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Downsampling (signal processing)

In digital signal processing, downsampling, subsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system.

Version
v1 · 2026-09-28 · History
Domain-specific #
9060
Domain group
Applied Sciences & Engineering
Origin domain
Engineering & Design (beyond software)
Subdomains
Digital Signal Processing, Multirate Systems → Engineering & Design (beyond software)

Core Idea

Downsampling (signal processing) is treated here as the recurring mathematics and formal science identity summarized by this source-grounded definition: In digital signal processing, downsampling, subsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. In digital signal processing, downsampling, subsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction (filtering) and sample-rate reduction.

How would you explain it like I'm…

Keep Every Tenth Picture

Imagine a flip-book with lots and lots of pages. If you keep only every tenth page, the book gets much shorter but still shows roughly the same story. Downsampling is doing that to a recording: keeping fewer of the little snapshots.

Keep Every Tenth Snapshot

A digital sound or picture is made of many tiny measurements called samples, taken one after another. Downsampling means keeping fewer of them, for example only every tenth one. The result is close to what you would have gotten if you had measured less often in the first place. Often you first smooth out the fastest wiggles, because with fewer samples those can no longer be captured properly. Downsampling is sometimes called decimation, even though that old word used to mean removing one in every ten.

Lowering the Sample Rate

A digital signal is a sequence of samples taken at some sampling rate, and downsampling lowers that rate. Downsampling by a factor of 10 (also called decimation by 10) means keeping only every tenth sample, which multiplies the time between samples by 10 and divides the rate by 10. The goal is an approximation of the sequence you would have recorded if you had sampled the original signal more slowly, or at lower density in the case of a photo. The words downsampling, subsampling, compression and decimation are sometimes used for just the sample-dropping step, and sometimes for the whole process of first filtering out fast detail and then reducing the rate. Oddly, 'decimation' historically meant removing every tenth item, but in signal processing it means keeping every tenth one.

 

Downsampling belongs to multi-rate digital signal processing, where a system operates on the same signal at more than one sample rate. Reducing the rate by an integer factor M keeps every Mth sample, so the sampling interval is multiplied by M and the sampling rate divided by M. Downsampling, decimation, subsampling and compression are overlapping terms: sometimes they name only this sample-rate reduction, and sometimes the full two-stage process of bandwidth reduction (lowpass filtering) followed by rate reduction. The goal in either case is an approximation of the sequence that direct sampling of the underlying signal or continuous function at the lower rate would have produced. The same idea applies spatially, as lowering pixel density in a photograph. Note the naming trap: 'decimation by 10' means keeping one sample in ten, not discarding one in ten as the word's historical meaning suggests.

Scope of Application

  • Downsampling by an integer factor. It is sometimes used in derivations of the polyphase method.

  • Downsampling by an integer factor. In this application, the filter is called an anti-aliasing filter, and its design is discussed below.

  • Downsampling by an integer factor. In a general purpose processor, after computing y[n], the easiest way to compute y[n+1] is to advance the starting index in the x[•] array by M, and recompute.

  • Downsampling by an integer factor. The equivalence of this inefficient method and the implementation described above is known as the first Noble identity.

  • Anti-aliasing filter. Let X(f) be the Fourier transform of any function, x(t), whose samples at some interval, T, equal the x[n] sequence.

Clarity

A clear use of Downsampling (signal processing) names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In digital signal processing, downsampling, subsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system.

Manages Complexity

Downsampling (signal processing) compresses multiple mathematics and formal science details into a stable diagnostic relation. The source shows both the central mechanism—rate reduction by an integer factor M can be explained as a two-step process, with an equivalent implementation that is more efficient.—and the practical consequence—but in signal processing, decimation by a factor of 10 actually means keeping only every tenth sample.

Abstract Reasoning

  1. Type the carrier. Identify the mathematics and formal science entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In digital signal processing, downsampling, subsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system.
  3. Check operation and conditions. The calculation performed by a decimating FIR filter for the n th output sample is a dot product.
  4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Downsampling (signal processing) transfers literally when a new case preserves the same carrier type, relation, and recognition test. It is sometimes used in derivations of the polyphase method. In this application, the filter is called an anti-aliasing filter, and its design is discussed below. Beyond the home domain. No canonical parent is asserted for Downsampling (signal processing). An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Neighborhood in Abstraction Space

Downsampling (signal processing) sits in a crowded region of the domain-specific corpus (34th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08