Repeat Prob XXXXXXXXXXfor the digital integrator in Prob. 5.1-2. Prob. 5.4-2 the digital integrator in Prob. 5.1-1. (a) Realize the system using gain, delay, and summing blocks. Apply δ[n] at the...

Prob. 5.4-2

the digital integrator in Prob. 5.1-1.

(a) Realize the system using gain, delay, and summing blocks. Apply δ[n] at the input of the realization, and find the resulting impulse response h[n] by inspection.

(b) Determine the unit impulse response h[n] by using the methods of Sec. 5.4.

Prob. 5.1-2

A digital integrator that uses a trapezoidal approximation is characterized by the difference equation

where T is the sampling interval. Assuming zero initial condition y[−1] = 0, solve this equation iteratively when the input x[n] is

(a) δ[n]

(b) u[n]

Comment on the performance of this system as an integrator.