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SIGNAL AND SYSTEM CT Fourier Transform

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Fourier’s Derivation of the CT Fourier Transform x(t) -an aperiodic signal -view it as the limit of a periodic signal as T→ ∞ For a periodic signal, the harmonic components are spaced ω0= 2π/T apart... As T→ ∞, ω0→0, and harmonic components are spaced closer and closer in frequency ⇓ Fourier series Fourier integral

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Motivating Example: Square wave

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Derivation

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Derivation(continued)

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For what kind of signals we do this

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Example

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CT Fourier Transforms of Periodic Signals

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Example

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Properties

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Properties(continued)

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5.Differentiation and Integration 6.Duality

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Properties(continued) 7.Parseval’s Relation 8.Multiplication Property 9.Convolution Property

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LTI System characterized by Differential Equations (Some slides are referred from MIT )

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