WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

FindPeaks
✖
FindPeaks

✖
FindPeaks[list]

gives positions and values of the detected peaks in list.

✖
FindPeaks[list,σ]

finds peaks that survive Gaussian blurring up to scale σ.

✖
FindPeaks[list,σ,s]

finds peaks with minimum sharpness s.

✖
FindPeaks[list,σ,s,t]

finds only peaks with values greater than t.

✖
FindPeaks[list,σ,{s,σs},{t,σt}]

uses different scales for thresholding sharpness and value.

Details and Options

  • FindPeaks finds local maxima using the given constraints, returning the result as {{x1,y1},{x2,y2},…}.
  • Input list can be of one of the following forms:
  • {y1,y2,…}a list of values
    TimeSeries[…]regularly sampled time series object
    EventSeries[…]regularly sampled event series object
  • FindPeaks[list] automatically chooses scale, sharpness and threshold parameters.
  • To avoid the detection of noise-related peaks, the input is regularized by performing a Gaussian filtering using the standard deviation σ.
  • The value of σ defaults to , with n being the number of data points in list. Larger values for σ reduce the number of peaks.
  • Peaks detected in the regularized data are traced back to the corresponding peaks in the original data.
  • By default, peaks are not filtered based on their sharpness (). The sharpness s is computed as the second derivative of the data with a Gaussian filter at scale σ. Specify a smaller scale using {s,σs}.
  • By default, peaks of any height are returned. Use a threshold t to dismiss peaks with smaller values. To apply the threshold at a scale other than 0, use {t,σt}.
  • FindPeaks[list,σ,s,t] is equivalent to FindPeaks[list,σ,{s,σ},{t,0}].
  • The following options can be given:
  • InterpolationOrder Automaticspline interpolation order of up to order 3
    Padding "Reflected"padding scheme to use
  • By default, InterpolationOrder1 is assumed for lists of data. For TimeSeries objects, the interpolation order is inherited.
  • The interpolation order is used when computing peak positions. Peaks may be located in between and possibly above {x,y} samples interpolation orders.
  • For interpolation orders 0 or 1, a plateau of two or more data samples is assigned a single peak at its center location.
  • For possible settings for Padding, see the reference page for ArrayPad.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Find position and height of dominant peaks in a list:

In[8]:=8
✖
https://wolfram.com/xid/05fgdikka8-2fs3ct
In[9]:=9
✖
https://wolfram.com/xid/05fgdikka8-b3ys52
Out[9]=9

Visualize list and the detected peaks:

In[10]:=10
✖
https://wolfram.com/xid/05fgdikka8-hk8x5i
Out[10]=10

Scope  (12)Survey of the scope of standard use cases

Data  (4)

Peaks of a 1D list:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-5ssec3
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-sbse5k
Out[3]=3

Peaks of a TimeSeries object:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-k2t1vh
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-ucf5vj
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-v7ro4i
Out[3]=3

Peaks of an EventSeries object:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-byvcsb
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-dhklb2
Out[2]=2

Find peaks:

In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-s18vb5
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-ommma5
Out[4]=4

Peaks of a list of Quantity objects:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-38ay6t
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-tazt6e
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-5j8b31
Out[3]=3

Threshold for values greater than 30 meters:

In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-em0v7i
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/05fgdikka8-3tmfx1
Out[5]=5

Parameters  (8)

By default, an automatic scale is used:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-6rvg58
Out[2]=2

Find all peaks at scale :

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-mdl0re
Out[1]=1

Compute peaks at different scales:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-3zis6i
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-5wsnr8
Out[2]=2

When finding peaks at scale , only peaks that sustain a blur up to scale are returned:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-za85pb
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-gv694d
Out[2]=2

Signal and its blurred version at scale :

In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-vze3r5
Out[3]=3

By default, peaks are not filtered based on their sharpness, equivalent to :

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-bxgmq8
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-5vw16h
Out[2]=2

Specify minimum sharpness value :

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-5zscki
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-sms3rx
Out[2]=2

Sharpness, defined by the negative second derivative, should be greater than the specified s:

In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-vwqgk7
Out[3]=3

Specify a minimum height value :

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-b9d18m
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-o3spf9
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-1sumov
Out[3]=3

Apply the value threshold after smoothing the data using a scale :

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-nazxke
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-jjctoa
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-1j9ty2
Out[3]=3

Options  (3)Common values & functionality for each option

InterpolationOrder  (1)

By default, InterpolationOrder1 is used:

