Undersampling and the DTFT: Example #2
Sampling frequency
![[Graphics:../Images/index_gr_119.gif]](../Images/index_gr_119.gif)
Continuous-time signal
![[Graphics:../Images/index_gr_120.gif]](../Images/index_gr_120.gif)
![[Graphics:../Images/index_gr_121.gif]](../Images/index_gr_121.gif)
CTFT of infinite-length x(t)
![[Graphics:../Images/index_gr_122.gif]](../Images/index_gr_122.gif)
![[Graphics:../Images/index_gr_123.gif]](../Images/index_gr_123.gif)
![[Graphics:../Images/index_gr_124.gif]](../Images/index_gr_124.gif)
![[Graphics:../Images/index_gr_125.gif]](../Images/index_gr_125.gif)
CTFT of finite-length x(t)
![[Graphics:../Images/index_gr_126.gif]](../Images/index_gr_126.gif)
![[Graphics:../Images/index_gr_127.gif]](../Images/index_gr_127.gif)
![[Graphics:../Images/index_gr_128.gif]](../Images/index_gr_128.gif)
![[Graphics:../Images/index_gr_129.gif]](../Images/index_gr_129.gif)
Sampled waveform (finite-length)
![[Graphics:../Images/index_gr_130.gif]](../Images/index_gr_130.gif)
![[Graphics:../Images/index_gr_131.gif]](../Images/index_gr_131.gif)
CTFT of infinite-length sampled signal
![[Graphics:../Images/index_gr_132.gif]](../Images/index_gr_132.gif)
![[Graphics:../Images/index_gr_133.gif]](../Images/index_gr_133.gif)
![[Graphics:../Images/index_gr_134.gif]](../Images/index_gr_134.gif)
![[Graphics:../Images/index_gr_135.gif]](../Images/index_gr_135.gif)
![[Graphics:../Images/index_gr_136.gif]](../Images/index_gr_136.gif)
DTFT of finite-length sampled signal
![[Graphics:../Images/index_gr_137.gif]](../Images/index_gr_137.gif)
![[Graphics:../Images/index_gr_138.gif]](../Images/index_gr_138.gif)
![[Graphics:../Images/index_gr_139.gif]](../Images/index_gr_139.gif)
Show all
![[Graphics:../Images/index_gr_140.gif]](../Images/index_gr_140.gif)
![[Graphics:../Images/index_gr_141.gif]](../Images/index_gr_141.gif)
Converted by Mathematica
March 25, 2003