Gibbs Phenomenon

Generating Basic signals – Rectangular Pulse and Power Spectral Density using FFT

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Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT).  Often we are confronted with the need to generate simple, standard signals (sine, cosine, Gaussian pulse, square wave, isolated rectangular pulse, exponential decay, chirp signal) for simulation purpose. I intend to show (in a series of articles) … Read more

Generating Basic signals – Square Wave and Power Spectral Density using FFT

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Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT).  Often we are confronted with the need to generate simple, standard signals (sine, cosine, Gaussian pulse, squarewave, isolated rectangular pulse, exponential decay, chirp signal) for simulation purpose. I intend to show (in a series of articles) how … Read more

Understanding Gibbs Phenomenon in signal processing

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Introduction Gibbs phenomenon is a phenomenon that occurs in signal processing and Fourier analysis when approximating a discontinuous function using a series of Fourier coefficients. Specifically, it is the observation that the overshoots near the discontinuities of the approximated function do not decrease with increasing numbers of Fourier coefficients used in the approximation. In other … Read more