Discrete_cosine_transform

# Discrete cosine transform  ## Microsims — p5.js ### Discrete cosine transform (p5.js) · `DCT` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/Xr0wpSfoW" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Discrete cosine transform — p5.js microsim"></iframe> </div> *A real-valued cousin of the DFT that packs signal energy into few coefficients — the engine of JPEG and MP3.* **Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/Xr0wpSfoW) · movement *II · Transforms & the frequency domain* · library `p5js` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Companding]] *(in tree)* - [[Convolution]] *(in tree)* - [[Data_compression]] *(in tree)* - [[Delta_modulation]] *(in tree)* - [[Detection_theory]] *(in tree)* - [[Differential_pulse-code_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)  `.m2ts` · `3GPP` · `3GP_and_3G2` · `842_(compression_algorithm)` · `A-law_algorithm` · `AAC-LD` · `AMV_video_format` · `APNG` · `ARPANET` · `ATSC_3.0` · `AV1` · `AV2` · `AVIF` · `Academic_Press` · `Adaptive_Huffman_coding` · `Adaptive_Multi-Rate_Wideband` · `Adaptive_Multi-Rate_audio_codec` · `Adaptive_coding` · `Adaptive_differential_pulse-code_modulation` · `Advanced_Audio_Coding` · `Advanced_Systems_Format` · `Advanced_Video_Coding` · `Advanced_z-transform` · `Alexander_Graham_Bell` · `Alfred_Vail` · `Algebraic_code-excited_linear_prediction` · `Algebraic_signal_processing` · `Aliasing` · `Alliance_for_Open_Media` · `Almon_Brown_Strowger` · `Amos_Dolbear` · `Amplitude` · `Android_(operating_system)` · `Animation` · `Anti-aliasing_filter` · `Antonio_Meucci` · `Apple_Inc.` · `Apple_Lossless_Audio_Codec` · `Apple_ProRes` · `Apple_Video` · `Apple_community` · `AptX` · `Arithmetic_coding` · `Artist` · `Asao_(codec)` · 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· [[Data_compression]] · `Data_compression_ratio` · `Data_compression_symmetry` · `Data_extraction` · `Daubechies_wavelet` · `David_A._Huffman` · `Dawon_Kahng` · `Deblocking_filter` · `Deflate` · `Delta_encoding` · [[Delta_modulation]] · [[Detection_theory]] · `Dictionary_coder` · [[Differential_pulse-code_modulation]] · `Digital_Audio_Broadcasting` · `Digital_Radio_Mondiale` · `Digital_Signal_Processing_(journal)` · `Digital_Video_Interactive` · `Digital_audio` · `Digital_audio_radio_service` · `Digital_camera` · `Digital_cinema` · `Digital_cinematography` · `Digital_distribution` · `Digital_electronics` · `Digital_image` · [[Digital_image_processing]] · `Digital_imaging` · `Digital_media` · `Digital_photography` · `Digital_radio` · [[Digital_signal_processing]] · `Digital_signal_processor` · `Digital_television` · `Digital_video` · `Digital_watermarking` · `Dihedral_group` · `Dirac_(video_compression_format)` · `Discrete-time_Fourier_transform` · `Discrete_Fourier_transform` · 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`Even_and_odd_functions` · `Event_data_recorder` · `Exponential-Golomb_coding` · `Extended_Adaptive_Multi-Rate_–_Wideband` · `FFTPACK` · `FFV1` · `FLAC` · `FM-index` · `FaceTime` · `Face_detection` · `Facial_recognition_system` · [[Fast_Fourier_transform]] · `Fastest_Fourier_Transform_in_the_West` · `Fax` · `Fiber-optic_communication` · `Fibonacci_coding` · `FidoNet` · `Film` · `Film_editing` · `Film_frame` · `Filter_(signal_processing)` · `Fingerprint` · `Flash_Video` · `Focus_(optics)` · `Fourier_series` · `Fourier_transform` · `Fractal_compression` · `Frame_rate` · `Francis_Blake_(inventor)` · `Free-space_optical_communication` · `Free_Lossless_Image_Format` · `Frequency-division_multiplexing` · `Full_Rate` · `Function_(mathematics)` · `G.711` · `G.718` · `G.719` · `G.722` · `G.722.1` · `G.723` · `G.723.1` · `G.726` · `G.728` · `G.729` · `G.729.1` · `GIF` · `Gardiner_Greene_Hubbard` · `General_Exchange_Format` · `Glitch_art` · `Golomb_coding` · `Google` · `Grammar-based_code` · 