  The phenomenon of superoscillation, where band limited signals can oscillate
over some time period with a frequency higher than the band limit, is not only
very interesting but it also seems to offer many practical applications. The
first reason is that the superoscillation frequency can be exploited to perform
tasks beyond the limits imposed by the lower bandwidth of the signal. The
second reason is that it is generic and applies to any wave form, be it
optical, electrical, sonic, or quantum mechanical. For practical applications,
it is important to overcome two problems. The first problem is that an
overwhelming proportion of the energy goes into the non superoscillating part
of the signal. The second problem is the control of the shape of the
superoscillating part of the signal. The first problem has been recently
addressed by optimization of the super oscillation yield, the ratio of the
energy in the superoscillations to the total energy of the signal. The second
problem may arise when the superoscillation, is to mimic a high frequency
purely perodic signal. This may be required, for example, when a
superoscillating force is to drive a harmonic oscillator at a high resonance
frequency. In this paper the degree of periodicity of a signal is defined and
applied to some yield optimized superoscillating signals.
