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{{short description|Visual representation of the spectrum of frequencies of a signal as it varies with time}}
{{redirect|Sonograph|the musical recording|Sonograph (EP)}}
{{for|the scientific instrument|Optical spectrograph}}
[[Image:Spectrogram-19thC.png|thumb|upright=1.35|Spectrogram of the spoken words "nineteenth century". Frequencies are shown increasing up the vertical axis, and time on the horizontal axis. The legend to the right shows that the color intensity increases with the density.]]
[[File:3D battery charger RF spectrum over time.jpg|thumb|upright=1.35|A 3D spectrogram: The RF spectrum of a battery charger is shown over time]]
When applied to an [[audio signal]], spectrograms are sometimes called '''sonographs''', '''voiceprints''', or '''voicegrams'''. When the data are represented in a 3D plot they may be called ''[[waterfall display]]s''.
Spectrograms are used
A spectrogram can be generated by an [[optical spectrometer]], a bank of [[band-pass filter]]s, by [[Fourier transform]] or by a [[wavelet transform]] (in which case it is also known as a '''scaleogram''' or '''scalogram''').<ref>{{Cite journal|last1=Sejdic|first1=E.|last2=Djurovic|first2=I.|last3=Stankovic|first3=L.|date=August 2008|title=Quantitative Performance Analysis of Scalogram as Instantaneous Frequency Estimator|journal=IEEE Transactions on Signal Processing|volume=56|issue=8|pages=3837–3845|doi=10.1109/TSP.2008.924856|bibcode=2008ITSP...56.3837S|s2cid=16396084|issn=1053-587X}}</ref>
[[Image:Scaleogram.png|thumb|250px|Scaleograms from the [[discrete wavelet transform|DWT]] and [[continuous wavelet transform|CWT]] for an audio sample]]
A spectrogram is usually depicted as a [[heat map]], i.e., as an image with the intensity shown by varying the [[colour]] or [[brightness]].
==Format==
A common format is a graph with two geometric dimensions: one axis represents [[time]], and the other axis represents [[frequency]]; a third dimension indicating the [[amplitude]] of a particular frequency at a particular time is represented by the [[Brightness|intensity]] or color of each point in the image.
There are many variations of format: sometimes the vertical and horizontal axes are switched, so time runs up and down; sometimes as a [[waterfall plot]] where the amplitude is represented by height of a 3D surface instead of color or intensity. The frequency and amplitude axes can be either [[linear]] or [[logarithm]]ic, depending on what the graph is being used for. Audio would usually be represented with a logarithmic amplitude axis (probably in [[decibel]]s, or dB), and frequency would be linear to emphasize harmonic relationships, or logarithmic to emphasize musical, tonal relationships.
{{Gallery
|mode=packed
|height=120
|File:Spectrogram of violin.png|Spectrogram of [[media:Violin for spectrogram.ogg|this recording of a violin playing]]. Note the harmonics occurring at whole-number multiples of the fundamental frequency.
|File:Spectrogram.png|3D surface spectrogram of a part from a music piece.
|File:Praat-spectrogram-tatata.png|Spectrogram of a male voice saying 'ta ta ta'.
|File:Dolphin1.jpg|alt6=|Spectrogram of dolphin vocalizations; chirps, clicks and harmonizing are visible as inverted Vs, vertical lines and horizontal striations respectively.
|File:VariableFrequency.jpg|Spectrogram of an [[Frequency modulation|FM]] signal. In this case the signal [[frequency]] is modulated with a [[sinusoidal]] frequency vs. time profile.
|File:PAL-I.png|Spectrum above and waterfall (Spectrogram) below of an 8MHz wide [[PAL]]-I Television signal.
|File:Parus major sonagram.jpg|Spectrogram of [[media:Parus major 15mars2011.ogg|great tit song]].
|File:GW170817 Gravitational Wave Chirp Spectrogram.jpg|alt8=|[[Constant-Q transform|Constant-Q]] spectrogram of a gravitational wave ([[GW170817]]).
|File:Waterfall_plot_of_a_whistle.png|alt9=|Spectrogram and waterfalls of 3 whistled notes.
|File:Mount Rainier soundscape.jpg|Spectrogram of the [[soundscape ecology]] of [[Mount Rainier National Park]], with the sounds of different creatures and aircraft highlighted
|File:SonogramVisibleSpeech.png|Spectrogram (generated with the freeware [https://github.com/Christoph-Lauer/Sonogram-Visible-Speech Sonogram visible Speech]).
|File:CQT-piano-chord.png|[[Variable-Q transform]] spectrogram of a piano chord (generated using [[FFmpeg]]'s showcqt filter).
