# What is the opposite of sampling called?

We call the conversion from a continuous time signal $f(t)$ to a discrete time signal $f_s[k]$ "sampling". Is there a name for the reverse operation, i.e. creating a continuous time signal from a discrete time signal?

• If by sampling you mean down-sampling, then the opposite is called up-sampling. – user13107 Aug 17 '13 at 12:00
• @user13107: Obviously Denwid does not. – chirlu Aug 17 '13 at 14:19

This is called reconstruction.

• How is that different from interpolation? – user13107 Aug 17 '13 at 11:50
• Interpolation refers to the act of increasing the sample rate of a discrete-time signal, but after you interpolate, the signal is still discrete. The term used to indicate conversion back to a continuous-time signal is "reconstruction", as pichenettes indicated. – Jason R Aug 17 '13 at 13:37
• @JasonR: Yet the reconstructed continuous time function is called "the interpolant"? – Wandering Logic Aug 17 '13 at 16:26
• @WanderingLogic: Nowhere on the linked-to page is the word "interpolant" used. – Peter K. Aug 18 '13 at 0:16
• When I taught signal processing I never used the interpolation word because it gave students all kinds of wrong ideas - in particular, that things like 'connect the dots' linear interpolation or fancy spline/polynomial methods would be acceptable solutions to a problem whose solution, in the equally spaced samples case, is undebatably a low-pass filter at half the sample-rate. Interpolation suggests that you are making things up and that there's no right or wrong solution; while reconstruction connects deeply with the sampling problem and emphasizes that there is only one way things could be. – pichenettes Aug 18 '13 at 7:22

The process of creating a Continuous time signal from Discrete time signal is called (in plain Signal processing terminology) as "Reconstruction". Another term you will find associated with this process is "Low Pass Filtering" as it's the process used for conversion

• "Low Pass Filtering" is way too generic. They are usually called, funnily enough, reconstruction filters. – Peter K. Aug 18 '13 at 0:20

In mathematics it is called interpolation. If you fill data in between data points (in signal processing we call them samples) it is called interpolation. If you try to fill missing data outside the range of the collected data/samples, it is called extrapolation. In signal processing, the operation of filling the data in between samples is called interpolation and the blocks that do this operation are called interpolation filters.

• interpolated signal is still discrete signal, so basically sampled signal only but with increased or decreased sampling rate – KharoBangdo Aug 4 '14 at 10:57
• No, in mathematics it is called interpolation. You fit a curve passing through those data points or samples and you take the curve as the generating function so you know everywhere the function value. Not just at some points. This is a broader view. In signal processing, you might call it as reconstruction. Of course, this is just one of the different ways of reconstruction. – Seetha Rama Raju Sanapala Aug 4 '14 at 23:37