0.4 Lab 4 - sampling and reconstruction  (Page 5/7)

To start the second experiment, double click on the icon named Sampling and Reconstruction Using A Sample and Hold . [link] shows the initial setup for this exercise. It contains 4 Scopes to monitor the processing done in the sampling and reconstruction system. It also contains a Network Analyzer for measuring the frequency response and the impulse response of the system.

The Network Analyzer works by generating a weighted chirp signal (shown on Scope 1 ) as an input to the system-under-test. The frequency spectrumof this chirp signal is known. The analyzer then measures the frequency content of theoutput signal (shown on Scope 4 ). The transfer function is formed by computing the ratio of the outputfrequency spectrum to the input spectrum. The inverse Fourier transform of this ratio, whichis the impulse response of the system, is then computed.

In the initial setup, the Sample-and-Hold and Scope 3 are not connected. There is no sampling in this system, just two cascaded low-pass filters.Run the simulation and observe the signals on the Scopes . Wait for the simulation to end.

Double-click the Sample-and-Hold and set its Sample time to 1. Now, insert the Sample-and-Hold in between the two filters and connect Scope 3 to its output. Run the simulation and observethe signals on the Scopes .

Discrete-time interpolation

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In the previous experiments, we saw that the frequency content of a signal must be limited to half the sampling rate in orderto avoid aliasing effects in the reconstructed signal. However, reconstruction can be difficultif the sampling rate is chosen to be just above the Nyquist frequency. Reconstruction is much easier for a higher samplingrate because the sampled signal will better “track” the original analog signal.

From another perspective, the analog output filter must have a very sharp cutoff in order to accurately reconstructa signal that was sampled just above the Nyquist rate. Such filters are difficult and expensive to manufacture.Alternatively, a higher sampling rate allows the use analog output filters that have a slow roll-off.These filters are much less expensive. However, a high sampling rate is not practical in most applications, asit results in unnecessary samples and excessive storage requirements.

A practical solution to this dilemma is to interpolate the digital signal to create new (artificial) samples between the existing samples.This may be done by first upsampling the digital representation, and then filtering out unwanted components using a discrete-time filter.This discrete-time filter serves the same purpose as an analog filter with a sharp cutoff, but it is generally simplerand more cost effective to implement.