The primary goal of spectral analysts ts to objectively tdenttfy all tm- 
portant frequenctes in a wave record. Since wave period in seconds is equal 
to the reciprocal of frequency in hertz, important wave periods are also 
identified. 
III. PRACTICAL LIMITATIONS OF SPECTRAL ANALYSIS 
1. Calculation Procedures. 
The appearance of a spectrum can be noticeably influenced by the methods 
used for calculation and display, neither of which is standardized in coastal 
and ocean engineering activities. 
Spectra are computed from both digital wave records and analog records for 
which an assortment of analog spectral analysis devices exists. A spectrum is 
computed from a digital wave record by either (a) computing the fourier trans- 
form of the autocovariance function of the record, or (b) computing the fourier 
transform of the record directly from the record using the fast fourier trans- 
form (FFT) approach (see Harris, 1974, for further detail). Both of these 
algorithms are used in conjunction with wave records subjected to various fil- 
ters and smoothing functions before analysis. Further, some form of smoothing, 
averaging, or summing is often applied to the computed spectral components. 
Different methods for calculating a spectrum will produce slightly different 
estimates of the spectrum when applied to a particular wave record. Major dif- 
ferences in the height of the spectral peak were shown by Wilson, Chakrabarti, 
and Snider (1974) when different approximations to the autocovariance function 
were used and different smoothing functions were applied to the spectrum of a 
field wave record (Fig. 2). Major differences in the height of the spectral 
peak and energy levels between peaks were noted by Harris (1974) when a time 
series composed of three superimposed sinusoidal waves was analyzed by several 
accepted methods (Fig. 3). 
Hindcast wave energy spectra are computed by estimating atmospheric input 
of energy to the sea surface and redistribution of energy within a spectrum. 
The estimates are based on a series of equations derived from the physics of 
air-sea interaction and waves. The quality and characteristics of hindcast 
spectra are a function of the model used to perform the calculations (Resio 
and Vincent, 1979) as well as the accuracy of the input wind field. 
Spectra obtained from either measurements or hindcasts are also limited by 
the resolution of the computation technique. The energy density and frequency 
at a spectral peak can be noticeably distorted if the frequency bandwidths, 
(Af);, are not small enough to permit clear definition of major peaks. 
2. Display Formats. 
The appearance of a spectrum can be strongly affected by the display format 
used. Harris (1972) showed five often used formats for plotting spectra (Fig. 
4). Each format alters the appearance of the spectrum. Format E shifts the 
relative magnitudes of spectral peaks enough that the second highest peak in 
formats A, B, C, and D becomes the highest peak in format E. A and C are the 
two most frequently used formats. 
