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Sampling Theorem
Oppenheim & Willsky, Ch. 7 — Sampling in Time and Frequency Domains
Signal
Single Sinusoid
Two Sinusoids
Band-limited (rect spectrum)
Signal freq f (Hz)
5
Second freq f
2
(Hz)
12
Sampling
Sampling freq f
s
(Hz)
30
Animation
▶ Sweep f
s
◀ −f
s
+f
s
▶
Display
Show Reconstruction
Show Spectral Copies
Nyquist Theorem
f
s
≥ 2f
max
Time domain:
Sampling = multiplying by impulse train with period T
s
= 1/f
s
Freq domain:
Sampling = convolving spectrum with impulse train at spacing f
s
→ periodic copies of X(f) at every k·f
s
When copies overlap →
aliasing
(irreversible distortion)