>On Thu, 05 Feb 2015 06:29:53 -0600, DigitalGeek wrote: > >> After considering a couple of advices and suggestions for upsampling >> techniques here, I finally converged to use the cubic interpolation >> technique to estimate the voltage values corresponding to intermediate >> samples present between the original or previous samples. I know that >> spline interpolation is basically used for getting smoother curves, but >> what makes it different from the normal cubic interpolation techniqueas>> both of them use a 3rd degree polynomial to estimate intermediatevalues?.>> >> Another implementation issue is that, for example, If I have somevoltages>> corresponding to some samples say >> >> V = 3.674, 6.791, 8.888, 9.667..... >> Sample = 2, 3, 4, 5..... >> >> Now, If we have to find the voltage information corresponding to the >> intermediate sample 3.5, then using cubic polynomial method, we arriveat 4>> equations and 4 unknowns obtained by using the information provided bythe>> neighboring samples closest to sample 3.5. >> >> V(2) = a + 2b + 4c + 8d >> V(3) = a + 3b + 9c + 16d >> V(4) = a + 4b + 16c + 64d >> V(5) = a + 5b + 125c + 125d >> >> So, solving these equations I arrived at >> >> a = -4.428 >> b = 4.3756 >> c = -0.06299 >> d = -0.04966 >> >> Using these values , we can calculate the voltage value at the sample3.5>> as >> >> V(3.5) = a + 3.5b + 12.25c + 42.875d >> V(3.5) = 7.186 Volts > >But if you have (many) more data points than 4, you're going to have to >do something more sophisticated (you surely don't want to go to a higher >order polynomial, as you apparently understand). The various flavors of >splines introduce different assumptions for how the splines should be >joined (e.g. minimizing "strain energy", usually limiting higher-order >error derivatives and the like). > >I understand that cubic interpolation can operate on 4 data points. Themore sophisticated technique I can think of is cubic spline. In case I am using the normal cubic interpolation, how about I loop through the "N" sample points i.e. 1024, for a condition below the "input sampling rate" i.e. 10 sps considering 4 data points each and then performing the interpolation function based on the up sampling factor between each of those 4 consecutive data points (Meaning - Interpolating/Estimating 10 values between each of those 4 data points) and then the function considers the next 4 data points to perform the same operation and it goes on until a 100 samples has bee acquired i.e. the output sampling rate!> >> Now my question - Is this method of interpolation suitable for large >> sampling rates?. How can I use this technique for upsampling a signalsay>> from 10 sps to 100 sps for N = 1024 sample points?. I know that i haveto>> develop a function that performs this cubic interpolation task between >> original samples, but I am just wondering how to implement it for >> upsampling for a continuous series of samples.Any suggestions, ideas or >> advices regarding the topic and its implementation would beappreciated.>> Thanks! > >You have to know enough about your signal to know whether these splines >provide a sufficiently good approximation to the real underlying process. >This will hinge on how completely your sample points cover what is really >happening, and the validity of the assumptions your spline knots/joints >require. This has more to do with the nature of your signal thananything>else. > >HTH! > > From my knowledge, I know that, my input signal is discrete, periodic innature (for a period of 1 sec) and lets say with a sampling rate of 10sps, therefore to up sample it to 100 sps, I am sure that I have to interpolate the input signal i.e. 10 sps by a factor of 10, by which I mean - Interpolating/Estimating 10 new samples or voltage values between each consecutive equally spaced 10 samples in the input signal to obtain a sampling rate of 100 sps! _____________________________ Posted through www.DSPRelated.com