ECE 438 Lecture 29 January 2016  

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Continuous-Time Fourer Transform (CTFT)

   

   

ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

10 CTFT and LTI Systems – Two Equivalent Representations  

   

where

x(t)↔CTFT

X( f )

h(t)↔CTFT

H ( f )

y(t)↔CTFT

Y ( f )

 

ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

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ECE 438 Lecture 29 January 2016  

15 CTFT of Periodic Signals and CTFT of Sampled Signals  

Definitions:

repT x(t)[ ] = x(t − kT )k=−∞

∞

∑

combT x(t)[ ] = x(kT )k=−∞

∞

∑ δ (t − kT )

Transform Pairs:

repT x(t)[ ] ↔CTFT 1

Tcomb 1

T

X( f )[ ]

combT x(t)[ ] ↔CTFT 1

Trep 1

T

X( f )[ ]  

 

The second relation follows from application of reciprocity to the first relation.      

ECE 438 Lecture 29 January 2016  

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