This chapter studies sampling between discrete-time rates: what happens when we keep only every Nth sample (downsampling/decimation) or insert zeros between samples (upsampling/interpolation). We show how multiplying a sequence by a periodic sampling function (an impulse train) creates spectral replicas, derive aliasing conditions, and explain how the frequency axis rescales after removing zeros. Practical Python examples illustrate spectra before/after sampling and the audible artifacts of aliasing. We conclude with perfect reconstruction conditions, including band-pass sampling, and summarize design rules for safe rate conversion.

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Sampling

  • Gerald Schuller

摘要

This chapter studies sampling between discrete-time rates: what happens when we keep only every Nth sample (downsampling/decimation) or insert zeros between samples (upsampling/interpolation). We show how multiplying a sequence by a periodic sampling function (an impulse train) creates spectral replicas, derive aliasing conditions, and explain how the frequency axis rescales after removing zeros. Practical Python examples illustrate spectra before/after sampling and the audible artifacts of aliasing. We conclude with perfect reconstruction conditions, including band-pass sampling, and summarize design rules for safe rate conversion.