# 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?

## 3 Answers

the topic that i think you're groping for is the Zero-order hold or "ZOH". i changed the tags a little to reflect this. conceptually, the ZOH is not quite the same thing as the Sample-and-hold circuit which has continuous functions going in and piecewise-constant signal coming out. the ZOH is a conceptual LTI system that has a string of dirac impulses going in and a piecewise-constant signal coming out.

The sample-and-hold circuit is a physical, analog electrical circuit and, by definition, its output is continuous.

The actual conversion to discrete time happens at the quantizer, not at the sampler. The output of the quantizer is a discrete sequence of numbers associated with time instants, so it can be said to be a discrete signal.

• well, the output is "continuous-time" (as opposed to "discrete-time"), but the output is not thought of as theoretically "continuous". it's a piecewise-constant function and there are step discontinuities. – robert bristow-johnson Feb 5 '16 at 5:25
• @robertbristow-johnson Ideally yes, you're right; but the output of a "physical, analog electrical circuit" is continuous both in theory and in practice. That is what I was referring to in my answer. – MBaz Feb 5 '16 at 14:54

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 $\{1,0,3\}$.