Convolution of real with complex signal
Discrete convolution is a linear operation, so yes

$$\begin{align*}x[n]*y[n] &amp;= (x*y)[n]\\
\\
&amp;= \sum_{m=-\infty}^{\infty} x[m]y[n-m] \\
\\
&amp;= \sum_{m=-\infty}^{\infty} x[m]\Re(y[n-m])+ jx[m]\Im(y[n-m]) \\
\\
&amp;= \left[\sum_{m=-\infty}^{\infty} x[m]\Re(y[n-m])\right] + \left[\sum_{m=-\infty}^{\infty} jx[m]\Im(y[n-m])\right] \\
\\
&amp;= x[n]*\Re(y[n])+jx[n]*\Im(y[n])\\
\end{align*}$$