}}[[File:Sound spectrography of infrasound recording 30301.webm|thumb|Sound spectrography of infrasound recording 30301]]
==Generation==
Spectrograms of light may be created directly using an [[optical spectrometer]] over time.
Spectrograms may be created from a [[time-___domain]] signal in one of two ways: approximated as a filterbank that results from a series of [[band-pass filter]]s (this was the only way before the advent of modern digital signal processing), or calculated from the time signal using the [[Fourier transform]]. These two methods actually form two different [[time–frequency representation]]s, but are equivalent under some conditions.
The bandpass filters method usually uses [[analog signal|analog]] processing to divide the input signal into frequency bands; the magnitude of each filter's output controls a transducer that records the spectrogram as an image on paper.<ref>{{cite web|url=https://www.sfu.ca/sonic-studio/handbook/Spectrograph.html|title=Spectrograph|website=www.sfu.ca|access-date=7 April 2018}}</ref>
Creating a spectrogram using the FFT is a [[Digital signal processing|digital process]]. Digitally [[sampling (signal processing)|sampled]] data, in the [[Time series|time ___domain]], is broken up into chunks, which usually overlap, and Fourier transformed to calculate the magnitude of the frequency spectrum for each chunk. Each chunk then corresponds to a vertical line in the image; a measurement of magnitude versus frequency for a specific moment in time (the midpoint of the chunk). These spectrums or time plots are then "laid side by side" to form the image or a three-dimensional surface,<ref>{{cite web|url=https://ccrma.stanford.edu/~jos/mdft/Spectrograms.html|title=Spectrograms|website=ccrma.stanford.edu|access-date=7 April 2018}}</ref> or slightly overlapped in various ways, i.e. [[Window function#Overlapping windows|windowing]]. This process essentially corresponds to computing the squared [[magnitude (mathematics)|magnitude]] of the [[short-time Fourier transform]] (STFT) of the signal <math>s(t)</math> — that is, for a window width <math>\omega</math>, <math>\mathrm{spectrogram}(t,\omega)=\left|\mathrm{STFT}(t,\omega)\right|^2</math>.<ref>{{cite web|url=http://zone.ni.com/reference/en-XX/help/371361E-01/lvanls/stft_spectrogram_core/#details|title=STFT Spectrograms VI – NI LabVIEW 8.6 Help|website=zone.ni.com|access-date=7 April 2018}}</ref>
==Limitations and resynthesis==
From the formula above, it appears that a spectrogram contains no information about the exact, or even approximate, [[Phase (waves)|phase]] of the signal that it represents. For this reason, it is not possible to reverse the process and generate a copy of the original signal from a spectrogram, though in situations where the exact initial phase is unimportant it may be possible to generate a useful approximation of the original signal. The Analysis & Resynthesis Sound Spectrograph<ref>{{cite web|url=http://arss.sourceforge.net|title=The Analysis & Resynthesis Sound Spectrograph|website=arss.sourceforge.net|access-date=7 April 2018}}</ref> is an example of a computer program that attempts to do this. The [[pattern playback]] was an early speech synthesizer, designed at [[Haskins Laboratories]] in the late 1940s, that converted pictures of the acoustic patterns of speech (spectrograms) back into sound.
