Sampling and Reconstruction of Analog Signals

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Sampling and reconstruction of analog signals • Analogy signals can be converted into discrete signals using sampling and quantization operations: analogy-to-digital conversion, or ADC • Digital signals can be converted into analog signals using a reconstruction operation: digital-to-analogy conversion, or DAC • Using Fourier analysis, we can describe the sampling operation from the frequency-domain view-point, analyze its effects and then address the reconstruction operation. • We will also assume that the number of quantization levels is sufficiently large that the effect of quantization on discrete signals is negligible.
Sampling Continuous-time Fourier transform and inverse CTFT X x a a ( jΩ) = ( t) = 1 2π ∫ ∫ +∞ −∞ +∞ −∞ x a X ( t) e a − jΩt ( jΩ) e dt jΩt dΩ 1. Absolutely integrable 2. Omega is an analogy frequency in radians/sec
Page 1: Sampling and Reconstruction of Anal
Page 5 and 6: The analog and digital frequencies
Page 7 and 8: X ( e ⎡ ⎢ ⎣ jω 1 + ∞ ω 2
Page 9 and 10: Sampling Principle • A band-limit
Page 11 and 12: Example 1 • Let x a (t)=e -1000|t
Page 13 and 14: Example 2a • Sample x a (t) in ex
Page 15 and 16: Reconstruction Impulse train conver
Page 17 and 18: Practical D/A converters • Zero-o
Page 19 and 20: Cubic-order-hold (COH) interpolatio
Page 21 and 22: Example 3 • From the sample x(n)
Page 23 and 24: Example 5a • Reconstruct signal f
Page 25 and 26: Example 6a • Reconstruct the samp

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