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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 I.13 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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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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