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Hello math goers,

My education in linear algebra is limited to an Intro course I took a year ago. So I am posting this to see if such a solution exists in the first place, at least so I can start learning about it.

The problem is: solve A for equation

[tex] u(t) = A \cdot v(t+t_o) [/tex]

[tex] \left[ \begin{array}{c} u(t_1)\\ u(t_2)\\ \vdots\\ u(t_n) \end{array} \right]=\left[ \begin{array}{cccc} a_1 & a_2 & \cdots & a_n \end{array} \right] \cdot \left[ \begin{array}{c} v(t_1+t_o) \\ v(t_2+t_o) \\ \vdots \\ v(t_n+t_o) \end{array} \right] [/tex]

Where [tex] t_o [/tex] is some known offset with respect to [tex] t [/tex] .

Essentially what these represent are two data signals [tex] v(t_v) [/tex] and [tex] u(t_u) [/tex], these two signals have some small time offset that I can calculate using a reference peak that both signals contain. However, getting A is not as simple as solving for A because the data is not continuous.

The "easy" way around this is to manually align every single value [tex] v(t_v) [/tex] with [tex] u(t_u)[/tex], but this is computationally expensive.

Any thoughts?

My education in linear algebra is limited to an Intro course I took a year ago. So I am posting this to see if such a solution exists in the first place, at least so I can start learning about it.

The problem is: solve A for equation

[tex] u(t) = A \cdot v(t+t_o) [/tex]

[tex] \left[ \begin{array}{c} u(t_1)\\ u(t_2)\\ \vdots\\ u(t_n) \end{array} \right]=\left[ \begin{array}{cccc} a_1 & a_2 & \cdots & a_n \end{array} \right] \cdot \left[ \begin{array}{c} v(t_1+t_o) \\ v(t_2+t_o) \\ \vdots \\ v(t_n+t_o) \end{array} \right] [/tex]

Where [tex] t_o [/tex] is some known offset with respect to [tex] t [/tex] .

Essentially what these represent are two data signals [tex] v(t_v) [/tex] and [tex] u(t_u) [/tex], these two signals have some small time offset that I can calculate using a reference peak that both signals contain. However, getting A is not as simple as solving for A because the data is not continuous.

The "easy" way around this is to manually align every single value [tex] v(t_v) [/tex] with [tex] u(t_u)[/tex], but this is computationally expensive.

Any thoughts?

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