Gibbs wiggles in field modulation

[stestoll]

When the spectral lines are very narrow, or if the spectrum is non-zero at the edges, the FFT-based convolution approach from fieldmod results in Gibbs wiggles.

B = linspace(200,400,1000);
spc = zeros(1,numel(B));
spc(500) = 1;
fieldmod(B,spc,1)

spc = ones(1,numel(B));
fieldmod(B,spc,1)

To fix this, improve the FFT approach, or implement a direct convolution without FFT. Both could be supported via an option.

[stestoll]

Here is the math for the modulated line shape in the field domain:

clear, clc, clf

% Parameters
B = linspace(300,400,1000);  % field range vector, mT
B0 = 361;  % line position, mT
A = 10; % line amplitude, arb.u.
Bpp = 10;  % peak-to-peak modulation amplitude, mT

% Generate spectrum with a single delta peak
spc = zeros(size(B));
idxB0 = interp1(B,1:length(B),B0,'nearest');
spc(idxB0) = A;

% Field modulation via Fourier transform
spc_FT = fieldmod(B,spc,Bpp);

% Explicit expression for field-modulated line
b = 2*(B-B0)/Bpp;
spc_explicit = -(1/pi/Bpp)*b./sqrt(1-b.^2);
dB = mean(diff(B));
spc_explicit = real(spc_explicit)*A*dB;

% Plotting
plot(B,spc_FT,B,spc_explicit);

[stestoll]

General lineshape expression for n-th harmonic is (-1)^n2T_n(B/Bm)/sqrt(Bm^2-B^2), where T_n is the Chebyshev polynomial of the first kind and order n. Here, Bm is the base-to-peak modulation amplitude. See my PhD thesis, eq. (3.8).