Smoothing complex data by convolution
If you filter complex data $x[n]$ with a filter with a real-valued impulse response $h[n]$, your complex-valued output is given by the convolution sum

$$y[n]=\sum_kx[k]h[n-k]\tag{1}$$

The real and imaginary parts are

$$y_R[n]=\sum_kx_R[k]h[n-k]\tag{2}$$

and

$$y_I[n]=\sum_kx_I[k]h[n-k]\tag{3}$$

So whatever you do, in order to compute the complex-valued output $y[n]$ you need to perform two real-valued convolutions / filtering operations.