Frequency Response of Linear Interpolation

Since linear interpolation can be expressed as a convolution of the samples with a triangular pulse, we can derive the frequency response of linear interpolation. Figure J.19 indicates that the triangular pulse $h_l(t)$ serves as an anti-aliasing lowpass filter for the subsequent downsampling by $M$. Therefore, it should ideally ``cut off'' all frequencies higher than $0.5f_s/M$.