A first-order hold (FOH) circuit can also be used to reconstruct a signal x(t) from its samples. The impulse response of this circuit is  where T is the sampling interval. (a) Using an impulse-sampled...

A first-order hold (FOH) circuit can also be used to reconstruct a signal x(t) from its samples. The impulse response of this circuit is
 where T is the sampling interval.

(a) Using an impulse-sampled signal x(t), show that the FOH circuit performs linear interpolation. In other words, the filter output consists of samples connected by straight-line segments.

(b) Determine the frequency and magnitude responses of the FOH filter. Compare these responses with both the ideal and ZOH reconstruction filters.

(c) This filter, being noncausal, is unrealizable. By delaying its impulse response, the filter can be made realizable. What is the minimum delay required to make it realizable? How does this delay affect the reconstructed signal and the filter frequency response?

(d) Show that the causal FOH circuit in part (c) can be realized by a cascade of two ZOH circuits, where each ZOH is constructed as shown in Fig. P3.2-3.