A Simple Method of Calculating the Characteristics of FSK Signals With Modulation Index 0.5

Abstract

Frequency-shift-keying (FSK) signals with modulation index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m = 0.5</tex> have two significant properties. They have no discrete frequency components and nearly all the signal energy is contained within a narrow frequency region equal to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\frac{3}{2}</tex> of the bit speed even without any band limiting. Unfortunately, a complete mathematical description of FSK signals in general is difficult, because FSK is a nonlinear process. A well-known exception is FSK with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m = 1</tex> , because this signal can be described as the summation of two AM signals. This makes it easy to describe frequency- and time-domain properties. In this paper it is shown that by decomposing FSK signals with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m = 0.5</tex> into two signals with well-understood spectral properties, it is possible to describe time- and frequency-domain properties and to calculate the effects of restricted bandwidth and linear distortion on the signal-space diagrams and eye patterns. Finally it is shown that duobinary FM can be treated as a special case of an FSK ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m = 0.5</tex> ) signal.