Багатоканальна система передачі даних у сплайнових базисах

Abstract

Запропоновано принцип побудови багатоканальної системи передавання даних з використанням сплайнів та проаналізовано статистичні результати дослідження побудованої моделі. The article deals with multichannel digital data transmission system in which the digital signal is transmitted through the manipulation of the harmonic function which performs subcarrier function with different frequency for different channels. However, so far as the video signal with rectangular shape is characterized by a wide spectrum, the resulting signal also has a wide spectrum, which is not acceptable for most of communication systems with a large number of channels. In order to limit the occupied bandwidth in the filter the Hermitian cubic spline filter’s function is used. The quantity of the points of spline filter is defined according to the task of smoothing of harmonic subcarrier’s sampling frequency of different channels. In this paper an analysis of the amplitude-frequency characteristics of spline filters for oddly even number of points has been conducted and the dependence of the filter’s bandwidth extension with the points quantity decrease has been revealed. Low slope recession and respectively bad filtering of copies of discrete signal are also typical for the spline’s characteristics with the points quantity less than 64. Total signal is the sum of values which come in succession from the interpolators of each of the channels. On the receiving side the separation of channel signals is done by Savitsky-Golay filters. Spline functions which were used for the interpolation on the transmission side (LSS-decomposition) are the basis of given filters. Since the spline filter’s frequency response corresponds in shape to a low pass filter the filter’s bandwidthes with different numbers of points intersect. But that does not prevent the exercise of the corresponding channel selection signal if you follow the order of separation from a more narrowband channel to a more broadband one. For the estimation of stability of the described system of transmission to the operation of additive Gaussian noise and violation of synchronization a two-channel model was built. 128 function points for the channel with higher transmission rate and 512 – for the channel with slower rate were used. The frequencies of the harmonic functions and the sampling frequencies of the channels were selected: F128 = 16 Hz, fs128 = 64 Hz, for a channel with the number of points 128 and F512 = 1 Hz, fs512 = 16 Hz, for a channel with the number of points 512. Shift keying period corresponds to the sine waves period what eliminates the open-phase fault. The results of the conducted analysis show transmission system’s high stability to the noises but low stability to the deviation of synchronization in the form of a considerable growth of error probability to bit.