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Unformatted text preview: 1 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #21 CT to DT Conversion: Sampling of CT signals Reading Assignment: Section 5.4 of Kamen and Heck We study this now for two reasons: The analysis uses CT FrequencyDomain System Analysis Methods Next we will study Fourier Transform ideas for DT signals and this gives a good transition 2 Ch. 1 Intro CT Signal Model Functions on Real Line DT Signal Model Functions on Integers System Properties LTI Causal Etc Ch. 2 Diff Eqs CT System Model Differential Equations DT Signal Model Difference Equations ZeroState Response ZeroInput Response Characteristic Eq. Ch. 2 Convolution CT System Model Convolution Integral DT System Model Convolution Sum Ch. 3: CT Fourier Signal Models Fourier Series Periodic Signals Fourier Transform (CTFT) NonPeriodic Signals New System Model New Signal Models Ch. 5: CT Fourier System Models Frequency Response Based on Fourier Transform New System Model Ch. 4: DT Fourier Signal Models DTFT (for Hand Analysis) DFT & FFT (for Computer Analysis) New Signal Model Powerful Analysis Tool Ch. 6 & 8: Laplace Models for CT Signals & Systems Transfer Function New System Model Ch. 7: Z Trans. Models for DT Signals & Systems Transfer Function New System Model Ch. 5: DT Fourier System Models Freq. Response for DT Based on DTFT New System Model Course Flow Diagram The arrows here show conceptual flow between ideas. Note the parallel structure between the pink blocks (CT Freq. Analysis) and the blue blocks (DT Freq. Analysis). 3 5.4 Sampling The Connection Between: Continuous Time & Discrete Time Warning: I dont really like how the book covers this! It is not that it is wrong it just fails to make the correct connection between the mathematics and physical reality!!!! Follow these notes and youll get it!!! 4 Sampled & Digitized music on a Compact Disc What ensures that we can perfectly reconstruct the music signal from its samples???!!!! 0.2 0.4 0.6 0. 8 1 2 1 1 2 Time Signal Value 1 1 2 Signal Value Amp Code Burn bits into CD Record Creates a sequence of samples (i.e., a sequence of numbers) Play Laser Sensor Decode Reconstruct Amp Microphone Speaker = Original? Time Sample & Digitize Sampling is Key Part of CD Scheme 5 Systems that use Digital Signal Proc. (DSP) generally get a continuoustime signal from a sensor a cont.time system modifies the signal an analogtodigital converter (ADC) samples the signal to create a discretetime signal A discretetime system to do the Digital Signal Processing and then (if desired) convert back to analog using a digital toanalog converter (DAC) Analog Electronics ADC DSP Computer Sampling is Key Part of Many Systems CT Signal CT System DT System CT Signal DT Signal DT Signal DAC CT Signal 6...
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This note was uploaded on 01/10/2010 for the course CDFS 21000 taught by Professor Alisone.baroody during the Summer '09 term at Vincennes.
 Summer '09
 AlisonE.Baroody

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