The band-limited continuous signal x(t) is sampled with impulse train p(t) with sampling period of T seconds. The output of the sampling circuitry is converted to sequence and is passed through a discrete time system with input of yin[n] and output of yout[n]. The discrete-time system is a single sample delay circuitry. The output of the delay circuitry yout[n] is then converted to a continuous impulse train yp(t) and passed through a zero-order hold circuitry. The output of this hold circuitry is called y0(t).
Draw the block diagram of the system
Write down time domain equations expressing the relation between input and output of each of the blocks.
Write down frequency domain equations expressing the relation between input and output of each of the blocks.
Draw frequency domain representations at the output of each block.
Design a reconstruction filter such that the output of the system is the delayed version of the input by T seconds, y(t) = x(t - T).