Consider the system depicted in Figure P13.12, where S1 is an LTI system with impulse re...

Consider the system depicted in Figure P13.12, where S₁ is an LTI system with impulse response h₁[n] and S₂ is a homomorphic system with convolution as the input and output operations; i.e., the transformation T₂{·} satisfies

Suppose that the complex cepstrum of the input x[n] is = δ[n] + δ[n − 1]. Find a closed-form expression for h1[n] such that the output is y[n] = δ[n].