Instantaneous Frequency Distribution Research Articles

Exponential-type distribution of human muscle sympathetic nerve activity results in an automatic quantification method

A new burst counting method based on a subject invariant characteristic demonstrates the limits of the actual automatic based methods. The exponential behaviour of the counted bursts in function of a variable threshold highlights a scaling property of the muscle sympathetic nerve activity. From experimental single unit recording results, we deduce the exponential-type (gamma) distribution of instantaneous spiking frequency within multi-unit recordings. We show that integrated muscle sympathetic nerve discharges must be gamma distributed with parameters proportional to the number of neurons in the recording pool and to the integration window width.

Instantaneous frequency and energy distribution of a signal

A theory is derived on a signal representation in an instantaneous frequency vs. time plane. It is observed that the usual frequency vs. time representation does not give a specific pattern for the signal. It is shown that by switching the frequency axis to an instantaneous frequency axis, and by distributing the energy of the signal on an instantaneous frequency vs. time plane it is possible to build up a coherent theory. As an example, patterns of speech signals (sustained vowels) are represented.

Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise

The probability distribution of the phase angle between two vectors perturbed by correlated Gaussian noises is studied in detail. Definite integral expressions are derived for the distribution function, and its asymptotic behavior for large signal-to-noise is found for "small," "near <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\pi/2</tex> ," and "large" angles. The results are applied to obtain new formulas for the symbol error rate in MDPSK, to calculate the distribution of instantaneous frequency, to study the error rate in digital FM with partial-bit integration in the postdetection filter, and to obtain a simplified expresion for the error rate in DPSK with a phase error in the reference signal. In the degenerate case in which one of the vectors is noise free, the results lead to the symbol error rate in MPSK.

Distribution of instantaneous frequency for signal plus noise

A concise formula is derived for the probability distribution of the instantaneous frequency of an arbitrary bandpass signal plus Gaussian noise. The results are presented in terms of Marcum's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -functions, with well-known properties. The results are applicable in the performance analysis of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -ary FM and PM data transmission systems. Illustrative examples of the application of the formula are worked out for binary FSK.

Convective heat transfer with light winds

A simple expression for sensible heat flux under pure ‘thermal’ convection is developed on the basis of a fortunate observation of the shape and behavior of the indidual convection cells. The cells of rising air were seen to be nearly circular in cross‐section, the diameter decreasing upward, and separated from the environment by a sharp boundary in the lower levels. The model developed yields an expression involving only readily measurable parameters: height, mean temperature gradient, and difference of the modes of the instantaneous temperature frequency distribution.