1. ## algebra of functions

Consider the function y(t) = x(t)*x(t-1). I am trying to prove that this function is linear. I was trying to use the relationship (fg)(x) = f(x) * g(x), but I can't figure out how to go backwards with y(t), to get (fg)(x). I'm not even sure you can since you have a "t" in one function and a "t-1" in the other function. As an FYI, to prove linearity you have to show that x1(t)x1(t-1) + x2(t)x2(t-1) = y1(t) + y2(t). Please be specific with your answer; it would help a lot.

thanks

2. Originally Posted by afried01
Consider the function y(t) = x(t)*x(t-1). I am trying to prove that this function is linear. I was trying to use the relationship (fg)(x) = f(x) * g(x), but I can't figure out how to go backwards with y(t), to get (fg)(x). I'm not even sure you can since you have a "t" in one function and a "t-1" in the other function. As an FYI, to prove linearity you have to show that x1(t)x1(t-1) + x2(t)x2(t-1) = y1(t) + y2(t). Please be specific with your answer; it would help a lot.

thanks

function is linear if shifted input produce shifted output

This is a bit beyond me. Can you use basic function relationships to prove this, i.e., something within pre-calculus math? Or at least explain that relationship above in more detail.

thanks