Filters for linear sea-wave prediction

Deterministic sea-wave prediction (DSWP) models are appearing in the literature designed for quiescent interval prediction in marine applications dominated by large swell seas. The approach has focused upon spectral methods which are straightforward and intuitively attractive. However, such methods have the disadvantage that while the sea is aperiodic in nature, the standard discrete spectral processing techniques force an absolutely periodic structure onto the resulting sea surface prediction models. As it is the shape of the sea surface that is important in such applications, particularly near the end of the domain which is important, the standard windowing techniques used in signal processing work to reduce leakage artifacts cannot be employed. This has necessitated the use of end matching methods that can be both inconvenient and may reduce the fraction of the time for which legitimate predictions are available. As a result, an investigation has been undertaken of the use of finite impulse response prediction filters to provide the necessary dispersive phase shifting required in DSWP systems. The present work examines the theoretical basis for such filters and explores their properties together with their application to both long and short crested swell seas. It is shown that wide band forms of such filters are only convergent in the sense of distributions having both infinite duration impulse responses and asymptotically divergent first derivatives. However, appropriate band limitation can produce useful finite impulse responses allowing implementation via standard discrete convolution methods. It is demonstrated that despite the prediction filters having a non-causal impulse response such filters can be used in practice due to a combination of the asymmetric nature of the impulse response and the fundamental nature of the prediction process. The findings are confirmed against actual sea-wave data.