Another definition for the finite difference is the backward difference:

∆₁[x(nT_s)] = x(nT_s) − x((n − 1)T_s)

(∆₁[x(nT_s)]/T_s approximates the derivative of x(t)).

(a) Indicate how this new definition connects with the finite difference defined earlier in this chapter.

(b) Solve Problem 14 with MATLAB using this new finite difference and compare your results with the ones obtained there.

(c) For the value of T_s = 0.1, use the average of the two finite differences to approximate the derivative of the analog signal x(t). Compare this result with the previous ones. Provide an expression for calculating this new finite difference directly.