## Power Systems and Evolutionary Algorithms - Sinusoidal Function

### Musical Analysis and Synthesis in Matlab

To complete this example, imagine a pulse train existing in an electronic circuit,with a frequency of 1 kHz, an amplitude of one volt, and a duty cycle of 0.2. The table in Fig. 13-12 provides the amplitude of each harmonic contained inthis waveform. Figure 13-12 also shows the synthesis of the waveform usingonly the of these harmonics. Even with this number of harmonics,the reconstruction is not very good. In mathematical jargon, the Fourier series very . This is just another way of saying that sharp edges in thetime domain waveform results in very high frequencies in the spectrum. Lastly,be sure and notice the overshoot at the sharp edges, i.e., the Gibbs effectdiscussed in Chapter 11.

### Lab 5 - Synthesis of Sinusoidal Signals

This second edition of Circuits and Networks: Analysis, Design, and Synthesis serves as a textbook for the undergraduate students of electrical, electronics, and instrumentation engineering. The new approach using MATLAB-based problem solving enhances the book’s utility among professionals and practitioners as well as for laboratory-based learning.The new edition is succinct in its method of explanation and provides increased number of solved examples for better understanding of concepts. It introduces new topics such as Bode plots, four-wire systems, and composite filters in a very lucid manner that enhances the overall coverage of the book. The vast number of numerical problems, neat circuit diagrams, and applications of various tools and techniques continue to be the best pedagogical features of this book. This book is an invaluable comprehensive resource for students, faculty, and professionals.

The basis set for the Fourier transform is the smooth sinusoidalfunction, which is optimized for expressing smooth rounded shapes. Butthe Fourier transform can actually represent any shape, even harshrectilinear shapes with sharp boundaries, which are the most difficultto express in the Fourier code, because they need so many higher orderterms, or higher harmonics. How these "square wave" functions areexpressed as smooth sinusoids will be demonstrated by example.