MATLAB: How to perform a proper interpolation with only few data points

interpolationregression

I want to interpolate the following data:

I was trying:

interpolation = interp1(frequency,linear scaling,'spline')

But this doesn't work well at all! Is there a better way?

Best Answer

You need a vector of independent values to interpolate. Note that the variable name ‘linear scaling’ (with the included space) is not a valid MATLAB variable name, and with the space would throw an error because there is no required comma (,) to separate the arguments. I added the underscore to rename it ‘linear_scaling’.

See if this improves your results:

freq_intrp = linspace(min(frequency), max(frequency), 50);
interpolation = interp1(frequency, linear_scaling, freq_intrp, 'spline');

I chose 50 points (third argument to linspace) between the frequency limits. Use as many points as you like.

Related Solutions

MATLAB: Designing an Arbitrary FIR Filter

This is probably as close as you can get:

Frequency = [100  125  160  200  250  315  400  500  630  800  1000  1250  1600  2000  2500  3150  4000  5000  6300  8000  10000];
Required_Filter_Response = [55.38  55.74  52.13  52.64  51.25  49.04  46.50  44.99  42.95  40.73  39.47  37.53  35.36  34.33  32.33  30.36  28.01  25.98  23.19  20.42 18.65];
Fs = 20000;                                                                 % Create Sampling Frequency (Not Supplied, Must Be > 20000 Here)
Fn = Fs/2;
Fnew = linspace(min(Frequency), max(Frequency), fix(numel(Frequency)/2)*2);
Rnew = interp1(Frequency, Required_Filter_Response, Fnew);
b = firls(100, Fnew/Fn, Rnew/max(Rnew));
figure
freqz(b, 1, 2^14, Fs)
[h,f] = freqz(b, 1, 2^14, Fs);
figure
plot(Fnew, 20*log10(Rnew/max(Rnew)))
hold on
plot(f, 20*log10(abs(h)))
hold off

Note that the filter and the desired response are essentially the same in the second plot.

MATLAB: Interpolation method (spline)

From the documentation:

'spline':

‘Spline interpolation using not-a-knot end conditions. The interpolated value at a query point is based on a cubic interpolation of the values at neighboring grid points in each respective dimension.’

It does not appear to be the same as 'cubic'. According to the documentation, 'cubic' is currently the same as 'pchip'.

Best Answer

Related Solutions

MATLAB: Designing an Arbitrary FIR Filter

MATLAB: Interpolation method (spline)

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