The Company asked the Question. I stumbled but eventually answered the Question. Or so I thought. While at dinner with a friend tonight, he asked me about the Question. When I told it to him, I initially tried guiding him to the Answer, but as he moved forward, I realized something. I had forgotten to take into account an equation in my solution, which meant my solution was wrong. I worked it out and figured out the Answer a few minutes later.
Here’s the Question:
Please design a discrete time LTI filter with the following three properties:
- For any input that is periodic with period 3, the output should be constant.
- If the input x[n] = n^2 (i.e. x[n] is a parabola), then the output y[n] = n^2.
- The impulse response h[n] of the filter should be even symmetric.