In fact, there is some phase information in the spectrogram, but it appears in another form, as time delay (or [[group delay]]) which is the [[Dual (mathematics)|dual]] of the [[instantaneous frequency]].<ref name="Boashash1992">{{cite journal | last=Boashash | first=B. | title=Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals | journal=Proceedings of the IEEE | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=80 | issue=4 | year=1992 | issn=0018-9219 | doi=10.1109/5.135376 | pages=520–538}}</ref>
The size and shape of the analysis window can be varied. A smaller (shorter) window will produce more accurate results in timing, at the expense of precision of frequency representation. A larger (longer) window will provide a more precise frequency representation, at the expense of precision in timing representation. This is an instance of the [[Heisenberg uncertainty principle]], that the product of the precision in two [[conjugate variables]] is greater than or equal to a constant (B*T>=1 in the usual notation).<ref>{{Cite web |url=http://fourier.eng.hmc.edu/e161/lectures/fourier/node2.html |title=Heisenberg Uncertainty Principle |access-date=2019-02-05 |archive-date=2019-01-25 |archive-url=https://web.archive.org/web/20190125182117/http://fourier.eng.hmc.edu/e161/lectures/fourier/node2.html |url-status=dead }}</ref>
==Applications==
* Early analog spectrograms were applied to a wide range of areas including the study of bird calls (such as that of the [[great tit]]), with current research continuing using modern digital equipment<ref>{{cite web|url=http://www.birdsongs.it/index.asp|title=BIRD SONGS AND CALLS WITH SPECTROGRAMS ( SONOGRAMS ) OF SOUTHERN TUSCANY ( Toscana – Italy )|website=www.birdsongs.it|access-date=7 April 2018}}</ref> and applied to all animal sounds. Contemporary use of the digital spectrogram is especially useful for studying [[frequency modulation]] (FM) in animal calls. Specifically, the distinguishing characteristics of FM chirps, broadband [[Clicking noise|clicks]], and social harmonizing are most easily visualized with the spectrogram.
* Spectrograms are useful in assisting in overcoming speech deficits and in speech training for the portion of the population that is profoundly [[hearing impairment|deaf]].<ref>{{cite journal|title=A wearable tactile sensory aid for profoundly deaf children|first1=Frank A.|last1=Saunders|first2=William A.|last2=Hill|first3=Barbara|last3=Franklin|date=1 December 1981|journal=Journal of Medical Systems|volume=5|issue=4|pages=265–270|doi=10.1007/BF02222144|pmid=7320662|s2cid=26620843}}</ref>
* The studies of [[phonetics]] and [[speech synthesis]] are often facilitated through the use of spectrograms.<ref>{{cite web|url=http://cslu.cse.ogi.edu/tutordemos/SpectrogramReading/spectrogram_reading.html|title=Spectrogram Reading|website=ogi.edu|access-date=7 April 2018|url-status=dead|archive-url=https://web.archive.org/web/19990427185722/http://cslu.cse.ogi.edu/tutordemos/SpectrogramReading/spectrogram_reading.html |archive-date=27 April 1999}}</ref><ref>{{cite web|url=http://www.fon.hum.uva.nl/praat/|title=Praat: doing Phonetics by Computer|website=www.fon.hum.uva.nl|access-date=7 April 2018}}</ref>
* In deep learning-keyed speech synthesis, spectrogram (or spectrogram in [[mel scale]]) is first predicted by a seq2seq model, then the spectrogram is fed to a neural vocoder to derive the synthesized raw waveform.
* By reversing the process of producing a spectrogram, it is possible to create a signal whose spectrogram is an arbitrary image. This technique can be used to hide a picture in a piece of audio and has been employed by several [[electronic music]] artists.<ref>{{cite web|url=http://www.bastwood.com/aphex.php|title=The Aphex Face – bastwood|website=www.bastwood.com|access-date=7 April 2018}}</ref> See also [[Steganography]].
* Some modern music is created using spectrograms as an intermediate medium; changing the intensity of different frequencies over time, or even creating new ones, by drawing them and then inverse transforming. See [[Audio timescale-pitch modification]] and [[Phase vocoder]].
