Sampling from a frequency-domain perspective: continuous frequency spectrum
Oversampled
Sampling frequency
![[Graphics:../Images/index_gr_71.gif]](../Images/index_gr_71.gif)
Frequency domain representation of signal
![[Graphics:../Images/index_gr_72.gif]](../Images/index_gr_72.gif)
![[Graphics:../Images/index_gr_73.gif]](../Images/index_gr_73.gif)
![[Graphics:../Images/index_gr_74.gif]](../Images/index_gr_74.gif)
Time-domain representation of signal
![[Graphics:../Images/index_gr_75.gif]](../Images/index_gr_75.gif)
![[Graphics:../Images/index_gr_76.gif]](../Images/index_gr_76.gif)
![[Graphics:../Images/index_gr_77.gif]](../Images/index_gr_77.gif)
![[Graphics:../Images/index_gr_78.gif]](../Images/index_gr_78.gif)
![[Graphics:../Images/index_gr_79.gif]](../Images/index_gr_79.gif)
Frequency spectrum of sampled signal
![[Graphics:../Images/index_gr_80.gif]](../Images/index_gr_80.gif)
![[Graphics:../Images/index_gr_81.gif]](../Images/index_gr_81.gif)
![[Graphics:../Images/index_gr_82.gif]](../Images/index_gr_82.gif)
![[Graphics:../Images/index_gr_83.gif]](../Images/index_gr_83.gif)
![[Graphics:../Images/index_gr_84.gif]](../Images/index_gr_84.gif)
Ideal filter
![[Graphics:../Images/index_gr_85.gif]](../Images/index_gr_85.gif)
![[Graphics:../Images/index_gr_86.gif]](../Images/index_gr_86.gif)
![[Graphics:../Images/index_gr_87.gif]](../Images/index_gr_87.gif)
Sampled, filtered spectrum
![[Graphics:../Images/index_gr_88.gif]](../Images/index_gr_88.gif)
![[Graphics:../Images/index_gr_89.gif]](../Images/index_gr_89.gif)
![[Graphics:../Images/index_gr_90.gif]](../Images/index_gr_90.gif)
Ideally reconstructed signal
![[Graphics:../Images/index_gr_91.gif]](../Images/index_gr_91.gif)
![[Graphics:../Images/index_gr_92.gif]](../Images/index_gr_92.gif)
![[Graphics:../Images/index_gr_93.gif]](../Images/index_gr_93.gif)
![[Graphics:../Images/index_gr_94.gif]](../Images/index_gr_94.gif)
![[Graphics:../Images/index_gr_95.gif]](../Images/index_gr_95.gif)
![[Graphics:../Images/index_gr_96.gif]](../Images/index_gr_96.gif)
![[Graphics:../Images/index_gr_97.gif]](../Images/index_gr_97.gif)
Undersampled
Sampling frequency
![[Graphics:../Images/index_gr_99.gif]](../Images/index_gr_99.gif)
Frequency domain representation of signal
![[Graphics:../Images/index_gr_100.gif]](../Images/index_gr_100.gif)
![[Graphics:../Images/index_gr_101.gif]](../Images/index_gr_101.gif)
![[Graphics:../Images/index_gr_102.gif]](../Images/index_gr_102.gif)
Time-domain representation of signal
![[Graphics:../Images/index_gr_103.gif]](../Images/index_gr_103.gif)
![[Graphics:../Images/index_gr_104.gif]](../Images/index_gr_104.gif)
![[Graphics:../Images/index_gr_105.gif]](../Images/index_gr_105.gif)
![[Graphics:../Images/index_gr_106.gif]](../Images/index_gr_106.gif)
![[Graphics:../Images/index_gr_107.gif]](../Images/index_gr_107.gif)
Frequency spectrum of sampled signal
![[Graphics:../Images/index_gr_108.gif]](../Images/index_gr_108.gif)
![[Graphics:../Images/index_gr_109.gif]](../Images/index_gr_109.gif)
![[Graphics:../Images/index_gr_110.gif]](../Images/index_gr_110.gif)
![[Graphics:../Images/index_gr_111.gif]](../Images/index_gr_111.gif)
![[Graphics:../Images/index_gr_112.gif]](../Images/index_gr_112.gif)
Ideal filter
![[Graphics:../Images/index_gr_113.gif]](../Images/index_gr_113.gif)
![[Graphics:../Images/index_gr_114.gif]](../Images/index_gr_114.gif)
![[Graphics:../Images/index_gr_115.gif]](../Images/index_gr_115.gif)
Sampled, filtered spectrum
![[Graphics:../Images/index_gr_116.gif]](../Images/index_gr_116.gif)
![[Graphics:../Images/index_gr_117.gif]](../Images/index_gr_117.gif)
![[Graphics:../Images/index_gr_118.gif]](../Images/index_gr_118.gif)
Ideally reconstructed signal
![[Graphics:../Images/index_gr_119.gif]](../Images/index_gr_119.gif)
![[Graphics:../Images/index_gr_120.gif]](../Images/index_gr_120.gif)
![[Graphics:../Images/index_gr_121.gif]](../Images/index_gr_121.gif)
![[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)
Converted by Mathematica
February 3, 2003