6.01 Lecture Notes - Lecture 18: Block Diagram, Geometric Progression, The Sequence
4 Apr 2023
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188 studying the unit-sample response of systems, and then generalize to more general input signals; similarly, we will begin by studying simple systems and generalize to more complex ones. Systems with feedback have a surprisingly di erent character. Finite inputs can result in persistent response; that is, in output signals with in nitely many non-zero samples. Furthermore, the quali- tative long-term behavior of this output is generally independent of the particular input given to the system, for any nite input. In this section, we will consider the class of rst-order systems, in which the denominator of the system function is a rst-order polynomial (that is, it only involves. R, but not r2 or other higher powers of r. ) R for which we can write an operator equation. Y = x + p0ry (1 p0r)y = x. 1 p0r and derive a system function. Recall the in nite series representation of this system function (derived in section 5. 4. 1):
). The distortion caused by multipath transmission can be partly corrected by a tapped delay line equalizer. Show that if α « 1, the distortion in the multipath system in figure (a) can be approximately corrected if the received signal is passed through the tapped delay line equalizer shown in next figure.