Sampling from a frequency-domain perspective: simple cosine

Oversampled [Graphics:../Images/index_gr_12.gif]

Sampling frequency
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Original waveform
[Graphics:../Images/index_gr_14.gif]
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Frequency spectrum (CT)
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Frequency spectrum of sampled signal
[Graphics:../Images/index_gr_22.gif]
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Ideal filter
[Graphics:../Images/index_gr_27.gif]
[Graphics:../Images/index_gr_28.gif]

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Sampled, filtered spectrum
[Graphics:../Images/index_gr_30.gif]
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[Graphics:../Images/index_gr_32.gif]

Ideally reconstructed signal
[Graphics:../Images/index_gr_33.gif]
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Undersampled [Graphics:../Images/index_gr_41.gif]

Sampling frequency
[Graphics:../Images/index_gr_42.gif]
Original waveform
[Graphics:../Images/index_gr_43.gif]
[Graphics:../Images/index_gr_44.gif]
[Graphics:../Images/index_gr_45.gif]

[Graphics:../Images/index_gr_46.gif]

Frequency spectrum (CT)
[Graphics:../Images/index_gr_47.gif]
[Graphics:../Images/index_gr_48.gif]
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Frequency spectrum of sampled signal
[Graphics:../Images/index_gr_51.gif]
[Graphics:../Images/index_gr_52.gif]

[Graphics:../Images/index_gr_53.gif]

[Graphics:../Images/index_gr_54.gif]

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Ideal filter
[Graphics:../Images/index_gr_56.gif]
[Graphics:../Images/index_gr_57.gif]

[Graphics:../Images/index_gr_58.gif]

Sampled, filtered spectrum
[Graphics:../Images/index_gr_59.gif]
[Graphics:../Images/index_gr_60.gif]

[Graphics:../Images/index_gr_61.gif]

Ideally reconstructed signal
[Graphics:../Images/index_gr_62.gif]
[Graphics:../Images/index_gr_63.gif]
[Graphics:../Images/index_gr_64.gif]

[Graphics:../Images/index_gr_65.gif]

[Graphics:../Images/index_gr_66.gif]

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[Graphics:../Images/index_gr_68.gif]

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Converted by Mathematica      February 3, 2003