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Interpolation is the process of upsampling and filtering a signal to increase its effective sampling rate. To be more specific, say that is an (unaliased) -sampled version of and is an -upsampled version version of . If we filter with an ideal -bandwidth lowpass filter (with DC gain ) to obtain , then will be a -sampled version of . This process is illustrated in .
We justify our claims about interpolation using frequency-domain arguments. From the sampling theorem, we know that - sampling to create yields
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