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Everything about Window function

Function used in signal processing

In signal processing and statistics, a window function is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are symmetric around the middle of the interval, approach a maximum in the middle, and taper away from the middle. Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window". Equivalently, and in actual practice, the segment of data within the window is first isolated, and then only that data is multiplied by the window function values. Thus, tapering, not segmentation, is the main purpose of window functions. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Window functionA 5-minute orientation
  2. Skim a recent paper: Computationally efficient memristor model based on Hann window functionInfluential work since 2022
  3. Pick up a classic book: Invariant sets for WindowsThe most-reprinted book on the subject
  4. Read the landmark paper: Experimental studies on round window structure: Function and permeabilityCited 127 times
  5. Go sideways: Kaiser windowA closely related topic
  6. Go sideways: Spectral leakageA closely related topic

📖 Definitions

Noun A function that performs a calculation using values from several rows, but does not group them into a single row.

Noun A function that limits a signal to a restricted portion of time or frequencies.

🗂️ The subject at a glance

  1. Applications
  2. Overlapping windows
  3. Two-dimensional windows
  4. Examples of window functions
  5. Page citations

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics