Transcription of Sampling and Reconstruction - Ptolemy Project
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Sampling and Reconstruction - Ptolemy Project
Chapter 11 Sampling and ReconstructionDigital hardware, including computers, take actions in discrete steps. So they can deal with discrete-time signals, but they cannot directly handle the continuous-time signals that are prevalent in thephysical world. This chapter is about the interface between these two worlds, one continuous, theother discrete. A discrete-time signal is constructed bysamplinga continuous-time signal , and acontinuous-time signal isreconstructedbyinterpolatinga discrete-time SamplingA sampler for complex-valued signals is a systemSamplerT:[Reals Complex] [Integers Complex],( )whereTis thesampling interval(it has units of seconds/sample). The system is depicted Thesampling frequencyorsample rateisfs=1/T, in units of samples/second (orsometimes, Hertz), or s=2 /T, in units radians/second. Ify=SamplerT(x)thenyis defined by n Integers,y(n) =x(nT).
The frequency domain analysis of the previous chapters relied heavily on complex exponential signals. Recall that a cosine can be given as a sum of two complex exponentials, using Euler’s relation, cos(2p. ft)=0: 5(e. i. 2p. ft + e ¡i. 2p. ft): One of the complex exponentials is at frequency. f, an the other is at frequency ¡f. Complex
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