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Signals and Systems For Dummies by Mark Wickert, PhD

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Chapter 8

Line Spectra and Fourier Series of Periodic Continuous-Time Signals

In This Chapter

arrow Checking out the frequency domain of sinusoidal signals using line spectra

arrow Navigating the Fourier series representation of periodic signals

arrow Relating Fourier coefficients between waveform transformations

Exploring the frequency distribution of a sinusoids-based signal is a first step into frequency domain analysis. I like to think of this topic in terms of music. If you play an instrument or even enjoy listening to music, you probably know that music is made up of sounds that occur at different frequencies. The rich harmony of multiple instruments playing together is full of different tones and frequencies. If you set out to electronically synthesize the sound produced by a particular instrument, knowing the frequency distribution for each playable note makes your task easier.

Line spectra and Fourier series function in a similar way to music; they team up to offer a spectral representation of a sinusoidal signal or a sum of many sinusoids. In other words, the amplitudes and frequencies of sinusoids produce the line spectra and are harmonically related.

All signals have a frequency distribution, ...

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