Quantization_(signal_processing)

# Quantization (signal processing)  ## Microsims — p5.js ### Quantization (signal processing) (p5.js) · `round(x/Δ)` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/syiqSjPjp" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Quantization (signal processing) — p5.js microsim"></iframe> </div> *Snapping each continuous sample to the nearest of a finite set of levels — the amplitude half of digitizing.* **Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/syiqSjPjp) · movement *I · Sampling, quantization & data conversion* · library `p5js` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Communication_channel]] *(in tree)* - [[Companding]] *(in tree)* - [[Convolution]] *(in tree)* - [[Data_compression]] *(in tree)* - [[Decibel]] *(in tree)* - [[Delta_modulation]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Links (Wikipedia order)  `842_(compression_algorithm)` · `A-law_algorithm` · `Acoustic_quieting` · `Acoustics` · `Active_noise_control` · `Adaptive_Huffman_coding` · `Adaptive_coding` · `Adaptive_differential_pulse-code_modulation` · `Additive_white_Gaussian_noise` · `Advanced_z-transform` · `Algebraic_code-excited_linear_prediction` · `Aliasing` · `Analog-to-digital_converter` · `Anisotropic_diffusion` · `Anti-aliasing_filter` · `Architectural_acoustics` · `Arithmetic_coding` · `Asymmetric_numeral_systems` · `Atmospheric_noise` · `Audio_bit_depth` · `Audio_codec` · `Audio_signal_processing` · `Autoencoder` · `Automatic_gain_control` · `Average_bitrate` · `Background_noise` · `Bernard_Widrow` · `Bilateral_filter` · `Bilinear_transform` · `Biology` · `Bit_rate` · `Block-matching_and_3D_filtering` · `Brotli` · `Brownian_noise` · `Burrows–Wheeler_transform` · `Burst_noise` · `Byte-pair_encoding` · `Bzip2` · `Canonical_Huffman_code` · `Carrier-to-noise_ratio` · `Centroid` · `Chain_code` · `Channel_noise_level` · [[Chemistry]] · `Chroma_subsampling` · `Circuit_noise_level` · [[Claude_Shannon]] · `Closed-form_expression` · `Code-excited_linear_prediction` · `Coding_tree_unit` · `Color_quantization` · `Color_space` · `Colors_of_noise` · [[Communication_channel]] · [[Companding]] · `Compressed_data_structure` · `Compressed_suffix_array` · `Compression_artifact` · `Constant-Q_transform` · `Constant_bitrate` · `Context_mixing` · `Context_tree_weighting` · `Contrast-to-noise_ratio` · `Convex_hull` · [[Convolution]] · `Cosmic_noise` · `DNA` · `Data_binning` · [[Data_compression]] · `Data_compression_symmetry` · `Daubechies_wavelet` · `David_A._Huffman` · `Deadband` · `Deblocking_filter` · [[Decibel]] · `Deflate` · `Delta_encoding` · [[Delta_modulation]] · [[Detection_theory]] · `Dictionary_coder` · [[Differential_pulse-code_modulation]] · [[Digital_image_processing]] · [[Digital_signal_processing]] · `Discrete-time_Fourier_transform` · `Discrete_Fourier_transform` · [[Discrete_cosine_transform]] · `Discrete_sine_transform` · [[Discrete_time_and_continuous_time]] · [[Discrete_wavelet_transform]] · `Discretization` · `Discretization_error` · `Display_resolution` · [[Distortion]] · `Dither` · `Downsampling_(signal_processing)` · `Dynamic_Markov_compression` · [[Dynamic_range]] · `Eb/N0` · `Effective_input_noise_temperature` · [[Electron]] · [[Electronics]] · `Elias_gamma_coding` · `Embedded_zerotrees_of_wavelet_transforms` · [[Entropy_(information_theory)]] · `Entropy_coding` · `Equivalent_noise_resistance` · `Equivalent_pulse_code_modulation_noise` · [[Estimation_theory]] · `Exponential-Golomb_coding` · `Exponential_distribution` · `FM-index` · [[Fast_Fourier_transform]] · `Fibonacci_coding` · `Film_frame` · `Finite_set` · `Flicker_noise` · `Focal_Press` · `Fourier_transform` · `Fractal_compression` · `Frame_rate` · `Gary_Sullivan_(engineer)` · `Gaussian_blur` · `Gaussian_noise` · 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[[Signal-to-noise_ratio]] · `Signal-to-noise_ratio_(imaging)` · `Signal-to-quantization-noise_ratio` · `Signal_reconstruction` · `Silence_compression` · [[Sine_wave]] · `Smallest_grammar_problem` · `Snappy_(compression)` · `Sound_masking` · `Sound_quality` · `Soundproofing` · `Spectrum_analyzer` · [[Speech_coding]] · `Speech_processing` · `Springer_Science+Business_Media` · `Standard_deviation` · `Standard_test_image` · `Starred_transform` · `Stochastic` · `Sub-band_coding` · `Texture_compression` · `Thermal_radiation` · `Timeline_of_information_theory` · `Toby_Berger` · `Total_variation_denoising` · `Transform_coding` · `Triangle_wave` · `Truncation` · `Tunstall_coding` · `Unary_coding` · `Undersampling` · `Universal_code_(data_compression)` · `Upsampling` · `Value_noise` · `Variable_bitrate` · `Vector_quantization` · `Video` · `Video_codec` · `Video_compression_picture_types` · `Video_quality` · `Warped_linear_predictive_coding` · `Wavelet` · `Wavelet_transform` · `White_noise` · `Worley_noise` · [[Z-transform]] · `Zak_transform` · `Zstd` > Signal Processing concept · part of the Signal Processing Portal · movement I · !73 計算 keisan.svg ## From the Real GENERATIVE library ![Animated: Quantization (signal processing)](https://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Frequency_spectrum_of_a_sinusoid_and_its_quantization_noise_floor.gif/300px-Frequency_spectrum_of_a_sinusoid_and_its_quantization_noise_floor.gif) *Animated: Quantization (signal processing) — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Information room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Frequency_spectrum_of_a_sinusoid_and_its_quantization_noise_floor.gif).* > Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. ([Wikipedia](https://en.wikipedia.org/wiki/Quantization_%28signal_processing%29))   ## Gallery ![Quantization error](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Quantization_error.png/440px-Quantization_error.png) *Quantization error: an analog signal and its quantized version — the difference between the two is the quantization error. [Details & license](https://commons.wikimedia.org/wiki/File:Quantization_error.png)* ![2-bit resolution analog comparison](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b1/2-bit_resolution_analog_comparison.png/220px-2-bit_resolution_analog_comparison.png) *An analog signal quantized at 2-bit resolution — $2^2 = 4$ levels. [Details & license](https://commons.wikimedia.org/wiki/File:2-bit_resolution_analog_comparison.png)* ![3-bit resolution analog comparison](https://upload.wikimedia.org/wikipedia/commons/thumb/b/b7/3-bit_resolution_analog_comparison.png/220px-3-bit_resolution_analog_comparison.png) *The same signal at 3-bit resolution — $2^3 = 8$ levels; each added bit halves the step size $\Delta$. [Details & license](https://commons.wikimedia.org/wiki/File:3-bit_resolution_analog_comparison.png)* !Quantization signal processing thumb.png *Quantization — Wikitube render for this article. MTN / Wikitube.io original · CC BY-SA 4.0* !Signal processing 工動.svg *Signal processing kanji card (engines · motion-drive, 工動). MTN / Wikitube.io original · CC BY-SA 4.0* !Signal processing 工機.svg *Signal processing kanji card (engines · machine, 工機). MTN / Wikitube.io original · CC BY-SA 4.0*  ## Media (PD/CC)  !Gif Library/Quantization (signal processing)/Frequency spectrum of a sinusoid and its quantization noise floor.gif *Frequency_spectrum_of_a_sinusoid_and_its_quantization_noise_floor.gif · CC0*  ## What it is Quantization is the process of mapping a large or continuous set of amplitude values onto a smaller, finite set of discrete levels — the step that converts the continuous *amplitude* of a sampled signal into one of the countable values a digital system can store. ## How it works / why it matters A quantizer partitions the input range into intervals and assigns each interval a single representative level; with $N$ bits there are $2^N$ levels, and in a **uniform** quantizer they are equally spaced by a step size $\Delta$. Rounding each sample to its level is irreversible and introduces **quantization error** (quantization noise), whose worst case is $\pm\Delta/2$. Rounding and truncation are the typical examples of quantization processes ([Wikipedia](https://en.wikipedia.org/wiki/Quantization_%28signal_processing%29)); as a rule of thumb, each added bit of resolution lowers the quantization-noise floor by about 6 dB — unsourced this pass. Together with [[Sampling_(signal_processing)]], quantization is one of the two operations inside every analog-to-digital converter; the choice of levels (uniform vs. non-uniform, such as $\mu$-law or A-law companding) trades resolution against dynamic range and bit rate. ## Signs & universals Instantiates: discretization · amplitude · encoding · noise.  > 🔣 **Shared sign-systems** — the semiotic threads this room weaves into the rest of the Wikitube (each opens its sign-system page; the number is how many rooms that notation bridges): kanji radicals (19) · circuit symbols iec (18) · acoustic diagrams (11) · peirce sign classes (10) · chart glyph dictionary (9) · morse code (5). Edges of the **semiotic spine** · index: SEMIOTICS PORTAL.  ## Related Quantization is the amplitude counterpart of [[Sampling_(signal_processing)]] and the source of Quantization error. It is a core stage of Analog-to-digital conversion performed by the Analog-to-digital converter, is central to Pulse-code modulation, and its fidelity is measured by the Signal-to-quantization-noise ratio. Oversampling can improve effective resolution. In this room, see also the sine wave (the test signal in the quantization-noise-floor animation below), [[Signal-to-noise_ratio]], and audio data compression. --- Back to Signal Processing Portal · the room · Semiotic gateway   *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*   **Microsim — three.js (Wikitube framework), pending deploy:** *Quantization: the staircase, the error and the noise floor* will play here once `https://wikitube-3d-microsims.netlify.app/signal/Quantization_(signal_processing).html` is live.  *Built from `MICROSIM_GUIDE/specs/sims/Quantization_(signal_processing).json`; part of the [[Signal_processing]] set ([[PORTAL_Signal_Processing]]).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Quantization_%28signal_processing%29) : [Wikitube](https://en.wikitube.io/wiki/Quantization_%28signal_processing%29) ## Previous hub tags Tree parents: [[Control_theory]] · [[Information_theory]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*