ABSTRACT
To overcome the problems associated with poor confidence levels in the raw
spectral estimates, the most common approach is to average over adjacent energy
bands. It will be seen that while this improves the confidence it also reduces the
frequency resolution, so that once the size of the data set has been determined there
is a trade-off between resolution and confidence. The effect of different effective
bandwidths is illustrated for an ocean wave data set containing 2048 values. Figure
48.1 shows the full spectrum without any smoothing. It is evident from the plot that
while the peak energy is associated with a frequency of approximately 0.12 Hz,
there are also a number of apparent spikes of energy in nearby frequency bands.
They key question is: how confident could one be in each of the individual energy
spikes? The quick answer is: not very. In fact, the 90% confidence interval for the
raw spectral estimates indicate that the height of any particular energy spike could
be between 0.33 and 19 times the height shown (see Chapter 47).
