| Summary: | The pre-emphasis problem for FM radiotelephony over an additive white Gaussian noise channel is investigated. A Gaussian model and an experimentally measured frequency spectrum density for speech are used to solve the optimum filtering problem analytically. The optimum pre-emphasis characteristic is expressed in terms of the message spectral power density, the noise power density and the LaGrange multiplier. An iterative algorithm for the determination of the multiplier is presented and solved numerically for typical values of the signal-to-noise ratio. The optimum filter is unrealizable. It is approximated by a whitening filter in cascade with a two pole network. The selection of the pole positions involves a trade-off between mean square error performance and spectral compression. The transmitted signal spectra are computed numerically for three choices of pole positions and compared to those for the currently employed prefilter. The mean square error is computed and compared to the optimum mean square error for typical values of the signal-to-noise ratio. The new designs have less distortion than the present design. The roll-off rate of the spectrum in the adjacent channel region is determined to be greater than 4 for the proposed filter. This compares favourably with the rate of 2 for the current filter. Interference coefficients are defined to measure the interference between adjacent channel signals. The cases of voice-to-voice, voice-to-digital and digital-to-voice interference are investigated. Four types of data signals are considered, PAM signals with a = 0 and a = 1, MSK and PSK signals. An improvement ranging from 4 to 19 dB is noted for the new network. The improvement is greatest for the bandlimited PAM signals. The effects of a different speech model on the previous results are investigated. Spectra and interference coefficients are computed for a second speech spectral density function. A computer simulation verifies that the proposed new design offers improved performance. === Applied Science, Faculty of === Electrical and Computer Engineering, Department of === Graduate
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