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This is a homework type problem, so I'll give you a few hints to help you solve it yourself (and learn something while doing so). From what is given, we can assume that the given difference equation describes a causal discrete-time system. Let $h[n]$ denote the impulse response. It must satisfy $$h[n]=h[n-1]+\frac{1}{N}\big(\delta[n]-\delta[n-N]\big),\...


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