Leo Lam © 2010-2011 Signals and Systems EE235. Leo Lam © 2010-2011 Futile Q: What did the monsterous voltage source say to the chunk of wire? A: "YOUR.

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Presentation transcript:

Leo Lam © Signals and Systems EE235

Leo Lam © Futile Q: What did the monsterous voltage source say to the chunk of wire? A: "YOUR RESISTANCE IS FUTILE!"

Leo Lam © Today’s menu Sampling/Anti-Aliasing Communications (intro)

Summary: Sampling Leo Lam © Review: –Sampling in time = replication in frequency domain –Safe sampling rate (Nyquist Rate), Shannon theorem –Aliasing –Reconstruction (via low-pass filter) More topics: –Practical issues: –Reconstruction with non-ideal filters –sampling signals that are not band-limited (infinite bandwidth) Reconstruction viewed in time domain: interpolate with sinc function

Quick Recap: Would these alias? Leo Lam © Remember, no aliasing if How about: NO ALIASING!

Would these alias? Leo Lam © Remember, no aliasing if How about: (hint: what’s the bandwidth?) Definitely ALIASING! Y has infinite bandwidth!

Would these alias? Leo Lam © Remember, no aliasing if How about: (hint: what’s the bandwidth?) Copies every ALIASED!

How to avoid aliasing? Leo Lam © We ANTI-alias. SampleReconstruct B w s > 2w c time signal x(t) X(w) Anti-aliasing filter w c < B Z(w) z(n)

How bad is anti-aliasing? Leo Lam © Not bad at all. Check: Energy in the signal (with example) Sampled at Add anti-aliasing (ideal) filter with bandwidth 7 sampler lowpass anti-aliasing filter

How bad is anti-aliasing? Leo Lam © Not bad at all. Check: Energy in the signal (with example) Energy of x(t)? sampler lowpass anti-aliasing filter

How bad is anti-aliasing? Leo Lam © Not bad at all. Check: Energy in the signal (with example) Energy of filtered x(t)? sampler lowpass anti-aliasing filter ~0.455

Bandwidth Practice Leo Lam © Find the Nyquist frequency for:

Bandwidth Practice Leo Lam © Find the Nyquist frequency for: const[rect(  /200)*rect(  /200)] =

Bandwidth Practice Leo Lam © Find the Nyquist frequency for: (bandwidth = 100) + (bandwidth = 50)