Products
  • Wolfram|One

    The definitive Wolfram Language and notebook experience

  • Mathematica

    The original technical computing environment

  • Wolfram Notebook Assistant + LLM Kit

    All-in-one AI assistance for your Wolfram experience

  • System Modeler
  • Wolfram Player
  • Finance Platform
  • Wolfram Engine
  • Enterprise Private Cloud
  • Application Server
  • Wolfram|Alpha Notebook Edition
  • Wolfram Cloud App
  • Wolfram Player App

More mobile apps

Core Technologies of Wolfram Products

  • Wolfram Language
  • Computable Data
  • Wolfram Notebooks
  • AI & Linguistic Understanding

Deployment Options

  • Wolfram Cloud
  • wolframscript
  • Wolfram Engine Community Edition
  • Wolfram LLM API
  • WSTPServer
  • Wolfram|Alpha APIs

From the Community

  • Function Repository
  • Community Paclet Repository
  • Example Repository
  • Neural Net Repository
  • Prompt Repository
  • Wolfram Demonstrations
  • Data Repository
  • Group & Organizational Licensing
  • All Products
Consulting & Solutions

We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technical expertise

  • Data & Computational Intelligence
  • Model-Based Design
  • Algorithm Development
  • Wolfram|Alpha for Business
  • Blockchain Technology
  • Education Technology
  • Quantum Computation

WolframConsulting.com

Wolfram Solutions

  • Data Science
  • Artificial Intelligence
  • Biosciences
  • Healthcare Intelligence
  • Sustainable Energy
  • Control Systems
  • Enterprise Wolfram|Alpha
  • Blockchain Labs

More Wolfram Solutions

Wolfram Solutions For Education

  • Research Universities
  • Colleges & Teaching Universities
  • Junior & Community Colleges
  • High Schools
  • Educational Technology
  • Computer-Based Math

More Solutions for Education

  • Contact Us
Learning & Support

Get Started

  • Wolfram Language Introduction
  • Fast Intro for Programmers
  • Fast Intro for Math Students
  • Wolfram Language Documentation

More Learning

  • Highlighted Core Areas
  • Demonstrations
  • YouTube
  • Daily Study Groups
  • Wolfram Schools and Programs
  • Books

Grow Your Skills

  • Wolfram U

    Courses in computing, science, life and more

  • Community

    Learn, solve problems and share ideas.

  • Blog

    News, views and insights from Wolfram

  • Resources for

    Software Developers

Tech Support

  • Contact Us
  • Support FAQs
  • Support FAQs
  • Contact Us
Company
  • About Wolfram
  • Career Center
  • All Sites & Resources
  • Connect & Follow
  • Contact Us

Work with Us

  • Student Ambassador Initiative
  • Wolfram for Startups
  • Student Opportunities
  • Jobs Using Wolfram Language

Educational Programs for Adults

  • Summer School
  • Winter School

Educational Programs for Youth

  • Middle School Camp
  • High School Research Program
  • Computational Adventures

Read

  • Stephen Wolfram's Writings
  • Wolfram Blog
  • Wolfram Tech | Books
  • Wolfram Media
  • Complex Systems

Educational Resources

  • Wolfram MathWorld
  • Wolfram in STEM/STEAM
  • Wolfram Challenges
  • Wolfram Problem Generator

Wolfram Initiatives

  • Wolfram Science
  • Wolfram Foundation
  • History of Mathematics Project

Events

  • Stephen Wolfram Livestreams
  • Online & In-Person Events
  • Contact Us
  • Connect & Follow
Wolfram|Alpha
  • Your Account
  • User Portal
  • Wolfram Cloud
  • Products
    • Wolfram|One
    • Mathematica
    • Wolfram Notebook Assistant + LLM Kit
    • System Modeler
    • Wolfram Player
    • Finance Platform
    • Wolfram|Alpha Notebook Edition
    • Wolfram Engine
    • Enterprise Private Cloud
    • Application Server
    • Wolfram Cloud App
    • Wolfram Player App

    More mobile apps

    • Core Technologies
      • Wolfram Language
      • Computable Data
      • Wolfram Notebooks
      • AI & Linguistic Understanding
    • Deployment Options
      • Wolfram Cloud
      • wolframscript
      • Wolfram Engine Community Edition
      • Wolfram LLM API
      • WSTPServer
      • Wolfram|Alpha APIs
    • From the Community
      • Function Repository
      • Community Paclet Repository
      • Example Repository
      • Neural Net Repository
      • Prompt Repository
      • Wolfram Demonstrations
      • Data Repository
    • Group & Organizational Licensing
    • All Products
  • Consulting & Solutions

    We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technical expertise

    WolframConsulting.com

    Wolfram Solutions

    • Data Science
    • Artificial Intelligence
    • Biosciences
    • Healthcare Intelligence
    • Sustainable Energy
    • Control Systems
    • Enterprise Wolfram|Alpha
    • Blockchain Labs

    More Wolfram Solutions

    Wolfram Solutions For Education

    • Research Universities
    • Colleges & Teaching Universities
    • Junior & Community Colleges
    • High Schools
    • Educational Technology
    • Computer-Based Math

    More Solutions for Education

    • Contact Us
  • Learning & Support

    Get Started

    • Wolfram Language Introduction
    • Fast Intro for Programmers
    • Fast Intro for Math Students
    • Wolfram Language Documentation

    Grow Your Skills

    • Wolfram U

      Courses in computing, science, life and more

    • Community

      Learn, solve problems and share ideas.

