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scipy.signal.

# find_peaks

scipy.signal.find_peaks(x, height=None, threshold=None, distance=None, prominence=None, width=None, wlen=None, rel_height=0.5, plateau_size=None)

  Find peaks inside a signal based on peak properties.

  This function takes a 1-D array and finds all local maxima by simple comparison of neighboring values. Optionally, a subset of these peaks can be selected by specifying conditions for a peak’s properties.

  Parameters:
    x sequence

      A signal with peaks.

    height number or ndarray or sequence, optional

      Required height of peaks. Either a number, `None`, an array matching x or a 2-element sequence of the former. The first element is always interpreted as the minimal and the second, if supplied, as the maximal required height.

    threshold number or ndarray or sequence, optional

      Required threshold of peaks, the vertical distance to its neighboring samples. Either a number, `None`, an array matching x or a 2-element sequence of the former. The first element is always interpreted as the minimal and the second, if supplied, as the maximal required threshold.

    distance number, optional

      Required minimal horizontal distance (>= 1) in samples between neighbouring peaks. Smaller peaks are removed first until the condition is fulfilled for all remaining peaks.

    prominence number or ndarray or sequence, optional

      Required prominence of peaks. Either a number, `None`, an array matching x or a 2-element sequence of the former. The first element is always interpreted as the minimal and the second, if supplied, as the maximal required prominence.

    width number or ndarray or sequence, optional

      Required width of peaks in samples. Either a number, `None`, an array matching x or a 2-element sequence of the former. The first element is always interpreted as the minimal and the second, if supplied, as the maximal required width.

    wlen int, optional

      Used for calculation of the peaks prominences, thus it is only used if one of the arguments prominence or width is given. See argument wlen in `peak_prominences` for a full description of its effects.

    rel_height float, optional

      Used for calculation of the peaks width, thus it is only used if width is given. See argument rel_height in `peak_widths` for a full description of its effects.

    plateau_size number or ndarray or sequence, optional

      Required size of the flat top of peaks in samples. Either a number, `None`, an array matching x or a 2-element sequence of the former. The first element is always interpreted as the minimal and the second, if supplied as the maximal required plateau size.

      Added in version 1.2.0.

  Returns:
    peaks ndarray

      Indices of peaks in x that satisfy all given conditions.

    properties dict

      A dictionary containing properties of the returned peaks which were calculated as intermediate results during evaluation of the specified conditions:

      - ‘peak_heights’

          If height is given, the height of each peak in x.

      - ‘left_thresholds’, ‘right_thresholds’

          If threshold is given, these keys contain a peaks vertical distance to its neighbouring samples.

      - ‘prominences’, ‘right_bases’, ‘left_bases’

          If prominence is given, these keys are accessible. See `peak_prominences` for a description of their content.

      - ‘widths’, ‘width_heights’, ‘left_ips’, ‘right_ips’

          If width is given, these keys are accessible. See `peak_widths` for a description of their content.

      - ‘plateau_sizes’, left_edges’, ‘right_edges’

          If plateau_size is given, these keys are accessible and contain the indices of a peak’s edges (edges are still part of the plateau) and the calculated plateau sizes.

          Added in version 1.2.0.

      To calculate and return properties without excluding peaks, provide the open interval `(None, None)` as a value to the appropriate argument (excluding distance).

  Warns:
    PeakPropertyWarning

      Raised if a peak’s properties have unexpected values (see `peak_prominences` and `peak_widths`).

  Warning

  This function may return unexpected results for data containing NaNs. To avoid this, NaNs should either be removed or replaced.

  See also

  `find_peaks_cwt`

    Find peaks using the wavelet transformation.

  `peak_prominences`

    Directly calculate the prominence of peaks.

  `peak_widths`

    Directly calculate the width of peaks.

  Notes

  In the context of this function, a peak or local maximum is defined as any sample whose two direct neighbours have a smaller amplitude. For flat peaks (more than one sample of equal amplitude wide) the index of the middle sample is returned (rounded down in case the number of samples is even). For noisy signals the peak locations can be off because the noise might change the position of local maxima. In those cases consider smoothing the signal before searching for peaks or use other peak finding and fitting methods (like `find_peaks_cwt`).