In[12]:=12
✖
https://wolfram.com/xid/05fgdikka8-tz4lp5
In[13]:=13
✖
https://wolfram.com/xid/05fgdikka8-rdzr9v
Out[13]=13
In[14]:=14
✖
https://wolfram.com/xid/05fgdikka8-8f90h9
Out[14]=14

Find peaks of the cubic interpolation:

In[9]:=9
✖
https://wolfram.com/xid/05fgdikka8-cfvc9j
Out[9]=9

Note that the number and position of peaks may vary depending on the interpolation order:

In[11]:=11
✖
https://wolfram.com/xid/05fgdikka8-ohyikf
Out[11]=11

Padding  (2)

By default, Padding"Reflected" is used:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-rn44wv
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-cxhghc
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-t0j53r
Out[3]=3

Specify a constant padding:

In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-nsz6d1
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/05fgdikka8-7f2z6p
Out[5]=5

Padding influences the occurrence and position of peaks at the boundary:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-fwe6xn

By default, "Reflected" padding causes a peak at position 1:

In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-t728lv
Out[2]=2

"Reversed" padding induces a peak at position 1/2:

In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-sahum6
Out[3]=3

"Fixed" padding results in no peak at the boundary:

In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-ly9xbo
Out[4]=4

Applications  (6)Sample problems that can be solved with this function

Find peaks in the stock price of Apple in the year 2013:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-17gbj3
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-nksa1y
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-dw9h9g
Out[3]=3

Highlight peaks on the plot of the data:

In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-qogmij
Out[4]=4

Find peaks in elevation data:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-0di62a
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-wn3y9v
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-vlvrbl
Out[3]=3

Mean daily temperatures for Chicago during a period of two months:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-r64lqt
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-h9eqq2
Out[2]=2

Find peaks in the temperature:

In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-izrizl
In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-zk3no2
Out[4]=4

Find peaks in an ECG signal:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-53gthj
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-2588qn
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-r4r45l
Out[3]=3

Detect the mode of a distribution using the peak of its histogram. Sample a Fréchet distribution:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-21h8fu
In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-mtyb69
Out[2]=2

Find the mode of the distribution:

In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-890gxb
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-l40zil
Out[4]=4

Compare the mode with the theoretical value of the Fréchet distribution:

In[5]:=5
✖
https://wolfram.com/xid/05fgdikka8-rpvszh
Out[5]=5

Use peaks of an audio power spectrum to detect pitches of the sound:

In[1]:=1
✖
https://wolfram.com/xid/05fgdikka8-d361hm
Out[1]=1

Compute the power periodogram:

In[2]:=2
✖
https://wolfram.com/xid/05fgdikka8-dvtv51

Find peaks of the power spectrum:

In[3]:=3
✖
https://wolfram.com/xid/05fgdikka8-p5vasx
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/05fgdikka8-42v0yk
Out[4]=4

Converting peak locations into corresponding frequencies:

In[5]:=5
✖
https://wolfram.com/xid/05fgdikka8-b5afv4
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/05fgdikka8-sfav1l
Out[6]=6
Wolfram Research (2014), FindPeaks, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPeaks.html (updated 2021).
✖
Wolfram Research (2014), FindPeaks, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPeaks.html (updated 2021).

Text

Wolfram Research (2014), FindPeaks, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPeaks.html (updated 2021).

✖
Wolfram Research (2014), FindPeaks, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPeaks.html (updated 2021).

CMS

Wolfram Language. 2014. "FindPeaks." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/FindPeaks.html.

✖
Wolfram Language. 2014. "FindPeaks." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/FindPeaks.html.

APA

Wolfram Language. (2014). FindPeaks. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindPeaks.html

✖
Wolfram Language. (2014). FindPeaks. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindPeaks.html

BibTeX

@misc{reference.wolfram_2025_findpeaks, author="Wolfram Research", title="{FindPeaks}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/FindPeaks.html}", note=[Accessed: 23-June-2025 ]}

✖
@misc{reference.wolfram_2025_findpeaks, author="Wolfram Research", title="{FindPeaks}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/FindPeaks.html}", note=[Accessed: 23-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_findpeaks, organization={Wolfram Research}, title={FindPeaks}, year={2021}, url={https://reference.wolfram.com/language/ref/FindPeaks.html}, note=[Accessed: 23-June-2025 ]}

✖
@online{reference.wolfram_2025_findpeaks, organization={Wolfram Research}, title={FindPeaks}, year={2021}, url={https://reference.wolfram.com/language/ref/FindPeaks.html}, note=[Accessed: 23-June-2025 ]}