Common terminology

Prefixes and suffixes

"Maxim-", "minim-", "extrem-" prefixes

• "Maxim-" refer to large/larger/etc
• "Minim-" refer to little/small/smaller/etc
• "Extrem-" refer to both large and small

"-a", "-um" suffixes

• The "-a" suffix (e.g. "maxima") means "of a part [of the data]"; there can be multiple maxima in a vector (or a part of a vector)
• The "-um" suffix (e.g. "maximum") means "of the whole [data]"; there can only be one maximum in a vector (or a part of a vector)

Peaks and characteristics

Peak (a.k.a. [local] extrema, maxima, minima, etc.)

Maxima and minima refer to the maximum or minimum (respectively) value within a window, and peak or extrema refers to both maxima and/or minima.

More technically, a peak is an element x[i] which is more extreme (i.e. larger or smaller) than all elements in the window x[i-w:i+w] where w is a positive integer. The simplest and most common case is w=1, which results in an element being more extreme than its neighbors.

In the animation below, the maximum in the window x[i-w:i+w] (grey band) is shown as the purple dot. When the maximum lines up with the current "time" (i.e. index, vertical black line), a peak is identified (red dot). Use the scroll bar at the bottom to understand why some "peaks" aren't found. (Hint: pay attention the window size and the window maximum.)

Plateau

A "flat" peak, where the value of the extrema occurs multiple times consecutively, but surrounding elements are less than the extremum. The first occurence of the extrema is considered the peak location. Uncommon for floating-point data.

Peak height

Peak height is the value of the signal for a specific peak. Mouse over (or touch) each peak to see its height.

Peak prominence

For maxima, peak prominence is the (absolute) difference between the height of a maxima and the larger of the two minimums in the adjacent reference ranges. Reference ranges cover the data between the current maxima and adjacent (i.e. previous and next) reference maxima, which must be at least as large as the current maxima, or the beginning/end of the array. The same is true of minima with opposite extrema/extremum (e.g. minima for maxima, and maximum for minimum, etc.).

Peak width

Peak width is measured as the distance (in units of indices) between the intersection of a horizontal reference line with the signal on either side of a peak, where the height of the reference line is offset from the peak height by a proportion of the peak prominence (keyword argument relheight for the peakwidths functions).

"Strict"-ness

The default behavior of peak finding and related functions (e.g. peakproms, etc.) is to only return results that are exactly correct, and to return nothing (i.e. ignore a potential peak), NaN, or missing, as appropriate for a given function. This behavior is controlled by the strict keyword argument (true by default). Setting the strict keyword to false allows these functions to relax some requirements. When strict == false, functions will make optimistic assumptions in an attempt to return useful information (e.g. something not NaN or missing) when data violates default requirements. This can produce results that are not correct according to the strictest definitions of peaks and their characteristics, however, sometimes relaxed behavior is desired/needed.

strict-ness should only affect new peaks/characteristics (i.e. only peaks detected with strict == false). Any observed behavior otherwise (i.e. characteristics of non-strict peaks are altered) is undesired^[1] and an issue should be opened.