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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 4.7 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$.



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