finding shift numbers to minimize the rms of four signals

Hi everyone,

I have four signals (1x10) which are right below;

A=[1 1 1 1 0 0 0 0 1 1];

B=[1 2 3 3 3 3 2 1 1 1];

C=[1 2 1 2 1 2 1 2 1 2];

D=[1 2 3 2 1 0 1 2 3 2];

and I want that:

• result = (minimize[rms[A,B,C,D]). size of result should be 1x15. We can add zeros to A, B, C, D to reach 1x15 size.
• To reach the best "result", all signals can be shifted and zeros can be added in x axes. I would like to determine the shifting parameter for each signal.

For example if I have the best result;

A must be shifted 3 digits by adding 3 zeros. and it will be new_A=[0 0 0 1 1 1 1 0 0 0 0 1 1 0 0], B will be new_B=[1 2 3 3 3 3 2 1 1 1 0 0 0 0 0]; C will be new_C=[0 0 0 0 0 1 2 1 2 1 2 1 2 1 2]; and new_D = [0 0 0 0 0 1 2 3 2 1 0 1 2 3 2 ].

So according to the upper result, I would like to determine four parameters that are A_t_shifted: 3, B_t_shifted= 0, C_t_shifted= 5, D_t_shifted= 5.

How can I determine these parameters to minize the result with a matlab code? (Maybe "corr" or "conv" can be helpful.)

kings regards

Cem

[Matt J]

It's not clear why you think this combination of zeros minimizes rms. The rms should not depend on the location of additional zeros in the signals.

rms([1 2 3 0 0 0 ])

ans = 1.5275

rms([0 1 2 3 0 0])

ans = 1.5275

rms([0 0 1 2 3 0 ])

ans = 1.5275