Abstract: This chapter introduces Fourier transforms. Conceptually, the Fourier series theorem is a mathematical statement of the property that any periodic signal, no matter how complicated, can be represented by a sum of sinusoids; specifically, a series of sinusoids that are the same as, or multiples of, the signal's frequency. Any periodic signal can be equivalently represented by sinusoids that are harmonically related to the base frequency of the signal. Converting a signal into its sinusoidal equivalent is known as a transformation. This transformation based on sinusoids is often referred to as the Fourier transform. The Fourier series analysis and related Fourier transform are not the only paths to a signal's frequency characteristics or spectrum, but they constitute the most general approach; they make the fewest assumptions about the signal. The notion of time- and frequency-domain signal representations and useful properties of the sinusoidal signal are also outlined in the chapter. The Fourier series analysis for symmetry is also discussed. Concepts related to frequency representation, complex representation, discrete Fourier series, and discrete Fourier transform are also elaborated.
Publication Year: 2012
Publication Date: 2012-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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