文档介绍：4 The continuous time Fourier transform
Representation of Aperiodic signals:
The Continuous time Fourier Transform
Development of the Fourier transform
representation of the continuous time Fourier
transform
4. The Continuous time Fourier Transform
4 The continuous time Fourier transform
(1) Example
( From Fourier series to Fourier transform )
4 The continuous time Fourier transform
(2) Fourier transform representation of Aperiodic
signal
For periodic signal :
For aperiodic signal x(t) :
4 The continuous time Fourier transform
T
4 The continuous time Fourier transform
When T,
So
4 The continuous time Fourier transform
Fourier transform:
Relation between Fourier series and
Fourier transform:
or
4 The continuous time Fourier transform
4 The continuous time Fourier transform
Convergence of Fourier transform
Dirichlet conditions:
(1) x(t) is absolutely integrable.
(2) x(t) have a finite number of maxima and minima
within any finite interval.
(3) x(t) have a finite number of discontinuity within
any finite interval. Furthermore, each of these
discontinuities must be finite.
4 The continuous time Fourier transform
Examples of Continuous time Fourier Transform
Example
Example (1)
Example (2)
4 The continuous time Fourier transform
The Fourier Transform for Periodic Signal
Periodic signal:
thus
Example