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Interpolation Basics

Interpolation Basics

Neil Robertson
TimelessBeginner

This article covers interpolation basics, and provides a numerical example of interpolation of a time signal. Figure 1 illustrates what we mean by interpolation. The top plot shows a continuous time signal, and the middle plot shows a sampled version with sample time Ts. The goal of interpolation is to increase the sample rate such that the new (interpolated) sample values are close to the values of the continuous signal at the sample times [1]. For example, if we increase the sample rate by the integer factor of four, the interpolated signal is as shown in the bottom plot. The time between samples has been decreased from Ts to Ts/4.


Summary

This article introduces the fundamentals of digital interpolation and resampling, explaining the goal of increasing sample rate so interpolated samples approximate the continuous-time signal. It includes a step-by-step numerical example that demonstrates upsampling by an integer factor and the practical considerations (timing, sample spacing, and filtering) needed to produce a smooth interpolated signal.

Key Takeaways

  • Explain the concept of interpolation and how it differs from signal reconstruction and simple sampling
  • Demonstrate how to perform integer-factor upsampling (e.g., factor-of-4) and compute new sample times
  • Apply a numerical example to generate interpolated samples and visualize the result relative to the continuous signal
  • Choose and understand the role of lowpass/anti-imaging filtering to remove spectral images introduced by upsampling

Who Should Read This

Early-career DSP engineers, signal-processing students, and practitioners in audio, communications, or radar who need a clear, practical introduction to interpolation and resampling.

TimelessBeginner

Topics

Multirate SystemsFilter DesignFFT/Spectral AnalysisAudio Processing

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