While learning sampling theory - I noticed that examples of continuous signal sampling always achieved the goal via multiplying the signal with a "Dirac Comb". I was intrigued by the requirement to use a Dirac Comb instead of a "Ones Comb" - I.E: multiply the signal by the value '1' at the sampling times.
The explanation I got: "That's necessary because multiplying by a Dirac function is equivalent to Convolution in the frequency domain which maintains the spectrum of the original sampled signal".
This made a lot of sense to me...But than, when I proceeded to learn about discrete domain sampling - I was surprised to find out that examples used a "Ones Comb" to sample a signal (not the "Dirac Comb").
Why the difference ? How does discrete time sampling get away with multiplying by a train of discrete ones ?