File talk:Synthesis square.gif

Why doesn't the red line up with the black? — Omegatron 18:32, 12 May 2006 (UTC)

Because it's wrong. Whoever made this plot made an error in the normalization. 24.61.43.18 18:59, 3 September 2006 (UTC)

• The normaliztion issue seems to have been fixed now and the image looks as I'd expect it to. However the current description ("This image is inaccurate. It neglects Gibb's phenomenon") is (and was) wrong. Gibb's phenomenon is clearly visible in both revisions as the "spikes" at the discontinuous points. Formally, the red will of course never line up completely with the black, since it's a discontinuous function. (Also, in practice we only have a finite number of terms). So I'll change the description.

• As a sidenote: The Gibb's phenomenon can however disappear in a raster plot like this, depending on how you plot it; Often the pixel x (an integer) is drawn as y = f(x) (with lines between the x values), despite that the pixel actually represents the entire area spanned from x (incl) to x + 1 (excl). As the width of the phenomenon decreases with the number of terms, it may well disappear "between" two pixels. However, in the present image, the discontinuities are located at integer values (which you'd often do when plotting a simple function like this). The nature of Gibb's phenomeon is such that the value of the expansion at the discontinuous point (x) is the average of the limits approaching that point in the original function. So what I believe will happen in this plot as the number of terms increases, is that f(x) will remain the midpoint, f(x-1) will converge to one level of the square function, and f(x+1) will converge to the other. In other words, the line connecting the levels will always appear to be at least three pixels wide, and never become vertical like the original, despite the actual deviations of f(x) being well within the pixel size. --130.237.179.166 17:08, 7 September 2006 (UTC)

It has been fixed now. It was not consistent before because it lined up the red with the tips of the Gibb's wing things instead of the correct value. — Omegatron 18:03, 7 September 2006 (UTC)