As a new to DSP concepts want to understand the meaning of impulse response and why we do $h(n-k)$ in convolution and $h(n+k)$ in correlation.

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    $\begingroup$ The direction in convolution does not matter, it can go either way. Convert convolution numerically into system of linear equations and everything becomes clear. $\endgroup$ – Andrew Polar Jan 10 at 16:47

The correlation is used to find the time shift between signsls while convolution represents system response to predefined input. Since the system response depends on previous input, rether then future input, the sign of the time distance is negative.

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