Sine Waves

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Sine Waves
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Notation

• s0 sn sN or s(0), s(n), s(N),
• d (n) 1, n 0
• 0, otherwise
• u (n) 1, n gt 0
• 0, n lt 0
• x (n) an

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Sine Wave Generation

• Point P moves at f Hz (cycles/s) ? duration of
  1cycle T 1/ f
• s(n) r sin(?(n)) , n refers to the nth sample
  time
• We have

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Sine Wave Generation in MATLAB

• function sig makesine (f, fs, timelen)
• t 0(1/fs)timelen-(1/fs)
• sig sin(2pift)
• plot (t, sig)
• grid

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Sampling when
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Phase

• p/2 rad (90) phase shift in sampling

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Aliasing

• What happens as we decrease the sampling rate?

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Conclusion

• We cannot recover signal components gtFs/2
• Nyquist Theorem
• If analog signal has frequency components gtFs/2,
  they will cause distortion by appearing as
  aliases
• Must use anti-aliasing filter before sampling