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[[Image:Spectrogram-19thC.png|thumb|right|175px|Typical spectrogram of the spoken words "nineteenth century".  The lower frequencies are more dense because it is a male voice. The legend to the right shows that the color intensity increases with the density.]]
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A '''spectrogram''', or '''sonogram''', is a visual representation of the [[spectral density|spectrum]] of frequencies in a sound or other signal as they vary with time or some other variable. Spectrograms are sometimes called  '''spectral waterfalls''', '''voiceprints''', or '''voicegrams'''.


Spectrograms can be used to identify spoken words [[phonetics|phonetic]]ally, and to analyse the various calls of animals. They are used extensively in the development of the fields of [[music]], [[sonar]], [[radar]], and [[speech processing]],<ref>JL Flanagan, Speech Analysis, Synthesis and Perception, Springer- Verlag, New York, 1972</ref> [[seismology]], etc.
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The instrument that generates a spectrogram is called a '''[[spectrograph]]'''.
The sample outputs on the right show a select block of frequencies going up the vertical axis, and time on the horizontal axis.
[[Image:Spectrogram of violin.png|thumb|175px|Spectrogram of [[media:Violin for spectrogram.ogg|the actual recording of this violin playing]]. Note the harmonics occurring at whole-number multiples of the fundamental frequency.  Note the fourteen draws of the bow, and the visual differences in the tones.]]
 
==Format==
[[Image:Spectrogram.png|thumb|right|175px|3D surface spectrogram of a part from a music piece.]]
A common format is a graph with two geometric dimensions: the horizontal axis represents [[time]] or rpm, the vertical axis is [[frequency]]; a third dimension indicating the [[amplitude]] of a particular frequency at a particular time is represented by the [[Brightness|intensity]] or colour 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 the amplitude is represented as the 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.
 
==Generation==
[[Image:Praat-spectrogram-tatata.png|thumb|right|175px|Spectrogram of a male voice saying 'tatata'.]]
[[Image:VariableFrequency.jpg|thumb|right|175px|Spectrogram of an [[Frequency modulation|FM]] signal.  In this case the signal [[frequency]] is modulated with a [[sinusoidal]] frequency vs. time profile]]
Spectrograms are usually created in one of two ways: approximated as a filterbank that results from a series of [[bandpass filter]]s (this was the only way before the advent of modern digital signal processing), or calculated from the time signal using the [[FFT]]. These two methods actually form two different Time-Frequency Distributions, 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>[http://www.sfu.ca/sonic-studio/handbook/Spectrograph.html Illustration of an electro-mechanical spectrograph]</ref>
 
Creating a spectrogram using the FFT is a [[digital (signal)|digital]] process. Digitally [[sample (signal)|sample]]d data, in the 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 spectrums or time plots are then "laid side by side" to form the image or a three-dimensional surface.<ref>[http://ccrma-www.stanford.edu/~jos/mdft/Spectrograms.html Spectrogram definition]</ref>
 
The spectrogram of a signal s(t) can be estimated by computing the squared [[magnitude (mathematics)|magnitude]] of the [[STFT]] of the signal s(t), as follows:<ref>[http://zone.ni.com/reference/en-XX/help/371361E-01/lvanls/stft_spectrogram_core/#details STFT spectrogram details]</ref>
 
: <math>\mathrm{spectrogram}(t,\omega)=\left|\mathrm{STFT}(t,\omega)\right|^2</math>
 
{{clear}}
 
==Applications==
[[Image:Dolphin1.jpg|thumb|175px|Spectrogram of dolphin vocalizations; chirps, clicks and harmonizing are visible as inverted Vs, vertical lines and horizontal striations respectively]]
[[File:Parus major 15mars2011.ogg|left|100px|thumb|Great Tit : song]]
[[File:Parus major sonagram.jpg|left|100px|thumb|Spectrogram of Great Tit song]]
 
* 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>[http://www.birdsongs.it/index.asp Bird Songs and Spectrograms of Southern Tuscany]</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 clicks, and social harmonizing are most easily visualized with the spectrogram.
* Spectrograms are useful in assisting in overcoming speech defects and in speech training for the portion of the population that is profoundly [[hearing impairment|deaf]]<ref>[http://www.springerlink.com/content/uv377604u5617x01/ A wearable tactile sensory aid for profoundly deaf children]</ref>
* The studies of [[phonetics]] and [[speech synthesis]] are often facilitated through the use of spectrograms.<ref>[http://cslu.cse.ogi.edu/tutordemos/SpectrogramReading/spectrogram_reading.html Spectrogram Reading]</ref><ref>[http://www.fon.hum.uva.nl/praat/ Praat - doing phonetics by computer]</ref>
* 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>[http://www.bastwood.com/aphex.php Several sound spectrogram examples, including the one by Aphex Twin]</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>[http://src.infinitewave.ca Example of using spectrograms to check filter responses]</ref>
* High definition spectrograms are used in the development of RF and microwave systems<ref>[http://www.constantwave.com/gallery.aspx High definition spectrograms of common RF signals]</ref>
* Spectrograms are now used to display S-parameters measured with vector network analyzers<ref>[http://www.constantwave.com/spectro_vna.aspx Spectrograms for vector network analyzers]</ref>
* The [[United States Geological Survey|US Geological Survey]] now provides real-time spectrogram displays from seismic stations<ref>[http://earthquake.usgs.gov/monitoring/spectrograms/24hr/ Real-time spectrogram displays from seismic stations]</ref>
 
{{clear}}
 
==Limitations and resynthesis==
From the formula above, it appears that a spectrogram contains no information about the exact [[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 [http://arss.sourceforge.net] is an example of a computer program that attempts to do this. The [[pattern playback|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#Instantaneous_frequency|Instantaneous Frequency]]; an experiment explaining and relating these two concepts is described in.<ref>B. Boashash, "Estimating and Interpreting the Instantaneous Frequency of a Signal-Part I: Fundamentals", Proceedings of the IEEE, Vol. 80, No. 4, pp. 519-538, April 1992, {{doi|10.1109/5.135376}}</ref>
 
== See also ==
 
* [[Acoustic signature]]
* [[Frequency spectrum]]
* [[Reassignment method]]
* [[Short-time Fourier transform]]
* [[Scaleogram]]
* [[Spectral music]]
* [[Spectrometer]]
* [[Spectrum]]
* [[Strobe tuner]]
* [[Time-frequency representation]]
* [[Waterfall plot]]
* [[Wavelet transform]]
 
==References==
{{reflist}}
 
==External links==
{{Commons category|Spectrogram}}
{{Wiktionary}}
* [http://www.audiocheck.net/audiocheck_spectrotyper.php Generating a tone sequence whose spectrogram matches an arbitrary text, online]
* [http://devrand.org/show_item.html?item=64&page=Project Further information on creating a signal whose spectrogram is an arbitrary image]
* [http://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.
 
[[Category:Acoustics]]
[[Category:Signal processing]]
[[Category:Time–frequency analysis]]

Revision as of 23:29, 7 February 2014

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