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$f[m]$, $g[m]$, and $c[m]$ are three distinct discrete-time functions. I want to find the coefficients of $f[m]$ such that the l2-norm of error (defined as $f(m)* g(m)-c(m)$) is minimized. Is this the correct representation in the time-domain?

\begin{equation} \sum_{m=1}^N| f(m)* g(m)-c(m)|^2 \end{equation}

I want to avoid writing them in the matrix/vector form and just work in the time domain.

dsp_guy2020
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  • What operation does the asterisk * represent? Is that just multiplication? Often an asterisk denotes convolution. – littleO Oct 25 '21 at 21:42
  • It is a convolution. – dsp_guy2020 Oct 25 '21 at 22:13
  • Ah, if it's a convolution, then I believe you should write $(f * g)(m)$ rather than $f(m) * g(m)$. Note that $f(m)$ is a number and $g(m)$ is a number, and we can't take the convolution of two numbers. – littleO Oct 25 '21 at 22:28

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