2.6 Noncausal Finite Impulse Response Filters In this exercise, you will learn how to implement a class of noncausal LTI systems whose impulse responses have a finite number of nonzero samples. MATLAB assumes all signals start with index one, but by defining a separate vector of time indices for each signal as shown in Tutorial 1.1, you can implement noncausal systems. The inputs and outputs of these LTI systems are related by the difference equation Basic Problems y[n] = b[m]x[n-m]. m=N₁ (2.16) (a). Find the impulse response of the LTI system whose input and output satisfy Eq. (2.16). What can you say about the value of N₁ if the system is not causal? (b). Suppose an LTI system whose impulse response h[n] is only nonzero in the range N₁ ≤ n ≤ N₂ is convolved with a finite-length signal r[n] which is only nonzero on the interval N n N4. The output of the system y[n] = x[n]+h[n] will also be finite-length, with its nonzero samples in the range N, n Ne. Find expressions for Ns and Ne in terms of N₁ through N.