Can't get better interpolation at some points

Hi all,

I would be grateful if someone could help with the following matter:

I have a set of complex data called [a2norm_real and a2norm_imag (as per attached)], and another set of complex data was generated as shown in the code. I tried to achieve better interpolation for the Gain, but it fails at certain points (as per attached). No matter how many points I generate, it fails at the same place each time. I have tried different 1D and 2D interpolation methods (including the one below), but this was the best one I could achieve. Thanks!

Here is the code:

data2 = readtable('System Gain.xlsx', 'VariableNamingRule', 'preserve');
% Process the second file
a2norm_real    = data2{:, 5};
a2norm_imag    = data2{:, 6};
a2norm_complx  = complex(a2norm_real,a2norm_imag);
Gain           = complex(data2{:, 1}, data2{:, 2});
a21_mag = linspace(min(abs(a2norm_complx)),max(abs(a2norm_complx)),31).';
a21_ph  = linspace(0,0,31).';
a21_complx     = a21_mag.*exp(1i*pi/180.*a21_ph);
% Perform the interpolation
Interp = griddata(a2norm_real, a2norm_imag, Gain, real(a21_complx), imag(a21_complx), 'nearest');
figure;
plot(abs(a2norm_complx), Gain, 'o', 'DisplayName', 'System gain');

Warning: Imaginary parts of complex X and/or Y arguments ignored.

hold on;
plot(abs(a21_complx), Gain, ':*', 'DisplayName', 'System\_Gain\_Selected');

Warning: Imaginary parts of complex X and/or Y arguments ignored.

legend('show'); % Displays the legend with the DisplayName labels
title('(Default) Linear Interpolation');
grid on;
legend('Location', 'best')

[Torsten]

System_Gain and System_Gain_Interp are undefined in your code.

[John D'Errico]

I looked at this question, and I could not decide if the problem is just that the code uses undefined variables named System_Gain, a21_target, and System_Gain_Interp (I may even have missed some others) or if there was some real question about interpolation.

I might guess the variable named Interp is intended to be System_Gain_Interp. Are errors like that just the cause of your problem? If so, then you just need to be more careful in how you write code, and don't assume MATLAB can guess what you meant. Computers tend to be very literal things, generally assuming your code is intended to be executed as you wrote it. ;-)

Or is the problem one where you are unhappy about some variety of interpolation artifact? We cannot see any problem, since your code is incomplete.

[Azam]

Sorry for this oversight, the code has been updated.

[Walter Roberson]

Gain           = complex(data2{:, 1}, data2{:, 2});

Inherently complex-valued.

plot(abs(a2norm_complx), Gain, 'o', 'DisplayName', 'System gain');

You are trying to plot the inherently complex value.

Answer 1

[nick]

Hello Azam,

I understand that you want to interpolate the 'Gain' variable.

As @Walter Roberson mentioned, the 'plot' function is incorrectly used with the complex valued variable 'Gain'. For interpolating the 'Gain', you can use the function 'interp1' for 1-D data interpolation, as shown below :

data2 = readtable('System Gain.xlsx', 'VariableNamingRule', 'preserve');
% Process the second file
a2norm_real    = data2{:, 5};
a2norm_imag    = data2{:, 6};
a2norm_complx  = complex(a2norm_real,a2norm_imag);
Gain           = complex(data2{:, 1}, data2{:, 2});
a21_mag = linspace(min(abs(a2norm_complx)),max(abs(a2norm_complx)),31).';
a21_ph  = linspace(0,0,31).';
a21_complx     = a21_mag.*exp(1i*pi/180.*a21_ph);

% Perform the interpolation
InterpolatedData = interp1(abs(a2norm_complx),abs(Gain),a21_mag);
figure;
plot(abs(a2norm_complx), abs(Gain), 'o', 'DisplayName', 'System gain');
hold on;
plot(abs(a21_complx), InterpolatedData, ':*', 'DisplayName', 'System\_Gain\_Selected');
legend('show'); % Displays the legend with the DisplayName labels
title('(Default) Linear Interpolation');
grid on;
legend('Location', 'best')

It fits the 'Gain' well, as can be seen in the plot :

You may refer to the following documentation of 'interp1' function to learn more about it :

https://www.mathworks.com/help/matlab/ref/interp1.html

Hope this helps!