Interpolation 2.14 2002/01/10 2005/10/01 15:14:14.178 GMT-5 Phil Schniter schniter@ee.eng.ohio-state.edu Adan Galvan jago@rice.edu Erin Maloney emaloney@rice.edu Phil Schniter schniter@ee.eng.ohio-state.edu CD compact disc digital audio interpolation interpolator oversampling upsampler upsampling zero-order hold Introduction of interpolation and it's application.

Interpolation Interpolation is the process of upsampling and filtering a signal to increase its effective sampling rate. To be more specific, say that x m is an (unaliased) T-sampled version of x c t and v n is an L-upsampled version version of x m . If we filter v n with an ideal L-bandwidth lowpass filter (with DC gain L) to obtain y n , then y n will be a TL -sampled version of x c t . This process is illustrated in .

We justify our claims about interpolation using frequency-domain arguments. From the sampling theorem, we know that T- sampling x c t to create x n yields X ω 1 T k k X c ω 2 k T After upsampling by factor L, implies V ω 1 T k k X c ω L 2 k T 1 T k k X c ω 2 L k T L Lowpass filtering with cutoff L and gain L yields Y ω L T kL k L X c ω 2 L k T L L T l l X c ω 2 l T L since the spectral copies with indices other than klL (for l) are removed. Clearly, this process yields a TL-shaped version of x c t . illustrates these frequency-domain arguments for L2.