Continuous-Time Fourer Transform (CTFT)ece438/lecture_notes/... · 2016. 2. 1. · reciprocity to...
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ECE 438 Lecture 29 January 2016
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Continuous-Time Fourer Transform (CTFT)
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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 )
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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.
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