Interpolated FIR filter (from Oppenheim and Schafer's Discrete-Time Signal Processing, 3rd ed)
The reason why &quot;interpolated FIR filter&quot; is an appropriate name is because the filter $h_2[n]$ has $M_1-1$ zeros between its (non-zero) filter taps, and the convolution with the filter $h_1[n]$ interpolates those $M_1-1$ values.

Eq. $(104)$ generally only represents an FIR filter if both $h_1[n]$ and $h_2[n]$ are FIR filters.