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

Before starting this experiment, use the MATLAB command close all to close all figures other than the Simulink windows. Double click on the icon named Sampling and Reconstruction Using An Impulse Generator to bring up the first experiment as shown in [link] . In this experiment, a sine wave is sampled at a frequencyof 1 Hz; then the sampled discrete-time signal is used to generaterectangular impulses of duration 0.3 sec and amplitude equal to the sample values.The block named Impulse Generator carries out both the sampling of the sine wave and its reconstruction with pulses. A single Scope is used to plot both the input and output of the impulse generator,and a Spectrum Analyzer is used to plot the output pulse train and its spectrum.

First, run the simulation with the frequency of input sine wave set to $0.1$ Hz (initial setting of the experiment). Let the simulation run until it terminates to getan accurate plot of the output frequencies. Then print the output of Scope and the Spectrum Analyzer . Be sure to label your plots.

Ideal impulse functions can only be approximated. In the initial setup, the pulse width is $0.3$ sec, which is less then the sampling period of 1 sec.Try setting the pulse width to $0.1$ sec and run the simulation. Print the output of the Spectrum Analyzer .

Set the pulse width back to $0.3$ sec and change the frequency of the sine wave to $0.8$ Hz. Run the simulation and print the output of the Scope and the Spectrum Analyzer .

Leave the input frequency at $0.8$ Hz. Now insert a filter right after the impulse generator.Use a 10th order Butterworth filter with acutoff frequency of $0.5$ Hz. Connect the output of the filter to the Spectrum Analyzer and the Mux . Run the simulation, and print the output of Scope and the Spectrum Analyzer .

Sampling and reconstruction with sample and hold

For help on printing figures in Simulink select the link.

In this section, we will sample a continuous-time signal using a sample-and-hold and then reconstruct it.We already know that a sample-and-hold followed by a low-pass filter does not result in perfect reconstruction.This is because a sample-and-hold acts like a pulse generator with a pulse duration of onesampling period. This “pulse shape” of the sample-and-hold is whatdistorts the frequency spectrum (see Section "Sampling and Reconstruction Using a Sample-and-Hold" ).