I am reading a textbook "Efficient Algorithms for Discrete Wavelet Transform". In that textbook (page 22), the authors are talking about filter banks for the discrete wavelet transform. Specifically, they mention that the impulse response is orthogonal to its even shifts.
Put in mathematical symbols, the authors say that if we have a discrete-time filter, g(n), with finite impulse response, then we have this property
My question is: what does this property mean? Why is it important?
And, most importantly, how did they derive this property?
I am trying to learn wavelets on my own, so I appreciate your help. Thanks