* Spectrograms can be used to analyze the results of passing a test signal through a signal processor such as a filter in order to check its performance.<ref>{{cite web|url=http://src.infinitewave.ca|title=SRC Comparisons|website=src.infinitewave.ca|access-date=7 April 2018}}</ref>
* High definition spectrograms are used in the development of RF and microwave systems.<ref>{{cite web|url=http://www.constantwave.com/gallery.aspx|title=constantwave.com – constantwave Resources and Information.|website=www.constantwave.com|access-date=7 April 2018}}</ref>
* Spectrograms are now used to display [[scattering parameters]] measured with vector network analyzers.<ref>{{cite web |url=http://www.constantwave.com/spectro_vna.aspx |title=Spectrograms for vector network analyzers |archive-url=https://web.archive.org/web/20120810020043/http://www.constantwave.com/spectro_vna.aspx |archive-date=2012-08-10 |url-status=dead }}</ref>
* The [[United States Geological Survey|US Geological Survey]] and the [[IRIS Consortium]] provide near real-time spectrogram displays for monitoring seismic stations.<ref>{{cite web|url=https://earthquake.usgs.gov/monitoring/spectrograms/24hr/|title=Real-time Spectrogram Displays|website=earthquake.usgs.gov|access-date=7 April 2018}}</ref><ref>{{Cite web|url=https://service.iris.edu/mustang/noise-spectrogram/docs/1/help/|title=IRIS: MUSTANG: Noise-Spectrogram: Docs: v. 1: Help}}</ref>
* Spectrograms can be used with [[recurrent neural network]]s for [[speech recognition]].<ref>{{Cite web|url=https://medium.com/@ageitgey/machine-learning-is-fun-part-6-how-to-do-speech-recognition-with-deep-learning-28293c162f7a|title=Machine Learning is Fun Part 6: How to do Speech Recognition with Deep Learning|last=Geitgey|first=Adam|date=2016-12-24|website=Medium|access-date=2018-03-21}}</ref><ref>See also [[Praat]].</ref>
* Individuals' spectrograms are collected by the [[Government of China|Chinese government]] as part of its [[Mass surveillance in China|mass surveillance]] programs.<ref>{{Cite news |date=November 23, 2023 |title=China's enormous surveillance state is still growing |newspaper=[[The Economist]] |url=https://www.economist.com/china/2023/11/23/chinas-enormous-surveillance-state-is-still-growing |url-access=subscription |access-date=2023-11-25 |issn=0013-0613}}</ref>
* For a vibration signal, a spectrogram's color scale identifies the frequencies of a waveform's amplitude peaks over time. Unlike a time or frequency graph, a spectrogram correlates peak values to time and frequency. Vibration test engineers use spectrograms to analyze the frequency content of a continuous waveform, locating strong signals and determining how the vibration behavior changes over time.<ref>{{Cite web|url=https://vibrationresearch.com/blog/what-is-a-spectrogram/|title=What is a Spectrogram? | access-date=2023-12-18}}</ref>
* Spectrograms can be used to analyze speech in two different applications: automatic detection of speech deficits in cochlear implant users and phoneme class recognition to extract phone-attribute features.<ref>{{cite journal|title=Multi-channel spectrograms for speech processing applications using deep learning methods|first1=Arias-Vergara |last1= T. |first2= Klumpp|last2=P.|first3= Vasquez-Correa|last3=J. C.|first4=Nöth|last4=E. |first5= Orozco-Arroyave|last5=J. R. |first6=Schuster |last6=M. |date=2021|journal=Pattern Analysis and Applications|volume=24 |issue=2 |pages=423–431 |doi=10.1007/s10044-020-00921-5 |doi-access=free}}</ref>
* In order to obtain a speaker's pronunciation characteristics, some researchers proposed a method based on an idea from bionics, which uses spectrogram statistics to achieve a characteristic spectrogram to give a stable representation of the speaker's pronunciation from a linear superposition of short-time spectrograms.<ref>{{cite journal|title=Speaker recognition based on characteristic spectrograms and an improved self-organizing feature map neural network|first1=Yanjie |last1= Jia |first2= Xi|last2=Chen|first3= Jieqiong|last3=Yu|first4=Lianming|last4=Wang|first5= Yuanzhe|last5= Xu |first6=Shaojin |last6=Liu |first7=Yonghui |last7=Wang |date=2021|journal=Complex & Intelligent Systems|volume=7 |issue=4 |pages=1749–1757 |doi=10.1007/s40747-020-00172-1 |doi-access=free}}</ref>
