Signal ratio and conversion: converting one signal to another?

Question

I am trying to connect the near coastal tidal signal ( point A ) to three points along the long border of the model ( BCD points ). I want to possibly have a relationship between the BCD , through which we can convert a prediction A in BC and D . I am currently doing one phase shift, an amplitude ration for levels above zero, an amplitude ration for levels below zero, and a mid-level shift.

This creates a kink in the tidal signal at the peak of ebb and Peak flood and leads to a model with prediction of recoil currents. I was wondering if anyone knows of more complex relationships for this kind of transformation?

One thing I would like to catch is the difference in the phase shift between high and low water (for example, the ratio of the period of positive periods to the period of negatives may differ for different points).

An example algorithm for the current process.

A = vector (size n x 1 ) units meters

time_A = vector (size n x 1 )

ph_B = phase shift for AvsB.

pos_amp_B = positive amplitude ration.
neg_amp_B = negative amplitude ration.

B_mean = long term mean of B.

A_mean = long term mean of A.

for i = 1:n
    a = A(i) - A_mean
    if a > 0
       B(i) = a*pos_amp_B
    else
       B(i) = a*neg_amp_B
    end
    time_B(i) = time_A(i) = ph_B
    B(i) = B(i) + B_mean
end

BTW: relationship is based on about 6 months of data.

EDIT 1: Well, first, just think of two sinusoidal signals (i.e., Amplitude, phase shift), but not regular, so for example, the period is 12.5 hours, but the slopes and periods of the positive half and negative half not all are the same. You do not need any contextual knowledge. I'm just looking for a conversion algorithm.

2:

fft (fft (12,5 ()), , ). - A. .

Answer 1

. , (LTI). , , .

, B, C D, A. ; , . , . , Matlab:

% Create an example signal at location 'A'
t = 0:0.1:10;
A = 0.35.*sin(2.*pi.*0.5.*t) + 1.*sin(2.*pi.*0.5175.*t) + 0.3.*sin(0.5255.*t);

% We want a complex version of A, so let apply a Hilbert transform to it
A = hilbert(A);

% Now we can create the other signals by transforming the amplitude and
% phase. Exactly what amplitude and phase to apply needs to be determined.
B = 0.9*exp(j*0.1).*A;
C = 0.8*exp(j*0.4).*A;
D = 0.7*exp(j*0.6).*A;

% Plot what these signals look like
figure(1); hold on;
plot(t,real(A),'k');
plot(t,real(B),'r');
plot(t,real(C),'g');
plot(t,real(D),'b');
xlabel('Time');
ylabel('Amplitude');
legend('A','B','C','D');

, , . LTI, .

, !

Answer 2

.

. ( , , ):

Das Nordseemodell der BAW zur Simulation der Tide in der Deutschen Bucht

, , , .

: A, B, C, D , , , . : .

, . 93 , GPLv2 2010

Answer 3

( ) .

ODE , :

   <<< tidal force field >>>

|         |         |         |
o -vvvvv- o -vvvvv- o -vvvvv- o
A         B         C         D

-vvvvv- .

, , , .

, , -I-wish-I-know, . -, (paywall), , , .

, , (.. , , ).