This gives the meaning of the terms as generally understood in the middle of the 18th century. Robert Hooper's Physician's Vade-Mecum, published in 1812 has been used as a source of terms in the early 19th century; many of the terms mentioned are still in common use.
In either case, the value at x = 0 is defined to be the limiting value sinc(0) = 1. The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of Ï).
For sine waves, RMS is always the peak value divided by the square of two (approximately 1.414). As one over the square root of two is approximately .707, the RMS value of any sine wave is approximately 70.7 percent of its peak value.