Stereo base broadening

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Stereo base broadening is an operation on a stereo signal that is intended to electrically simulate the change in the stereo base , i.e. the pushing apart or moving closer together of the stereo speakers .

Theoretical background

If one observes the deflections on the two stereo channels at a fixed point in time, the new signal values result after the stereo base broadening with the parameter ${\displaystyle u_{\mathrm {l} },u_{\mathrm {r} }}$ ${\displaystyle p}$ ${\displaystyle y_{\mathrm {l} },y_{\mathrm {r} }}$

${\displaystyle y_{\mathrm {l} }={\frac {1}{2}}\cdot ((1+p)\cdot u_{\mathrm {l} }+(1-p)\cdot u_{\mathrm {r} })}$

${\displaystyle y_{\mathrm {r} }={\frac {1}{2}}\cdot ((1-p)\cdot u_{\mathrm {l} }+(1+p)\cdot u_{\mathrm {r} })}$.

This can be seen as a matrix multiplication

${\displaystyle {\begin{pmatrix}y_{\mathrm {l} }\\y_{\mathrm {r} }\end{pmatrix}}=S_{p}\cdot {\begin{pmatrix}u_{\mathrm {l} }\\u_{\mathrm {r} }\end{pmatrix}}}$

with writing. ${\displaystyle S_{p}={\frac {1}{2}}\cdot {\begin{pmatrix}1+p&1-p\\1-p&1+p\end{pmatrix}}}$

The sequential execution of two stereo base extensions can be combined into one, because the following applies:

${\displaystyle S_{p}\cdot S_{q}=S_{p\cdot q}}$.

The following applies to the matrix power

${\displaystyle S_{p}^{x}=S_{p^{x}}}$,

ie you can also use an additive quantity as a parameter. For example one could put ( Euler's number ) and ${\displaystyle p=e}$

${\displaystyle T_{a}=S_{e^{a}}}$,

then applies

${\displaystyle T_{a}\cdot T_{b}=T_{a+b}}$ and

${\displaystyle T_{a}^{x}=T_{a\cdot x}}$.