Of course with a capacitance and the resistance in the circuit, there is some time delay before the voltage across the capacitance approaches the input voltage. These circuits must then be triggered at the right time, and possibly cascaded to achieve the needed delay. But implementing a continuously changing delay time makes it interesting. Since the samples are always taken one sampling period apart, you can't create a delay line whose delay is not an integral multiple of the sampling period. You can get around this by using interpolation .
Interpolation is simple estimating a value of a function between two points.
In this case, we have two samples and we want to get a value in between them. A simple method of interpolating is to connect the points with a line, and then read the desired value from that line. Although linear interpolation is simple, it can be noisy due to aliasing. It may be acceptable with very high sampling rates, but in some cases, a more computationally expensive interpolation method may be needed. There is an interesting possibility when using a flanger with a musical instrument.