Reconstruction of signal in Zero Order Hold Filter

The analog Signal (continuous - time signal) is multiplied with a periodic impulse train, referred to as Sampling Function. A sampled signal is then obatained as shown in figure below.

The ideally sampled signal xp(t) is the product of the impulse train p(t) and the analog signal xc(t) and may be written as

The ZOH Sampled Signal xZOH (t) can be regarded as the convolution of ho(t) and a sampled signal xp(t)