51 Sampling Theorem

1

• 5-1 Sampling Theorem
• A continuous signal can be processed by its
  discrete samples
• However, the number of samples must large
  enough, otherwise you cannot properly reconstruct
  the original signal

2

• Recall Example 3.8 (p. 212)
• Eqs. (3.80) and (3.81) are instructive for many
  issues in signal processing
• From Eq. (3.81)

3

• Recall Frequency Shifting

• Therefore

• If we can reconstruct from then we are
  done

4

• Compare the picture of with
• If there is no any overlap between successive
  cycles of then ...

5

• In fact, there is no overlap, if

• is called the Nyquist rate for f(t)
• T is called the Nyquist interval for f(t)
• Question How could we reconstruct a complete
  stuff from a partial piece of information?

6

• Recall
• (p.245)

• Example 5.1