Validation of Retardation Function (Frequency Response of Impulse Signals)

Retardation function K(t) is computed from the added mass and potential damping. In order to validate the computation, we try to compute the added mass and potential damping from retardation function. Here is the MATLAB codes:

load retardationK.mat
% the file consists of:
% Aa: Added mass vector
% Bp: Potential damping vector
% Ainf: Added mas at infinite frequency
% K: retardation: impulse response (time-series signal)
% omega: frequency of Aa and Bp
% time: time vector of K


% frequency response of impulse signal
Ts = time(2)-time(1);
fs = 1/Ts;
Nfft = length(K);
[H,f]=freqz(K,1,Nfft,fs); 
H=H*Ts;

Bhat = real(H); % B(w) from K(jw)
Ahat = imag(H)./(2*pi*f) + Ainf; % A(w) from K(jw)


figure;
subplot(211);
plot(omega,Aa,2*pi*f,Ahat); grid on;
subplot(212);
plot(omega,Bp,2*pi*f,Bhat);grid on

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