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`Image_analysis` · [[Image_compression]] · `Image_file_format` · `Image_noise` · `Image_resolution` · `Image_segmentation` · `Image_texture` · `Impulse_invariance` · `Incremental_encoding` · `Indeo` · `Information_Age` · [[Information_theory]] · `Innocenzo_Manzetti` · `Inpainting` · `Institute_of_Electrical_and_Electronics_Engineers` · `Institution_of_Engineering_and_Technology` · `Integer` · [[Integral_transform]] · `Integrated_circuit` · `Interchange_File_Format` · `Interlaced_video` · `International_Electrotechnical_Commission` · `International_Organization_for_Standardization` · `Internet` · `Internet2` · `Internet_Engineering_Task_Force` · `Internet_Low_Bitrate_Codec` · `Internet_Speech_Audio_Codec` · `Internet_video` · `Interpolation` · `Intra-frame_coding` · `JANET` · `JBIG` · `JBIG2` · `JPEG` · `JPEG_2000` · `JPEG_XL` · `JPEG_XR` · `JPEG_XS` · `JPEG_XT` · `Jagadish_Chandra_Bose` · `Johann_Philipp_Reis` · `John_Bardeen` · `John_Logie_Baird` · `Joint_Photographic_Experts_Group` · 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`Windows_Media` · `Windows_Media_Audio` · `Windows_Media_Video` · `Wireless` · `Wireless_Application_Protocol_Bitmap_Format` · `Wireless_network` · `Wireless_sensor_network` · `World_Scientific` · `World_Wide_Web` · `World_Wide_Web_Consortium` · `YIQ` · `YULS` · `YouTube` · [[Z-transform]] · `Zak_transform` · `Zstd` · `École_Polytechnique_Fédérale_de_Lausanne` > Signal Processing concept · part of the Signal Processing Portal · movement II · !31 変換 henkan.svg  !480 *Rendered from the live microsim (▶ motion).*  ## See it next [![Discrete-time Fourier transform|200](Discrete-time_Fourier_transform_thumb.png)](Discrete-time_Fourier_transform) *→ Discrete-time Fourier transform*  --- Back to Signal Processing Portal · the room · Semiotic gateway  ## From the Real GENERATIVE library ![Animated: Discrete cosine transform](https://upload.wikimedia.org/wikipedia/commons/5/5e/Idct-animation.gif) *Animated: Discrete cosine transform — 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:Idct-animation.gif).* > A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. ([Wikipedia](https://en.wikipedia.org/wiki/Discrete_cosine_transform))  ## Media (PD/CC)  !Gif Library/Discrete cosine transform/Idct-animation.gif *Idct-animation.gif · Hanakus · CC BY-SA 3.0 · [source](https://commons.wikimedia.org/wiki/File:Idct-animation.gif)*  ## What it is The discrete cosine transform expresses a finite sequence of samples as a weighted sum of cosine functions oscillating at different frequencies, using only real-valued cosine basis functions. ## How it works / why it matters The widely used DCT-II computes X_k = sum over n of x_n cos[(pi/N)(n+1/2)k], and because it implicitly assumes an even (mirror) extension of the signal it concentrates most of a natural signal's energy into a few low-frequency coefficients, giving strong energy compaction. This property makes it the mathematical core of lossy compression standards such as JPEG for images and MP3 or AAC for audio. ## Signs & universals Instantiates: transformation, frequency, spectrum. ## Related See Discrete-time Fourier transform, [[Fast_Fourier_transform]], [[Discrete_wavelet_transform]], Fourier transform, Discrete Fourier transform, and [[Fourier_analysis]].   *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Discrete_cosine_transform) : [Wikitube](https://en.wikitube.io/wiki/Discrete_cosine_transform) ## Previous hub tags Tree parent: [[Information_theory]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*