Continuous-time Fourier Transform
description
Transcript of Continuous-time Fourier Transform
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Continuous-time Fourier Transform
Prof. Siripong Potisuk
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Derivation of CTFT
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obtain we),(~ ofexpansion FS theinto ngSubstituti txak
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CT Fourier Transform Pair
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Conditions for Existence
Applicable for aperiodic signal of finite and infinite duration which satisfies:
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)( of ansformFourier tr inverse theNote t
Examples
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Example: Real Exponential Function
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Example: Square Pulse
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Example: Gaussian-shaped Signal
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Example: Gaussian-shaped Signal (cont’d)
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Example of ICTFT: An Ideal Lowpass Filter
Impulse Response Frequency Response
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CTFT of Periodic Signals
Recall the following CTFT pair:
Represent periodic signal x(t) in terms of FS
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Example: Sinusoidal Signal
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where
Example: A Pulse Train (Sampling Function)