picions were correct. Zero-order sampling xs(t) Ts 2Ts 3Ts Figure 4.6 Input and output of zero-order field sampling Chapter Four Ideal sampling h(t)= x((t) xs(t) Figure 4.7 What goes on in zero-order hold sampling We want to figure out if we can get x(t) back from X's (t), because if we can, then we know that all the information in x(t) is saved in X's (t) Take a look at Figure 4.7. We can see that, to recover the original X (t) from the sampled X's (t) , we want to (1) undo the effects of the LTI system with response h (t), then (2) undo the effects of the ideal sampling (multiplication by (t)). Figure 4.8 shows us a system that can h-1(t) undo the effects of the xs(t) LTI system h (t) and fc = fs/2 then the effects of the gain = Ts ideal sampling. Here, the effects of the LTI Figure 4.8 System undoing the effects of zero-order hold sampling system with response h (t) are undone first by applying the inverse LTI system, the system with impulse response h-st(s) Then, the effects of the ideal sampling are undone by (as we saw earlier) using a low-pass filter with cutoff frequency f==f/2. Here's an important note-the ideal sampling effects can only be undone if we sample at f > 2fm So again, as long as fs > 2fm then all the effects of the sampling can be undone. Example 4.2 Determine the output (in the time domain) of a zero-order hold sampler with sampling rate 2 Hz (sampling time 0.5 s) when the input corresponds to x(t)=sin.ru (E4.8) Source Coding and Decoding: Making it Digital Solution: In the zero-order hold sampler, two things happen: first, you have your ideal sampling, which creates impulses at the sample times of 0, 0.5 S, 1 S, 1.5 S, and SO on. The output of the ideal sampler is shown in Figure E4.2(a). Then, you follow that with the "hold" circuit, the LTI system which effectively "holds" each sample for the sampling time of 0.5 S. Its output is drawn in Figure E4.2(b). x((t) sintt xs(t) Figure E4.2 (a) After sampling (b) After "holding" 4.1.3 Natural Sampling Another practical method to sample Carl's s