Sampling from a frequency-domain perspective: simple cosine
Oversampled
Sampling frequency
![[Graphics:../Images/index_gr_13.gif]](../Images/index_gr_13.gif)
Original waveform
![[Graphics:../Images/index_gr_14.gif]](../Images/index_gr_14.gif)
![[Graphics:../Images/index_gr_15.gif]](../Images/index_gr_15.gif)
![[Graphics:../Images/index_gr_16.gif]](../Images/index_gr_16.gif)
![[Graphics:../Images/index_gr_17.gif]](../Images/index_gr_17.gif)
Frequency spectrum (CT)
![[Graphics:../Images/index_gr_18.gif]](../Images/index_gr_18.gif)
![[Graphics:../Images/index_gr_19.gif]](../Images/index_gr_19.gif)
![[Graphics:../Images/index_gr_20.gif]](../Images/index_gr_20.gif)
![[Graphics:../Images/index_gr_21.gif]](../Images/index_gr_21.gif)
Frequency spectrum of sampled signal
![[Graphics:../Images/index_gr_22.gif]](../Images/index_gr_22.gif)
![[Graphics:../Images/index_gr_23.gif]](../Images/index_gr_23.gif)
![[Graphics:../Images/index_gr_24.gif]](../Images/index_gr_24.gif)
![[Graphics:../Images/index_gr_25.gif]](../Images/index_gr_25.gif)
![[Graphics:../Images/index_gr_26.gif]](../Images/index_gr_26.gif)
Ideal filter
![[Graphics:../Images/index_gr_27.gif]](../Images/index_gr_27.gif)
![[Graphics:../Images/index_gr_28.gif]](../Images/index_gr_28.gif)
![[Graphics:../Images/index_gr_29.gif]](../Images/index_gr_29.gif)
Sampled, filtered spectrum
![[Graphics:../Images/index_gr_30.gif]](../Images/index_gr_30.gif)
![[Graphics:../Images/index_gr_31.gif]](../Images/index_gr_31.gif)
![[Graphics:../Images/index_gr_32.gif]](../Images/index_gr_32.gif)
Ideally reconstructed signal
![[Graphics:../Images/index_gr_33.gif]](../Images/index_gr_33.gif)
![[Graphics:../Images/index_gr_34.gif]](../Images/index_gr_34.gif)
![[Graphics:../Images/index_gr_35.gif]](../Images/index_gr_35.gif)
![[Graphics:../Images/index_gr_36.gif]](../Images/index_gr_36.gif)
![[Graphics:../Images/index_gr_37.gif]](../Images/index_gr_37.gif)
![[Graphics:../Images/index_gr_38.gif]](../Images/index_gr_38.gif)
![[Graphics:../Images/index_gr_39.gif]](../Images/index_gr_39.gif)
![[Graphics:../Images/index_gr_40.gif]](../Images/index_gr_40.gif)
Undersampled
Sampling frequency
![[Graphics:../Images/index_gr_42.gif]](../Images/index_gr_42.gif)
Original waveform
![[Graphics:../Images/index_gr_43.gif]](../Images/index_gr_43.gif)
![[Graphics:../Images/index_gr_44.gif]](../Images/index_gr_44.gif)
![[Graphics:../Images/index_gr_45.gif]](../Images/index_gr_45.gif)
![[Graphics:../Images/index_gr_46.gif]](../Images/index_gr_46.gif)
Frequency spectrum (CT)
![[Graphics:../Images/index_gr_47.gif]](../Images/index_gr_47.gif)
![[Graphics:../Images/index_gr_48.gif]](../Images/index_gr_48.gif)
![[Graphics:../Images/index_gr_49.gif]](../Images/index_gr_49.gif)
![[Graphics:../Images/index_gr_50.gif]](../Images/index_gr_50.gif)
Frequency spectrum of sampled signal
![[Graphics:../Images/index_gr_51.gif]](../Images/index_gr_51.gif)
![[Graphics:../Images/index_gr_52.gif]](../Images/index_gr_52.gif)
![[Graphics:../Images/index_gr_53.gif]](../Images/index_gr_53.gif)
![[Graphics:../Images/index_gr_54.gif]](../Images/index_gr_54.gif)
![[Graphics:../Images/index_gr_55.gif]](../Images/index_gr_55.gif)
Ideal filter
![[Graphics:../Images/index_gr_56.gif]](../Images/index_gr_56.gif)
![[Graphics:../Images/index_gr_57.gif]](../Images/index_gr_57.gif)
![[Graphics:../Images/index_gr_58.gif]](../Images/index_gr_58.gif)
Sampled, filtered spectrum
![[Graphics:../Images/index_gr_59.gif]](../Images/index_gr_59.gif)
![[Graphics:../Images/index_gr_60.gif]](../Images/index_gr_60.gif)
![[Graphics:../Images/index_gr_61.gif]](../Images/index_gr_61.gif)
Ideally reconstructed signal
![[Graphics:../Images/index_gr_62.gif]](../Images/index_gr_62.gif)
![[Graphics:../Images/index_gr_63.gif]](../Images/index_gr_63.gif)
![[Graphics:../Images/index_gr_64.gif]](../Images/index_gr_64.gif)
![[Graphics:../Images/index_gr_65.gif]](../Images/index_gr_65.gif)
![[Graphics:../Images/index_gr_66.gif]](../Images/index_gr_66.gif)
![[Graphics:../Images/index_gr_67.gif]](../Images/index_gr_67.gif)
![[Graphics:../Images/index_gr_68.gif]](../Images/index_gr_68.gif)
![[Graphics:../Images/index_gr_69.gif]](../Images/index_gr_69.gif)
Converted by Mathematica
February 3, 2003