phase, which could lead to erroneous decisions in the demodulated bits. For example, Costas loop exhibits phase ambiguity of integral multiples of radians at the lock-in points. As … Read more

Complex Baseband Equivalent Models

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Key focus: Complex Baseband Equivalent Models are behavioral models that simplify the simulation, saves computation memory requirements and run time. This article is part of the book Digital Modulations using Matlab : Build Simulation Models from Scratch Introduction The passband model and equivalent baseband model are fundamental models for simulating a communication system. In the … Read more

Passband Simulation Models – Introduction

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For a given modulation technique, there are two ways to implement the simulation model: passband model and equivalent baseband model. The passband model is also called waveform level simulation model. The waveform level simulation techniques, described in this chapter, are used to represent the physical interactions of the transmitted signal with the channel. In the waveform … Read more

Phase demodulation via Hilbert transform: Hands-on

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Key focus: Demodulation of phase modulated signal by extracting instantaneous phase can be done using Hilbert transform. Hands-on demo in Python & Matlab. Phase modulated signal: The concept of instantaneous amplitude/phase/frequency are fundamental to information communication and appears in many signal processing application. We know that a monochromatic signal of form x(t) = a cos(ω … Read more

Extract envelope, phase using Hilbert transform: Demo

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Key focus: Learn how to use Hilbert transform to extract envelope, instantaneous phase and frequency from a modulated signal. Hands-on demo using Python & Matlab. If you would like to brush-up the basics on analytic signal and how it related to Hilbert transform, you may visit article: Understanding Analytic Signal and Hilbert Transform Introduction The … Read more

Understanding Analytic Signal and Hilbert Transform

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Key focus of this article: Understand the relationship between analytic signal, Hilbert transform and FFT. Hands-on demonstration using Python and Matlab. Introduction Fourier Transform of a real-valued signal is complex-symmetric. It implies that the content at negative frequencies are redundant with respect to the positive frequencies. In their works, Gabor [1] and Ville [2], aimed … Read more

Choosing FIR or IIR ? Understand design perspective

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“What is the best filter that I should use? FIR or IIR ?” is often the question asked by many. There exists two different types of Linear Time Invariant (LTI) filters from transfer function standpoint : FIR (Finite Impulse Response) and IIR (Infinite Impulse Response) filters and myriad design techniques for designing them.  The mere fact … Read more