    • Blog

      News, views and insights from Wolfram

    • Resources for

      Software Developers
    • Tech Support
      • Contact Us
      • Support FAQs
    • More Learning
      • Highlighted Core Areas
      • Demonstrations
      • YouTube
      • Daily Study Groups
      • Wolfram Schools and Programs
      • Books
    • Support FAQs
    • Contact Us
  • Company
    • About Wolfram
    • Career Center
    • All Sites & Resources
    • Connect & Follow
    • Contact Us

    Work with Us

    • Student Ambassador Initiative
    • Wolfram for Startups
    • Student Opportunities
    • Jobs Using Wolfram Language

    Educational Programs for Adults

    • Summer School
    • Winter School

    Educational Programs for Youth

    • Middle School Camp
    • High School Research Program
    • Computational Adventures

    Read

    • Stephen Wolfram's Writings
    • Wolfram Blog
    • Wolfram Tech | Books
    • Wolfram Media
    • Complex Systems
    • Educational Resources
      • Wolfram MathWorld
      • Wolfram in STEM/STEAM
      • Wolfram Challenges
      • Wolfram Problem Generator
    • Wolfram Initiatives
      • Wolfram Science
      • Wolfram Foundation
      • History of Mathematics Project
    • Events
      • Stephen Wolfram Livestreams
      • Online & In-Person Events
    • Contact Us
    • Connect & Follow
  • Wolfram|Alpha
  • Wolfram Cloud
  • Your Account
  • User Portal
Wolfram Language & System Documentation Center
InverseSpectrogram
  • See Also
    • InverseShortTimeFourier
    • ShortTimeFourier
    • SpectrogramArray
    • Spectrogram
    • Audio
    • PeriodogramArray
    • Fourier
  • Related Guides
    • Fourier Analysis
    • Signal Visualization & Analysis
    • Audio Analysis
    • Audio Representation
    • See Also
      • InverseShortTimeFourier
      • ShortTimeFourier
      • SpectrogramArray
      • Spectrogram
      • Audio
      • PeriodogramArray
      • Fourier
    • Related Guides
      • Fourier Analysis
      • Signal Visualization & Analysis
      • Audio Analysis
      • Audio Representation

InverseSpectrogram[data]

reconstructs the signal from the magnitude spectrogram data.

InverseSpectrogram[img]

reconstructs the signal, assuming that the image img is the magnitude spectrogram.

InverseSpectrogram[input,n]

assumes the spectrogram data was computed with partitions of length n.

InverseSpectrogram[input,n,d]

assumes partitions with offset d.

InverseSpectrogram[input,n,d,wfun]

assumes a smoothing window wfun was applied to each partition.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
MaxIterations  
Method  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • InverseShortTimeFourier
    • ShortTimeFourier
    • SpectrogramArray
    • Spectrogram
    • Audio
    • PeriodogramArray
    • Fourier
  • Related Guides
    • Fourier Analysis
    • Signal Visualization & Analysis
    • Audio Analysis
    • Audio Representation
    • See Also
      • InverseShortTimeFourier
      • ShortTimeFourier
      • SpectrogramArray
      • Spectrogram
      • Audio
      • PeriodogramArray
      • Fourier
    • Related Guides
      • Fourier Analysis
      • Signal Visualization & Analysis
      • Audio Analysis
      • Audio Representation

InverseSpectrogram

InverseSpectrogram[data]

reconstructs the signal from the magnitude spectrogram data.

InverseSpectrogram[img]

reconstructs the signal, assuming that the image img is the magnitude spectrogram.

InverseSpectrogram[input,n]

assumes the spectrogram data was computed with partitions of length n.

InverseSpectrogram[input,n,d]

assumes partitions with offset d.

InverseSpectrogram[input,n,d,wfun]

assumes a smoothing window wfun was applied to each partition.

Details and Options

  • InverseSpectrogram approximates an inverse of the magnitude spectrogram.
  • To compute the short-time Fourier transform of lists and audio signals, use ShortTimeFourier.
  • InverseSpectrogram assumes that real matrix input is a magnitude spectrogram without the redundant part. This means that the window size used was 2(size-1), where size is the second dimension of the input matrix.
  • The inverse spectrogram can be computed from the spectrogram if the offset d is smaller than half the size of the partition length n.
  • The following options can be given:
  • FourierParameters{1,-1}Fourier parameters to be used
    MaxIterations Automaticmaximum number of iterations
    Method Automaticthe method to use
  • Possible method settings include:
  • Automaticuses automatic method
    "GriffinLim"iteratively approximates the phase
    "SPSI"uses single-pass spectrogram inversion
    "Hybrid"uses the SPSI as the inital phase for Griffin–Lim
  • The "Hybrid" method is used by default.

