% Fourier transform of a differential operator for a lowpass filter.
function Dfft = D_lowpass(omega)
% omega = angular frequency in radians/sec.

R = 100;     % 100 ohm resistor
C = 0.01e-6; % 0.01 uF capacitor

Dfft = 1 + i*omega*R*C;
% Practical problem: The imaginary part is discontinuous at the
% Nyquist frequency.


% Derivation:
%             R 
%  E(t) >---/\/\/----------> V(t)
%                   |
%                  === C
%                   |
%                  --- ground
%                  \\\
% V = q/C
% (E-V)/R = I = dq/dt = C dV/dt
% RC dV/dt + V(t) = E(t)   (time domain)
% (1 + iwRC) V(w) = E(w)   (frequency domain)
