Showing papers on "Time–frequency analysis published in 1981"

A Sampling Theorem For The Complex Spectrogram, And Gabor's Expansion Of A Signal In Gaussian Elementary Signals

Abstract: The complex spectrogram of a signal is defined as the Fourier transform of the product of the signal and the shifted and complex conjugated version of a so-called window function; it is thus a function of time and frequency, simultaneously, from which the signal can be reconstructed uniquely. It is shown that the complex spectrogram is completely determined by its values on the points of a certain time-frequency lattice. This lattice is exactly the one suggested by Gabor in 1946; it arose in connection with Gabor's sugges-tion to expand a signal into a discrete set of Gaussian elementary signals. Such an expansion is a special case of the more general expansion of a signal into a discrete set of properly shifted and modulated window functions. It is shown that this expansion exists. Furthermore, a set of functions is constructed, which is bi-orthonormal to the set of shifted and modulated window functions. With the help of this bi-orthonormal set of functions, the expansion coefficients can be determined easily.

Time-Frequency HOP Signals Part II: Coding Based upon Quadratic Congruences

Abstract: High-efficiency multicomponent signals for maximization of signalto-noise ratio are investigated. Maximization of signal-to-noise ratio in colored noise requires control of volume distribution of the signal ambiguity function and transmission of unity efficiency signals. Signal efficiency is defined as the ratio of average power to the peak power. It is concluded that the signals must be frequency hop pulse trains. Quadratic congruences are chosen to place the components in time-frequency space. The number-theoretic properties of these signals provide bounds on the position and amplitude of the various peaks of the signal ambiguity function. The tradeoffs are shown between volume removal, number of component signals, and the time-bandwidth product.

Time-frequency signal analysis by means of the Wigner distribution

Abstract: The Wigner distribution is a signal transformation that exhibits some very interesting properties with regard to time-frequency signal analysis. The most important of these properties are discussed. The Wigner distribution is then compared with other time-frequency signal representations, such as the spectrogram. It appears that the Wigner distribution is better able to display non-stationarities in the signals.