# Should digital-to-analogue converter produce analogue signal?

Here is the question. (My inquiry is at the bottom of this page about the shape of the graph.)  The ADC (analogue-to-digital converter) samples the analogue signal at a frequency of 5.0 kHz. Each sample from the ADC is a four-bit digital number where the smallest bit represents 1.0 mV. The first sample is taken at time zero.

The digital signal is transmitted and then converted to an analogue form by the DAC (digital-to-analogue converter). Using data from Fig. 12.2, draw, on the axes of Fig. 12.3, the output level of the transmitted analogue signal for time zero to time 1.2 ms.

The graph shown below is the solution.

What I'm confused is why the shape of the graph is like a digital signal, which has a squared-shape graph, yet it should be an analogue signal since DAC converting digital into the analogue signal. • Have you tried increasing the resolution of your ADC/DAC. – niki_t1 Mar 4 '17 at 11:53

The ADC (analogue-to-digital converter) samples the analogue signal at a frequency of 5.0 kHz

This is essentially the reason.

Your original signal is a continuous analog signal. Your ADC has some method of turning that signal into a discrete digital signal. We're given a sampling frequency and minimum sensitivity.

So now we have all of these bits of data that are sent to our DAC (I assume they were unchanged in the process, if not we aren't told how so it couldn't really be answered). The DAC has to convert these 0's and 1's into a an output signal that can be used. This signal is still discrete, so the DAC output is still discrete unless some sort of filter is applied.

The big thing here is you assume it has a reconstruction filter while the answer seems to suggest it is a very simple DAC that just turns it into an analog signal which is as discrete as the digital signal given.

• And the ADC is only 4 bits so can only distinguish 16levels. A 16bit ADC with 65000 output levels would look a lot more "analogue" – Martin Beckett Mar 4 '17 at 4:08
• @MartinBeckett If you assume that it's sensitive to such small changes on a reasonable timescale, absolutely. It would also give you a much more accurate reading. You can filter the digital signal to make it look more analogue even if your ADC wasn't high resolution. – JMac Mar 4 '17 at 4:33

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).

• Would it still not be considered a DAC without the filtering? It's completely impractical without any filters, but it is turning the digital signal into an analog signal. There is just no filtering to make that signal resemble a non-discrete signal. – JMac Mar 4 '17 at 15:28
• I should probably have said "Making the DAC output continuous time", rather then "analogue", you can have a discrete time analogue system, but it is naff all use for a voice band link. – Dan Mills Mar 4 '17 at 16:48
• Yeah, I do understand his confusion. This is really terrible at doing what it's supposed to with the information (and answer) given. – JMac Mar 4 '17 at 17:58