# Effect of delayed feedback on sinusoid of frequency corresponding to delay

Question: What is the effect of a delayed feedback path with nonunity gain G on a sinusoid of frequency corresponding to the delay? Plot the effective gain as a function of G.

I think this will amplify successive periods of the sinusoid, with it becoming unstable and growing to infinity. Does that sound correct?

I'm a bit confused by this topic so I wanted to check my understanding. Id really appreciate any help, thanks!

• Hi moinudin! This sounds like a homework problem or quiz? We're happy to help with your learning; It may become unstable or it may converge, and I am guessing your complete understanding of that is the purpose of this exercise and to know the difference when that occurs. What course is this for? Mar 7 at 20:32
• They're questions in a book I'm studying alone, and not being part of a class when I get stuck I have nowhere else to go really. I see how it can become unstable, but not how it could converge. The delay is equal to the frequency, so won't each successive cycle be larger? Mar 7 at 21:21
• What book and what is your background? What is your motivation in studying this (trying to find the right starting point and understand where you are headed; I might recommend some further study first) Mar 7 at 21:53
• I'm reading Digital Signal Processing by Jonathan Stein. It's targeted at Computer Scientists, which is my background. My motivation for studying is to build an Android app for processing Arabic speech. Mar 7 at 22:15
• This is the problem I'm working towards trying to solve: dsp.stackexchange.com/questions/73342/… Mar 7 at 22:15