If you precisely define what you mean by "smoothness" then you will (most likely) find how to calculate it yourself (that is, without the use of a "specialized" software).
Without any further information, the first thing coming into my mind judging the "smoothness" of a curve is to have a look at the derivatives (e,g, the 2nd), possibly at the variance of the derivatives sampled at some coordinates. But this is just a quick idea, it might be inappropriate for your problem or might have to be further elaborated.
I don't think the question, as posed, is solvable. You would have to make assumptions about the very thing you'd want to know - that is, the smoothness of the curve. You have a finite number of data points (say N), and these can be fit by piecewise N horizontal segments (after all, you have no idea what is going on between the data points!). So, you'd have to rule out whole classes of possible solutions like this, and that means making assumptions about the smoothness.
Perhaps you can give more information about your question of interest and your data that would help us figure out what you need.
you should use R or SPSS program for this work. (simply search name of this program and "smoothing" word in google )
If you have some data points which give you some sort of curve and you are not satisfied with its curvature. Use Regression of Y on x and estimate value of expected y for all possible data points from your lowest data point to the highest. This way you will get a smooth nice curve.
Hope this helps.
I agree with others that this question seems to be incomplete, but given that this is listed under the time series topic I'll throw in a thought along those lines.
If you are looking at time series or similar "signal like" data you may want to look at the power spectrum, periodogram or semi-variogram in one time dimension. These statistical summaries provide a breakdown of the signal in terms of trends (low frequency cycles) more rapid cycles, and random noise. Most any statistical software provides this functionality. This is pretty general, but also differs from others advice recommending smoothing the data, which begins with the assumption of a particular level of smoothness, when I assume you want a metric to identify the level of smoothness. After understanding the level of smoothness, a sensible model for the signal would follow..perhaps regression model, perhaps a non-parametric smoother, etc.
The book below is a good start into this area.
http://www.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/?view=usa&ci=9780198522263
This kind of treatment for data. Is used when exist temporal series
I believe I need to do some more research to properly frame the question but I am very grateful for your responses
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