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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'''.
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| 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]]'''.
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| The sample outputs on the right show a select block of frequencies going up the vertical axis, and time on the horizontal axis.
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| [[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.]]
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| ==Format==
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| [[Image:Spectrogram.png|thumb|right|175px|3D surface spectrogram of a part from a music piece.]]
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| 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.
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| 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.
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| ==Generation==
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| [[Image:Praat-spectrogram-tatata.png|thumb|right|175px|Spectrogram of a male voice saying 'tatata'.]]
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| [[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]]
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| 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.
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| 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>
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| 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>
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| 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>
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| : <math>\mathrm{spectrogram}(t,\omega)=\left|\mathrm{STFT}(t,\omega)\right|^2</math>
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| {{clear}}
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| ==Applications==
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| [[Image:Dolphin1.jpg|thumb|175px|Spectrogram of dolphin vocalizations; chirps, clicks and harmonizing are visible as inverted Vs, vertical lines and horizontal striations respectively]]
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| [[File:Parus major 15mars2011.ogg|left|100px|thumb|Great Tit : song]]
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| [[File:Parus major sonagram.jpg|left|100px|thumb|Spectrogram of Great Tit song]]
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| * 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.
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| * 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>
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| * 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>
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| * 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]].
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| * 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]].
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| * 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>
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| * 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>
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| * 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>
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| * 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>
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| {{clear}}
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| ==Limitations and resynthesis==
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| 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.
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| 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>
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| == See also ==
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| * [[Acoustic signature]]
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| * [[Frequency spectrum]]
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| * [[Reassignment method]]
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| * [[Short-time Fourier transform]]
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| * [[Scaleogram]]
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| * [[Spectral music]]
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| * [[Spectrometer]]
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| * [[Spectrum]]
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| * [[Strobe tuner]]
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| * [[Time-frequency representation]]
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| * [[Waterfall plot]]
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| * [[Wavelet transform]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| {{Commons category|Spectrogram}}
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| {{Wiktionary}}
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| * [http://www.audiocheck.net/audiocheck_spectrotyper.php Generating a tone sequence whose spectrogram matches an arbitrary text, online]
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| * [http://devrand.org/show_item.html?item=64&page=Project Further information on creating a signal whose spectrogram is an arbitrary image]
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| * [http://kdenlive.org/users/granjow/introducing-scopes-audio-spectrum-and-spectrogram Article describing the development of a software spectrogram]
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| * [http://www.spectrogramsforspeech.com/background/history-of-spectrograms/ History of spectrograms & development of instrumentation]
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| * [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.
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| [[Category:Acoustics]]
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| [[Category:Signal processing]]
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| [[Category:Time–frequency analysis]]
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Hello, I'm Randell, a 29 year old from Aichhorn, Austria.
My hobbies include (but are not limited to) Shooting sport, Bus spotting and watching Doctor Who.
my web blog; replica christian louboutin