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 technique as both of them use a 3rd degree polynomial to estimate intermediate values?. Another implementation issue is that, for example, If I have some voltages 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 arrive at 4 equations and 4 unknowns obtained by using the information provided by the 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 sample 3.5 as V(3.5) = a + 3.5b + 12.25c + 42.875d V(3.5) = 7.186 Volts Now my question - Is this method of interpolation suitable for large sampling rates?. How can I use this technique for upsampling a signal say from 10 sps to 100 sps for N = 1024 sample points?. I know that i have to 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 be appreciated. Thanks! _____________________________ Posted through www.DSPRelated.com

# What is the difference between cubic interpolation and cubic “Spline” interpolation?. How to use it for upsampling purpose?

Started by ●February 5, 2015

Reply by ●February 5, 20152015-02-05

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 technique as > both of them use a 3rd degree polynomial to estimate intermediate values?. > > Another implementation issue is that, for example, If I have some voltages > 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 arrive at 4 > equations and 4 unknowns obtained by using the information provided by the > 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 sample 3.5 > as > > V(3.5) = a + 3.5b + 12.25c + 42.875d > V(3.5) = 7.186 VoltsBut 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).> Now my question - Is this method of interpolation suitable for large > sampling rates?. How can I use this technique for upsampling a signal say > from 10 sps to 100 sps for N = 1024 sample points?. I know that i have to > 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 be appreciated. > 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 than anything else. HTH!

Reply by ●February 6, 20152015-02-06

>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