Spectrogram

A spectrogram is a visual representation of the

Spectrograms are used extensively in the fields of music, linguistics, sonar, radar, speech processing,^[1] seismology, ornithology, and others. Spectrograms of audio can be used to identify spoken words phonetically, and to analyse the various calls of animals.

A spectrogram can be generated by an optical spectrometer, a bank of band-pass filters, by Fourier transform or by a wavelet transform (in which case it is also known as a scaleogram or scalogram).^[2]

A spectrogram is usually depicted as a

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 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

Spectrograms of light may be created directly using an optical spectrometer over time.

Spectrograms may be created from a

The bandpass filters method usually uses 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.^[3]

Creating a spectrogram using the FFT is a digital process. Digitally sampled 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 midpoint of the chunk). These spectrums or time plots are then "laid side by side" to form the image or a three-dimensional surface,^[4] or slightly overlapped in various ways, i.e. windowing. This process essentially corresponds to computing the squared magnitude of the short-time Fourier transform (STFT) of the signal ${\displaystyle s(t)}$ — that is, for a window width ${\displaystyle \omega }$, ${\displaystyle \mathrm {spectrogram} (t,\omega )=\left|\mathrm {STFT} (t,\omega )\right|^{2}}$.^[5]

Limitations and resynthesis

From the formula above, it appears that a spectrogram contains no information about the exact, or even approximate, 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^[6] 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

• Early analog spectrograms were applied to a wide range of areas including the study of bird calls (such as that of the
  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
  deaf^[10]
• The studies of phonetics and speech synthesis are often facilitated through the use of spectrograms.^[11][12]
• 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.^[13] 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.[14]
• High definition spectrograms are used in the development of RF and microwave systems^[15]
• Spectrograms are now used to display scattering parameters measured with vector network analyzers^[16]
• The US Geological Survey and the IRIS Consortium provide near real-time spectrogram displays for monitoring seismic stations^[17][18]
• Spectrograms can be used with recurrent neural networks for speech recognition.^[19][20]
• Individuals' spectrograms are collected by the Chinese government as part of its mass surveillance programs.^[21]
• 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. ^[22]
• 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. ^[23]
• 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 speakers' pronunciation from a linear superposition of short-time spectrograms.^[24]
• 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.^[25]
• 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. ^[26]
• 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. ^[27]

See also

References

External links

Wikimedia Commons has media related to Spectrogram.

Look up spectrogram in Wiktionary, the free dictionary.

• See an online spectrogram of speech or other sounds captured by your computer's microphone.
• Generating a tone sequence whose spectrogram matches an arbitrary text, online
• Further information on creating a signal whose spectrogram is an arbitrary image
• Article describing the development of a software spectrogram
• History of spectrograms & development of instrumentation
• How to identify the words in a spectrogram from a linguistic professor's Monthly Mystery Spectrogram publication.
• Sonogram Visible Speech GPL Licensed freeware for the Spectrogram generation of Signal Files.