* Researchers explore a novel approach to ECG signal analysis by leveraging spectrogram techniques, possibly for enhanced visualization and understanding. The integration of MFCC for feature extraction suggests a cross-disciplinary application, borrowing methods from audio processing to extract relevant information from biomedical signals.<ref>{{cite journal|url=https://link.springer.com/article/10.1007/s12652-021-02926-2|title=Spectrogram analysis of ECG signal and classification efficiency using MFCC feature extraction technique|first1=Arpitha |last1= Yalamanchili |first2= G. L.|last2=Madhumathi |first3= N.|last3=Balaji |date=2022|journal=Journal of Ambient Intelligence and Humanized Computing|volume=13 |issue=2 |pages=757–767 |doi=10.1007/s12652-021-02926-2 |s2cid=233657057 |url-access=subscription }}</ref>
* Accurate interpretation of temperature indicating paint (TIP) is of great importance in aviation and other industrial applications. 2D spectrogram of TIP can be used in temperature interpretation.<ref>{{cite journal|url=https://www.sciencedirect.com/science/article/pii/S0263224123008813|title=Temperature interpretation method for temperature indicating paint based on spectrogram|first1=Junfeng |last1= Ge |first2= Li|last2=Wang |first3= Kang|last3=Gui |first4= Lin|last4=Ye |date=30 September 2023|journal=Measurement|volume=219 |doi=10.1016/j.measurement.2023.113317 |bibcode=2023Meas..21913317G |s2cid=259871198 |url-access=subscription }}</ref>
* The spectrogram can be used to process the signal for the rate of change of the human thorax. By visualizing respiratory signals using a spectrogram, the researchers have proposed an approach to the classification of respiration states based on a neural network model.<ref>{{cite journal|title=Classification of Respiratory States Using Spectrogram with Convolutional Neural Network|first1=Cheolhyeong |last1= Park |first2= Deokwoo|last2=Lee |date=11 February 2022|journal=Applied Sciences|volume=12 |issue=4 |page=1895 |doi=10.3390/app12041895 |doi-access=free }}</ref>
{{clear}}
== See also ==
{{div col|colwidth=20em}}
* [[Acoustic signature]]
* [[Chromagram]]
* [[Fourier analysis]] for computing periodicity in evenly spaced data
* [[Generalized spectrogram]]
* [[Least-squares spectral analysis]] for computing periodicity in unevenly spaced data
* [[List of unexplained sounds]]
* [[Reassignment method]]
* [[Spectral music]]
* [[Spectrometer]]
* [[Strobe tuner]]
* [[Waveform]]
{{div col end}}
==References==
{{reflist}}
==External links==
{{Commons category|Spectrograms}}
{{Wiktionary}}
*[https://auditoryneuroscience.com/acoustics/spectrogram See an online spectrogram of speech or other sounds captured by your computer's microphone.]
* [http://www.audiocheck.net/audiocheck_spectrotyper.php Generating a tone sequence whose spectrogram matches an arbitrary text, online]
* [https://web.archive.org/web/20110725231858/http://devrand.org/show_item.html?item=64&page=Project Further information on creating a signal whose spectrogram is an arbitrary image]
* [https://web.archive.org/web/20120331164713/https://kdenlive.org/users/granjow/introducing-scopes-audio-spectrum-and-spectrogram Article describing the development of a software spectrogram]
* [http://www.spectrogramsforspeech.com/background/history-of-spectrograms/ History of spectrograms & development of instrumentation]
* [http://home.cc.umanitoba.ca/~robh/howto.html How to identify the words in a spectrogram] from a linguistic professor's ''Monthly Mystery Spectrogram'' publication.
* [https://github.com/Christoph-Lauer/Sonogram Sonogram Visible Speech] GPL Licensed freeware for the Spectrogram generation of Signal Files.
[[Category:Acoustic measurement]]
[[Category:Signal processing]]
[[Category:Time–frequency analysis]]
[[Category:Spectrum (physical sciences)]]
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