finding shift numbers to minimize the rms of four signals

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cem
cem 2023-4-10
编辑： Matt J 2023-4-10
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
  1 个评论
Matt J
Matt J 2023-4-10
编辑：Matt J 2023-4-10
Ran in:
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

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