Question

I need help with the following signals problems for parts A, B, C, and D. Thanks in advanced.

Prob. 3 The frequency response of a causal, LTI system is given as Hj (20 + ju)2000ju0000+ 2020js+) (a) Graph the straight-line approximation of the Bode plot (magnitude response only).

Answer 1

H (j w) = 1/(20 + j w) (2000 + j w) = 1/20 (1 + j w) times 2000 (1 + j w/2000) = 1/40000/(1 + j w/20) (1 + j w/2000) rightarrow Initially the bode plot will be a straight line passing through 20 log_10 (1/40000) = -92.04 d B on the magnitude ( Vertical-bar H (j w) Vertical-bar ) axis rightarrow There is a pole at w = 20 rad/sec, hence, the slope drops by - 20 d B/decade at w = 20 rad/sec rightarrow There is a pole at w = 2000 rad/sec hence, the slope further drops at w = 2000 rad/sec, by - 20 d B/decade Hence, we draw the straight line approximation of the bode plot as, The frequency response H (j w) of a system is also the transfer function of the system, given by, H (j w) = Y (j w)/X (j w) where Y (j w) = o/p response X (j w) = I/P applied