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