# What is a “window of length N” in a signal processing algorithm?

I am reading a scientific paper in which an algorithm for evaluating an electromyography signal is described and I just don't get the meaning of the word "window" in the following part of a sentence: (First full paragraph of page 4)

"Fig. 5 shows ... signals ... over two windows of length N = 500 "

What is window supposed to mean here?

• Where in that paper does that specific quote occur? It appears that you may have paraphrased a sentence from the first full paragraph on page 4. But in paraphrasing, you stripped quite a bit of context out of the quote. – user16 Jun 28 '15 at 15:53
• Current response though very broad is accurate. If you have access to Digital Signal Processing by Sanjit Mitra, 4th edition, read chapter 10. If you have access to Digital Signal Processing: Principles, Algorithms and Applications by John G. Proakis and Dimitris K Manolakis, read chapter 8. – Mahendra Gunawardena Jun 28 '15 at 17:49
• @MahendraGunawardena: Proakis and Manolakis is one of my favourite DSP textbooks. Good recommendation. – Li-aung Yip Jun 28 '15 at 19:23
• @MahendraGunawardena I fixed your links, but substituted the publisher's website for the first since I did not immediately find the exact link you used. – Air Jun 29 '15 at 16:47

"Window" is often used to mean a successive set of samples processed as a batch. In this case it appears that the algorithm works on batches of 500 samples at a time.

• it refers to a successive set or in other terms a square bracket (samples needn't be discrete, can be continuous). in the charts, it probably means the x axis size of the data, maybe cropped from a larger set of data/measurements. – Gürkan Çetin Jun 28 '15 at 17:22
• @Gürkan: In this case "N = 500" makes it clear that data comes in discrete sample. – Olin Lathrop Jul 30 '15 at 11:16
• Oh, yes of course. I was focusing on the term window, N normally represents some integers. – Gürkan Çetin Jul 31 '15 at 13:28

The term time-window or often just window is used to mean a short period of time during which something is possible, or during which you observe something, or during which you look for something.

Note that the paper introduces this concept earlier on when it says

For that, the recorded EMG-data were rectified and smoothed with a root mean square (RMS) function, working on a 250 ms time-window.

The full quote from the paper you mentioned says

Fig. 5 shows the CCF the healthy (left) and the spastic hemiparetic lower limb EMG signals of sTA and sGL over two windows of length N = 500.

In this case you can see from the graphs in Fig. 5 that the window-length is 500ms (0.5 seconds).

According to one online etymology dictionary, the term was first used with this meaning during the space-program to describe the short period of time during which a launch was possible, the launch window. And the English idiom window of opportunity came from this use. Note that in this context the window is defined by what's possible, or by some physical constraints that change over time, but in the paper you mentioned the window seems to be deliberately constrained by the experimenters, probably to get better accuracy after smoothing/filtering the signal, or to recognise patterns that happen within their defined window while excluding matching patterns that happen over longer periods.