SpectrogramArray

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`SpectrogramArray`

Updated in 14.1

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SpectrogramArray[list]

returns the spectrogram data of list.

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SpectrogramArray[list,n]

uses partitions of length n.

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SpectrogramArray[list,n,d]

uses partitions with offset d.

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SpectrogramArray[list,n,d,wfun]

applies a smoothing window wfun to each partition.

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SpectrogramArray[list,n,d,wfun,m]

pads partitions with zeros to length m prior to the computation of the transform.

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SpectrogramArray[audio,…]

returns spectrogram data of audio.

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SpectrogramArray[video]

returns the spectrogram data of the first audio track in video.

Details and Options

SpectrogramArray[list] returns the discrete Fourier transform (DFT) of partitions of list, also known as short-time Fourier transform (STFT).
Plot the spectrogram using Spectrogram.
SpectrogramArray[list] uses partitions of length and offset , where is Length[list].
The partition length n and offset d can be expressed as an integer number (interpreted as number of samples) or as time or sample quantities.
If necessary, fixed padding is used on the right to make all the partitions the same size.
In SpectrogramArray[list,n,d,wfun], the smoothing window wfun can be specified using a window function that will be sampled between and or a list of length n. The default window is DirichletWindow, which effectively does no smoothing.
SpectrogramArray works with numeric lists as well as Audio and Sound objects.
For multichannel sound objects, the spectrogram is computed over the sum of all channels.
SpectrogramArray accepts the FourierParameters option. The default setting is FourierParameters->{1,-1}.

Examples

open allclose all

Basic Examples (2)Summary of the most common use cases

Short-time Fourier transform of a sine wave:

In[1]:=1

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https://wolfram.com/xid/0c0oo62gvdnoa-wvztxa

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0c0oo62gvdnoa-de01nz

Short-time Fourier transform of an audio signal:

In[1]:=1

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https://wolfram.com/xid/0c0oo62gvdnoa-uiu2h9

Plot the result:

In[2]:=2

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https://wolfram.com/xid/0c0oo62gvdnoa-jx4m04

Out[2]=2

Scope (2)Survey of the scope of standard use cases

Magnitude spectrum of a single partition:

In[1]:=1

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https://wolfram.com/xid/0c0oo62gvdnoa-msbstc

In[2]:=2

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https://wolfram.com/xid/0c0oo62gvdnoa-rz6di3

Out[2]=2

Plot of the magnitude of the SpectrogramArray data:

In[3]:=3

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https://wolfram.com/xid/0c0oo62gvdnoa-sfk80j

Out[3]=3

Apply a smoothing window function:

In[4]:=4

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https://wolfram.com/xid/0c0oo62gvdnoa-sus5t3

Out[4]=4

Short-time Fourier transform of the audio track of a video:

In[1]:=1

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https://wolfram.com/xid/0c0oo62gvdnoa-zqcc73

Plot the result:

In[2]:=2

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https://wolfram.com/xid/0c0oo62gvdnoa-z1xfpa

Out[2]=2

Applications (2)Sample problems that can be solved with this function

Short-time energy of an audio object:

In[2]:=2

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https://wolfram.com/xid/0c0oo62gvdnoa-4g7uj3

In[2]:=2

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https://wolfram.com/xid/0c0oo62gvdnoa-r37fb6

In[3]:=3

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https://wolfram.com/xid/0c0oo62gvdnoa-im0rtg

Out[3]=3

Identify the numbers pressed on a phone keypad from a spectrogram:

In[1]:=1

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https://wolfram.com/xid/0c0oo62gvdnoa-nhm07a

Create a sound with digits seven and three:

In[2]:=2

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https://wolfram.com/xid/0c0oo62gvdnoa-71ynp8

Out[2]=2

Magnitude of the spectrogram array of the sound:

In[3]:=3

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https://wolfram.com/xid/0c0oo62gvdnoa-4r1lz5

In[4]:=4

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https://wolfram.com/xid/0c0oo62gvdnoa-oimf2e

Out[4]=4

Find the peaks and calculate the frequencies:

In[5]:=5

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https://wolfram.com/xid/0c0oo62gvdnoa-uytks7

Out[5]=5

In[6]:=6

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https://wolfram.com/xid/0c0oo62gvdnoa-fuqms9

Out[6]=6

Properties & Relations (2)Properties of the function, and connections to other functions

Fourier of partitions of lists is equivalent to SpectrogramArray:

In[1]:=1

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https://wolfram.com/xid/0c0oo62gvdnoa-e8vxak

Out[2]=2

Compute the inverse of spectrogram of non-overlapping partitions:

In[1]:=1

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https://wolfram.com/xid/0c0oo62gvdnoa-v6zbk6

Out[1]=1

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