![]() There is little that you can do to remove aliased power once you have discretely sampled a signal. Any frequency component outside of the range (-Ny, Ny ) is aliased (falsely translated) into that range by the very act of discrete sampling. In that case, it turns out that all of the power spectral density that lies outside the frequency range -Ny < nf < Ny is spuriously moved into that range. The bad news concerns the effect of sampling a continuous function that is not bandwidth limited to less than the Nyquist critical frequency. This is a remarkable theorem for many reasons, among them that it shows that the "information content" of a bandwidth limited function is, in some sense, infinitely smaller than that of a general continuous function. ![]() The concept of a spectrum is based on work by Joseph Fourier (1768 - 1830), who showed that almost any function \displaystyle. The spectrum gives the distribution of wave energy among different wave frequencies of wave-lengths on the sea surface. The simplifications lead to the concept of the spectrum of ocean waves. ![]() We can however, with some simplifications, come close to describing the surface. How can we describe this surface? The simple answer is, Not very easily. The surface appears to be composed of random waves of various lengths and periods. If we look out to sea, we notice that waves on the sea surface are not simple sinusoids. ![]()
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