By Robert M. Young
An advent to Non-Harmonic Fourier sequence, Revised variation is an replace of a well-known and hugely revered vintage textbook. through the e-book, fabric has additionally been further on fresh advancements, together with balance conception, the body radius, and functions to sign research and the keep an eye on of partial differential equations.
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Additional resources for An introduction to nonharmonic Fourier series
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It is possible to reconstruct the signal waveform from such a sparse sequence of sample values because the signal is ergodic and quasi-stationary. The parameters do not vary during the time period it is being observed. Under these conditions, a reduced number of independent sample values are needed to reconstruct it by estimating all three parameters (amplitude, frequency and phase angle) of all signal components. In this case, the time intervals between the sampling instants might be large and the mean sampling rate used in this particular case is 80 MS/s.
Use of nonorthogonal transforms might be mentioned as an example illustrating this. Their first application was reconstruction of nonuniformly sampled signal waveforms. Then it was discovered that they are also good for processing signals at extremely low frequencies. For example, they can be used to remove the negative effect caused by cutting off part of a signal period when, according to the classical definition, the processing should be carried out over a number of integer signal periods (or the periods of their separate components).