SPFirst-L09

SPFirst-L09 - Signal Processing First READING ASSIGNMENTS...

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8/22/2003 1 Signal Processing First Lecture 9 D-to-A Conversion 8/22/2003 3 READING ASSIGNMENTS ± This Lecture: ± Chapter 4: Sections 4-4, 4-5 ± Other Reading: ± Recitation: Section 4-3 (Strobe Demo) ± Next Lecture: Chapter 5 (beginning) 8/22/2003 4 LECTURE OBJECTIVES ± FOLDING: a type of ALIASING ± DIGITAL-to-ANALOG CONVERSION is ± Reconstruction from samples ± SAMPLING THEOREM applies ± Smooth Interpolation ± Mathematical Model of D-to-A ± SUM of SHIFTED PULSES ± Linear Interpolation example 8/22/2003 5 ± A-to-D ± Convert x(t) to numbers stored in memory ± D-to-A ± Convert y[n] back to a “continuous-time” signal, y(t) ± y[n] is called a “ discrete-time ” signal SIGNAL TYPES COMPUTER D-to-A A-to-D x(t) y(t) y[n] x[n]
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8/22/2003 6 SAMPLING x(t) ± UNIFORM SAMPLING at t = nT s ± IDEAL: x[n] = x(nT s ) C-to-D x(t) x[n] 8/22/2003 7 NYQUIST RATE ± “Nyquist Rate” Sampling ± f s > TWICE the HIGHEST Frequency in x(t) ± “Sampling above the Nyquist rate” ± BANDLIMITED SIGNALS ± DEF: x(t) has a HIGHEST FREQUENCY COMPONENT in its SPECTRUM ± NON-BANDLIMITED EXAMPLE ± TRIANGLE WAVE is NOT BANDLIMITED 8/22/2003 8 SPECTRUM for x[n] ± INCLUDE ALL SPECTRUM LINES ± ALIASES ± ADD INTEGER MULTIPLES of 2 π and - 2 π ±
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SPFirst-L09 - Signal Processing First READING ASSIGNMENTS...

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