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What is Decimation?

Processing that lowers the sampling frequency by an integer factor. Before keeping one sample out of every M (downsampling), components above the new Nyquist frequency fs/(2M) are removed with a digital low-pass filter (a decimation filter). Downsampling without the filter folds those components back onto the signal band. For example, reducing 48 kHz by 1/4 gives 12 kHz, so everything above 6 kHz must be removed first. Outputs for the discarded samples need not be computed, so polyphase structures and similar techniques reduce the computation. Decimation is also used to turn the output of a delta-sigma ADC into high-resolution data.

Japanese name: デシメーション

Decimation appears in 2 practice questions across 2 topics, including Digital Signal Processing Basics, A/D and D/A conversion.

Field: Digital Signal Processing Basics

Try it: questions about Decimation

A signal sampled at 48 kHz is reduced to 12 kHz by keeping one sample out of every four (decimation by 4). Which of the following frequency components should the low-pass filter placed before the downsampling remove?

  1. AComponents above 6 kHz
  2. BComponents above 12 kHz
  3. CComponents above 24 kHz
Show answer and explanation

Answer: A. Components above 6 kHz

After downsampling, the sampling frequency is 48 ÷ 4 = 12 kHz and its Nyquist frequency is 6 kHz. If components above 6 kHz remain when the samples are dropped, they fold back under 12 kHz sampling and overlap the band below 6 kHz (for example, a 9 kHz component appears at 12 − 9 = 3 kHz). A digital low-pass filter therefore attenuates everything above 6 kHz sufficiently before the downsampling.

Decimation in the explanations

Questions that mention Decimation (2)

  1. A signal sampled at 48 kHz is reduced to 12 kHz by keeping one sample out of every four (decimation by 4). Which of the following frequency components should the low-pass filter placed before the downsampling remove?
  2. In a delta-sigma ADC, which digital circuit converts the fast, coarse quantized output into high-resolution data at a lower sampling rate?

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Related terms

Nyquist frequency Delta-sigma ADC FIR filter Convolution Difference equation Discrete Fourier transform Fast Fourier transform (FFT) Frequency resolution Group delay IIR filter

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