Suppose an LTI system with impulse response h(t) has frequency response H(ω) shown below: What is the following equal to: ∫−∞∞ (∫−∞∞ h(τ)h(t−τ)dτ) e−jtdt None of these 6 1 2 1/π 12 0 8 3 11 4 2π
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Suppose an LTI system with impulse response has frequency response shown below:
![30 points. Determine the impulse response and frequency response of the system defined by the difference equation y[n] = ay[n−1] + x[n−1] assuming |a| < 1. Your answers will be a function of a. 3.30 points. Suppose you have an LTI system with impulse response h[n] = {1 n = −1, 0, 10 otherwise (a) Determine whether this LTI system is causal and/or stable. (b) Determine the output of this system to the input x[n] = cos(2πn/3 + π/6) for all n.](https://www.doubtrix.com/uploads/editor/4603478099LZJFvHUsCR.png)
![3.41. In Figure P3.41-1, h[n] is the impulse response of the LTI system within the inner box. The input to system h[n] is v[n], and the output is w[n]. The z-transform of h[n], H(z), exists in the following region of convergence: . 0 < rmin < |z| < rmax < ∞. (a) Can the LTI system with impulse response h[n] be BIBO stable? If so, determine inequality constraints on rmin and rmax such that it is stable. If not, briefly explain why. (b) Is the overall system (in the large box, with input x[n] and output y[n] ) LTI? If so, find its impulse response g[n]. If not, briefly explain why. (c) Can the overall system be BIBO stable? If so, determine inequality constraints relating α, rmin, and rmax such that it is stable. If not, briefly explain why. Figure P3.41-1](https://www.doubtrix.com/uploads/editor/8252444907vePtflDPFT.png)
