I know that the frequency response of a filter is described by equation:
H(w) = 1-1.176*e^(-jw) + e^(-j2w) , where w is the angular frequency.
Then in time domain I have a filter that is described by difference equation:
y(k) = x(k)-1.176*x(k-1)+x(k-2)
Now I'm asked to explain the connection between these equations and why the coefficients for the both equations are the same
[1 -1.176 1]?
I've been reading books and trying to find information around the internet but without any solutions for this. Could someone explain me the connection of these equations? Why are the coefficients same?
I have an idea that these two equations might represent the same filter but in different domains (time and frequency). Does convolution have something to do with this?