Digital filters with a Fibonacci-based impulse response

The impulse response h(n<inf>1</inf>, n<inf>2</inf>) of the all-pole two-dimensional recursive digital filter whose transfer function is H(z, z) = 1/ 1 - a<inf>10</inf>z<inf>1</inf>^-1-a<inf>01</inf>z<inf>2</inf>^-1-a<inf>20</inf>z<inf>1</inf>^-1is shown to be determined everywhere by the response h(n<inf>1</inf>, 0) along the z<inf>1</inf>-axis. When a<inf>10</inf>= 1 = a<inf>20</inf>, h(n<inf>1</inf>, 0) is the n<inf>1</inf>th number in the Fibonacci sequence 1, 1, 2, 3, ..., f<inf>k</inf>= f<inf>k-1</inf>+ f<inf>k-2</inf>,.... This particular example suggests a class of all-pole digital filters which similarly have a Fibonacci-based impulse response characteristic.