Continuoustime Signal Sampling

1、continuous-time signal sampling elec 309 prof. siripong potisuk why digital domain luniform representation of analog signals i.e., a sequence of 0s and 1s. loperation of digital circuits not dependent on precise values of the digital signals lrequire only bistable circuits and storage medium to proc

2、ess, store, and transmit signals lpossibility of perfect signal regeneration llow cost of digital processor hardware benefits (continued) lany desirable accuracy achievable by increasing the binary wordlength subject to cost limitation lthe same digital computer technology used for general informati

3、on processing can be used for dsp lapplicability to very low frequency signals (seismic applications) disadvantages lincreased system complexity (a/d and d/a) llimited range of frequencies available for processing because of the sampling requirement ldigital systems mostly constructed using active d

4、evices that consume electrical power ladvantages far outweigh disadvantages analog-to-digital conversion ldiscretize the independent variable or time of an analog signal (sampling) ldiscretize the dependent variable or amplitude of an analog signal by rounding off to the nearest integer (quantizatio

5、n) leach quantization level represented using binary encoding scheme (encoding) why sampling lnecessary for digital processing of analog signals, e.g., x(t) ltaking snapshots of x(t) every ts seconds leach snapshot is called a sample lts is the so-called sampling interval, i.e., the time interval be

6、tween each sample (second/sample) lprefer regularly spaced samples, though not necessary analog-to-digital conversion (a/d) mathematical description of sampling lthe sequence of samples is given by l is the sampling frequency or rate lthe unit of sampling frequency is samples/second, but often expre

7、ssed in terms of hz to match the highest frequency in hz of the analog signal s s t f 1 inntxnx s ),( sampling interval selection lby sampling, we throw out a lot of information in between samples la set of samples can represent more than one distinct signal sampling interval selection lgiven a set

8、of sampling points, under what conditions can we reconstruct the original ct signals from which those samples came? lin other words, all values of x(t) between sampling points are lost because of sampling lneed to consider the frequency contents of the ct signal being sampled fourier transform impul

9、se sampling frequency-domain analysis of sampling t fs s 2 2 ft where and using the multiplication property of ctft, thus, assuming x(t) is band-limited, i.e., frequency-domain analysis of sampling m jx , 0)( no overlap between shifted spectra! reconstruction of the ct signal from its samples if the

10、re is no overlap between shifted spectra, we can use a lowpass filter to reconstruct the original ct signal original spectrumreconstructed spectrum nyquist sampling theorem .frequencynyquist andfrequency sampling 2 where ratenyquist 2 if ),( samples itsby determineduniquely is )( then, . , 0)( such

11、that signal limited-band a be )(let m m t inntx tx jx tx s ms practical sampling aliasing effect distortion of filtered spectrum caused by aliasing common samples obtained from sampling two sinusoids of different frequencies anti-aliasing filter band-limiting operation done on the analog signal befo

12、re sampling to prevent aliasing passing it through an analog lowpass filter, e.g. butterworth, chebyshev, elliptical alternatively called guard filter remove all frequency components outside the range -fc, fc where fc fd signal reconstruction three interpolation methods band-limited interpolation zero-order hold