Examples

open all close all

Basic Examples  (3)

Generate an audio signal, assuming a cellular automaton evolution to be the magnitude spectrum:

Reconstruct a signal from a magnitude spectrum:

Construct an Audio object from an Image:

Compute the spectrogram of the resulting signal:

Scope  (3)

The partition size must match the value inferred from the input data:

The inferred partition size is 2×(size-1), where size is the second dimension of the input matrix:

By default, the partition offset is of the inferred partition size:

Specify a different partition offset:

Specify a smoothing window:

Options  (2)

MaxIterations  (1)

Use the MaxIterations option to control the quality of the result and the speed of the operation:

Method  (1)

The "Griffin-Lim" method uses an iterative algorithm to approximate the original signal:

The "SPSI" method approximates the signal in a non-iterative way, which is relatively fast:

The "Hybrid" method uses the result of the "SPSI" method as the starting guess for iterative method "Griffin-Lim", which may converge faster:

Applications  (2)

Reconstruct an Audio object from its magnitude spectrum:

Construct an Audio object from image data:

Convert the image to grayscale and rotate appropriately:

Reconstruct the signal with the assumption that the image was its spectrogram:

Compute the spectrogram of the resulting signal:

Properties & Relations  (1)

Compute the spectrogram of a signal and its approximate inverse:

Compute the short-time Fourier transform:

Discard the redundant part and take the absolute value to get the magnitude spectrogram:

Use InverseSpectrogram to compute the approximated inverse of the spectrogram:

Possible Issues  (1)

The partition size must match the value inferred for the input data:

The inferred partition size is 2×(size-1), where size is the second dimension of the input matrix:

Signal reconstruction cannot be done with other partition sizes:

See Also

InverseShortTimeFourier  ShortTimeFourier  SpectrogramArray  Spectrogram  Audio  PeriodogramArray  Fourier

Related Guides

    ▪
  • Fourier Analysis
  • ▪
  • Signal Visualization & Analysis
  • ▪
  • Audio Analysis
  • ▪
  • Audio Representation

History

Introduced in 2019 (12.0)

Wolfram Research (2019), InverseSpectrogram, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSpectrogram.html.

Text

Wolfram Research (2019), InverseSpectrogram, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSpectrogram.html.

CMS

Wolfram Language. 2019. "InverseSpectrogram." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseSpectrogram.html.

APA

Wolfram Language. (2019). InverseSpectrogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseSpectrogram.html

BibTeX

@misc{reference.wolfram_2025_inversespectrogram, author="Wolfram Research", title="{InverseSpectrogram}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/InverseSpectrogram.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_inversespectrogram, organization={Wolfram Research}, title={InverseSpectrogram}, year={2019}, url={https://reference.wolfram.com/language/ref/InverseSpectrogram.html}, note=[Accessed: 01-December-2025]}

Top
Introduction for Programmers
Introductory Book
Wolfram Function Repository | Wolfram Data Repository | Wolfram Data Drop | Wolfram Language Products
Top
  • Products
  • Wolfram|One
  • Mathematica
  • Notebook Assistant + LLM Kit
  • System Modeler

  • Wolfram|Alpha Notebook Edition
  • Wolfram|Alpha Pro
  • Mobile Apps

  • Wolfram Player
  • Wolfram Engine

  • Volume & Site Licensing
  • Server Deployment Options
  • Consulting
  • Wolfram Consulting
  • Repositories
  • Data Repository
  • Function Repository
  • Community Paclet Repository
  • Neural Net Repository
  • Prompt Repository

  • Wolfram Language Example Repository
  • Notebook Archive
  • Wolfram GitHub
  • Learning
  • Wolfram U
  • Wolfram Language Documentation
  • Webinars & Training
  • Educational Programs

  • Wolfram Language Introduction
  • Fast Introduction for Programmers
  • Fast Introduction for Math Students
  • Books

  • Wolfram Community
  • Wolfram Blog
  • Public Resources
  • Wolfram|Alpha
  • Wolfram Problem Generator
  • Wolfram Challenges

  • Computer-Based Math
  • Computational Thinking
  • Computational Adventures

  • Demonstrations Project
  • Wolfram Data Drop
  • MathWorld
  • Wolfram Science
  • Wolfram Media Publishing
  • Customer Resources
  • Store
  • Product Downloads
  • User Portal
  • Your Account
  • Organization Access

  • Support FAQ
  • Contact Support
  • Company
  • About Wolfram
  • Careers
  • Contact
  • Events
Wolfram Community Wolfram Blog
Legal & Privacy Policy
WolframAlpha.com | WolframCloud.com
© 2025 Wolfram
© 2025 Wolfram | Legal & Privacy Policy |
English