Digital Signal Processing: Interpolation, Decimation, and Combined Interpolation-Decimation

This article explores three fundamental concepts in digital signal processing: interpolation, decimation, and combined interpolation-decimation operations. Interpolation involves estimating new sample values from existing known samples using various mathematical techniques. In code implementations, interpolation algorithms typically utilize digital filters (such as FIR filters) to insert additional samples while maintaining signal integrity. Decimation refers to the process of extracting lower sampling rate signals from higher sampling rate signals, often implemented through downsampling algorithms that reduce computational load by selecting every M-th sample. Combined interpolation-decimation operations integrate both processes to achieve efficient conversion between different sampling rates, enabling either upsampling (low-rate to high-rate) or downsampling (high-rate to low-rate) transformations.

In digital signal processing, L-fold interpolation and M-fold decimation represent core operations frequently combined to achieve rational L/M sampling rate conversion. L-fold interpolation involves inserting L-1 additional samples between existing samples using interpolation filters to prevent aliasing artifacts. M-fold decimation systematically selects every M-th sample from the original high-rate signal while employing anti-aliasing filters to avoid frequency folding. The combined L/M interpolation-decimation operation implements both processes sequentially (typically interpolation followed by decimation) to achieve precise rational sampling rate changes. This combined approach proves essential in multirate signal processing systems where computational efficiency and signal quality must be balanced.

Consequently, interpolation, decimation, and combined interpolation-decimation constitute vital concepts in digital signal processing with extensive applications across various signal processing domains. The integration of interpolation and decimation enables efficient signal processing and transmission workflows. Through practical algorithm implementations—often using polyphase filter structures for computational optimization—these techniques maintain signal fidelity while adapting sampling rates. This discussion provides readers with comprehensive understanding of these fundamental DSP operations and their implementation methodologies.