The DC gain of an LTI System is dened as the value of the (constant) output yea) produced by the constant input 936(t) = 1. The knee frequency of a...

Assume all systems below are real and causal. 

PROBLEM 1:

• Attachment 1
• Attachment 2
• Attachment 3

The DC gain of an LTI System is defined as the value of the (constant) output yea) produced bythe constant input 936(t) = 1. The knee frequency of a filter is the frequency at which the power(not amplitude) of the transfer function drops by one-half from the pass band. For the simple filters we consider, we can use the definitions IH (jwkneenz = é|H(U)|2 for a lowpass filter, and1IH (jwknee) '2 = lim —|H(jcu)l|2 for a highpass filter. Lil—$00 Note: you may see knee frequencies defined as where the power drops by 3 decibels (dB). DecibelsP signal. The 3 dB are “10 log 10” of signal power relative to a reference power, dB = lOlogm ( Pref rule is chosen because 10 logm (1/2) a —3.