November 2010
Intermediate to advanced
288 pages
8h 34m
English
book
Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
by C. Britton Rorabaugh
Content preview from Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
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Note 10. Fourier Series
The Fourier series forms a mathematical link between periodic continuous-time signals and their discrete-frequency spectra. In many books and engineering courses, the Fourier series is often introduced merely as a stepping stone on the way to the Fourier transform. However, within DSP, the Fourier series plays an important role in the design of finite-impulse-response (FIR) digital filters, which are discussed in Note 32.
10.1. Classical Form
The “classical” presentation of the Fourier series (FS) is given in a form that emphasizes that the time signal is being represented by a weighted sum of discrete sinusoids:
10.1
where
Using a few trigonometric identities, the FS can be put in the magnitude-and-phase form given ...
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