  Some additional comments on specifying conditions:

  - Almost all conditions (excluding distance) can be given as half-open or closed intervals, e.g., `1` or `(1, None)` defines the half-open interval \([1, \infty]\) while `(None, 1)` defines the interval \([-\infty, 1]\). The open interval `(None, None)` can be specified as well, which returns the matching properties without exclusion of peaks.

  - The border is always included in the interval used to select valid peaks.

  - For several conditions the interval borders can be specified with arrays matching x in shape which enables dynamic constrains based on the sample position.

  - The conditions are evaluated in the following order: plateau_size, height, threshold, distance, prominence, width. In most cases this order is the fastest one because faster operations are applied first to reduce the number of peaks that need to be evaluated later.

  - While indices in peaks are guaranteed to be at least distance samples apart, edges of flat peaks may be closer than the allowed distance.

  - Use wlen to reduce the time it takes to evaluate the conditions for prominence or width if x is large or has many local maxima (see `peak_prominences`).

  Added in version 1.1.0.

  Array API Standard Support

  `find_peaks` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ⛔
  PyTorch | ⛔ | ⛔
  JAX | ⛔ | ⛔
  Dask | ⛔ | n/a

  > See Support for the array API standard for more information.

  Examples

  To demonstrate this function’s usage we use a signal x supplied with SciPy (see `scipy.datasets.electrocardiogram`). Let’s find all peaks (local maxima) in x whose amplitude lies above 0.

      >>> import numpy as np
      >>> import matplotlib.pyplot as plt
      >>> from scipy.datasets import electrocardiogram
      >>> from scipy.signal import find_peaks
      >>> x = electrocardiogram()[2000:4000]
      >>> peaks, _ = find_peaks(x, height=0)
      >>> plt.plot(x)
      >>> plt.plot(peaks, x[peaks], "x")
      >>> plt.plot(np.zeros_like(x), "--", color="gray")
      >>> plt.show()

  We can select peaks below 0 with `height=(None, 0)` or use arrays matching x in size to reflect a changing condition for different parts of the signal.

      >>> border = np.sin(np.linspace(0, 3 * np.pi, x.size))
      >>> peaks, _ = find_peaks(x, height=(-border, border))
      >>> plt.plot(x)
      >>> plt.plot(-border, "--", color="gray")
      >>> plt.plot(border, ":", color="gray")
      >>> plt.plot(peaks, x[peaks], "x")
      >>> plt.show()

  Another useful condition for periodic signals can be given with the distance argument. In this case, we can easily select the positions of QRS complexes within the electrocardiogram (ECG) by demanding a distance of at least 150 samples.

      >>> peaks, _ = find_peaks(x, distance=150)
      >>> np.diff(peaks)
      array([186, 180, 177, 171, 177, 169, 167, 164, 158, 162, 172])
      >>> plt.plot(x)
      >>> plt.plot(peaks, x[peaks], "x")
      >>> plt.show()

  Especially for noisy signals peaks can be easily grouped by their prominence (see `peak_prominences`). E.g., we can select all peaks except for the mentioned QRS complexes by limiting the allowed prominence to 0.6.

      >>> peaks, properties = find_peaks(x, prominence=(None, 0.6))
      >>> properties["prominences"].max()
      0.5049999999999999
      >>> plt.plot(x)
      >>> plt.plot(peaks, x[peaks], "x")
      >>> plt.show()

  And, finally, let’s examine a different section of the ECG which contains beat forms of different shape. To select only the atypical heart beats, we combine two conditions: a minimal prominence of 1 and width of at least 20 samples.

      >>> x = electrocardiogram()[17000:18000]
      >>> peaks, properties = find_peaks(x, prominence=1, width=20)
      >>> properties["prominences"], properties["widths"]
      (array([1.495, 2.3  ]), array([36.93773946, 39.32723577]))
      >>> plt.plot(x)
      >>> plt.plot(peaks, x[peaks], "x")
      >>> plt.vlines(x=peaks, ymin=x[peaks] - properties["prominences"],
      ...            ymax = x[peaks], color = "C1")
      >>> plt.hlines(y=properties["width_heights"], xmin=properties["left_ips"],
      ...            xmax=properties["right_ips"], color = "C1")
      >>> plt.show()