MODULE-7 - MODULE 7 DIGITAL PROCESSING OF ANALOG SIGNALS...

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Unformatted text preview: MODULE 7 DIGITAL PROCESSING OF ANALOG SIGNALS • Analog-Digital Conversion • The Sampling Theorem • Digital-Analog Conversion • Zero-Order Hold Page 7.1 INDEX Digital Processing of Analog Signals Analog-to-Digital Conversion Ideal Sampler Oversampling Critical Sampling Undersampling Anti-Aliasing Anti-Aliasing Filter Anti-Aliased Signal Anti-Aliasing Example Digital Filter Output Digital-to-Analog Conversion D/A Reconstruction Ideal Reconstruction Impulse Invariance Reconstruction by Zero-Order Hold Compensation for Zero-Order Hold Analog Compensation for Z.O.H. Digital Compensation for Z.O.H. MAIN INDEX Page 7.2 7. DIGITAL PROCESSING OF ANALOG SIGNALS index READ : Chapter 4 of Oppenheim & Schafer. Work as many related problems as possible. • In this module we shall use specific notation to distinguish between continuous-time and discrete-time signals and systems: Signals: x a ( t ) (continuous) vs. x d ( n ) (discrete) X a ( Ω ) (continuous) vs. X d ( e j ϖ ) (discrete) Systems: h a ( t ) (continuous) vs. h d ( n ) (discrete) H a ( Ω ) (continuous) vs. H d ( e j ϖ ) (discrete) • As always we will use t = continuous time Ω = continuous frequency n = discrete time ϖ = discrete frequency • Often we wish to approximate an analog linear system by a digital system . We shall study this task in this module, and as a by-product, develop the Sampling Theorem . Page 7.3 • The following block diagram depicts a discrete-time filter with a continuous-time input and a continuous-time output . H d ( e j ϖ ) digital filter A/D D/A x a ( t ) x d ( n ) y a ( t ) y d ( n ) H a ( Ω ) Two Questions: • Does the overall system H a ( Ω ) approximate a transfer function of some linear continuous system? • The system has input x a ( t ) ℑ ↔ X a ( Ω ) and output y a ( t ) ℑ ↔ Y a ( Ω ). For a specified analog transfer function H a ( Ω ), is it possible to design- analog-to-digital conversion (A/D)- digital-to-analog conversion (D/A)- digital filter H d ( e j ϖ ) so that ) ( ) ( Ω Ω a a X Y ≈ H a ( Ω ) ? Page 7.4 Analog-to-Digital Conversion index • The analog system will be well-approximated digitally only if the analog input is sufficiently well-approximated in digital form . • The following block diagram illustrates the stages of analog-to- digital (A/D) conversion . A/D x a ( t ) x d ( n ) F a ( Ω ) Anti-aliasing filter (lowpass) Q [ · ] Amplitude quantizer Ideal sampler T s • Sampling is the process of conversion from continuous-time to discrete-time. Information is generally lost (Sampling Theorem). • Anti-aliasing is a technique for reducing sampling (aliasing) errors resulting from frequency folding. • Quantization is the process of conversion from continuous- amplitude to discrete-amplitude . We will not analyze this part yet - later, it will be done in some depth....
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This note was uploaded on 05/06/2010 for the course ECE 539 taught by Professor Alanc.bovik during the Spring '04 term at University of New Brunswick.

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MODULE-7 - MODULE 7 DIGITAL PROCESSING OF ANALOG SIGNALS...

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