17 x n SYS 1 SYS 2 y n The impulse response of SYS 1 is h 1 n \u03b4 n 0 5 \u03b4 n 1 5 \u03b4

# 17 x n sys 1 sys 2 y n the impulse response of sys 1

This preview shows page 17 - 21 out of 150 pages.

17  is described by the difference equation y ( n ) - 1 3 y ( n - 1) = x ( n ) - 2 x ( n - 1) . What is the impulse response of the stable inverse of this system? 1.6 Difference Equations 1.6.1 A causal discrete-time system is described by the difference equation, y ( n ) = x ( n ) + 3 x ( n - 1) + 2 x ( n - 4) (a) What is the transfer function of the system? (b) Sketch the impulse response of the system. 1.6.2 Given the impulse response . . . 1.6.3 A causal discrete-time LTI system is implemented using the difference equation y ( n ) = x ( n ) + x ( n - 1) + 0 . 5 y ( n - 1) where x is the input signal, and y the output signal. Find and sketch the impulse response of the system. 1.6.4 Given the impulse response . . . 19 1.6.5 Given two discrete-time LTI systems described by the difference equations T 1 : y ( n ) + 1 3 y ( n - 1) = x ( n ) + 2 x ( n - 1) T 2 : y ( n ) + 1 3 y ( n - 1) = x ( n ) - 2 x ( n - 1) let T be the cascade of T 1 and T 2 in series. What is the difference equation describing T ? Suppose T 1 and T 2 are causal systems. Is T causal? Is T stable? 1.6.6 Consider the parallel combination of two causal discrete-time LTI systems. - SYS 1 - SYS 2 x ( n ) ? 6 l + - r ( n ) You are told that System 1 is described by the difference equation y ( n ) - 0 . 1 y ( n - 1) = x ( n ) + x ( n - 2) and that System 2 is described by the difference equation y ( n ) - 0 . 1 y ( n - 1) = x ( n ) + x ( n - 1) . Find the difference equation of the total system.  #### You've reached the end of your free preview.

Want to read all 150 pages?

• • • 