Should digital-to-analogue converter produce analogue signal?
There are really two things wrong with the block diagram and the description. 

Firstly, where are the anti aliasing and reconstruction filters, these are kind of important to reconstructing a signal that actually resembles the input. In particular that output graph is taken before the reconstruction filter which is a vital part of making a DAC actually output analogue.... 

The requirement is that the sample rate MUST be greater then twice the bandwidth present at the sampler input, and the output must be filtered to a bandwidth less then half the sample rate.

Secondly, you really need dither (canonically triangular probability distribution noise added at the input with a peak level equal to 1 quantisation step), this makes the quantiser output switch between two states such that the average value exactly matches the input. It converts a non linear system with discrete steps to a linear one with noise, do this right and you can hear signals below the broadband noise floor. 

If that lot came from a text book of some kind, it is a horrible description probably written by someone who has never actually implemented a digital voice channel (Apart from anything else, 5ks/s is really too slow, even the phone system uses 8k, for an audio bandwidth of approximately 3.5kHz).