# Does the hold part in sample and hold turns the signal from discrete to continuous?

I am trying to link sample and hold to discrete and continuous time domain. Could someone please confirm:

When sampling but not holding for "an extended" period of time, you have discrete samples.

When sampling AND holding you lose the "discretion" and obtain an approximated continuous signal.

Is this correct?

Yes. Conceptually (or mathematically), the sample part turns the signal from a continuous-in-time signal to a discrete-in-time signal; the hold part turns it back into a continuous-in-time signal. Of course, if you sample at only finitely many points, you will only have finitely many (but still unconstrained) amplitudes. So after the sample-and-hold the output amplitudes will have a discrete but not quantized set of possible values. For example, if you sampled at three points in time, say 1sec, 2sec, 3sec, the set of amplitudes at those three points might be $\{1, 0.25, \pi\}$. Quantizing would then be some form of "rounding" those output values, say to $\{1,0,3\}$.