The Performance and Robustness of One-Parameter Fractional Linear Prediction

This paper deals with the problem of signal modeling using fractional-order linear prediction. In this research, we obtain the closed-form expression of the optimum sampling frequency of the One-Parameter Fractional-order Linear Prediction (OPFLP) and examine the performance when the fractional order (alpha) is in (0<=alpha<=2). Our investigation focuses on determining optimum alpha within the individual ranges of 0<=alpha<=1 and 1<=alpha<=2 while considering various influential parameters, such as sampling frequency and environmental interferences. We initiate our study by examining the impact of the sampling frequency, a critical parameter that demands meticulous selection, on the optimal value ‎of‎‎ alpha. Simulation Results demonstrate that if the sampling rate falls within five to six times the maximum frequency of the signal under scrutiny, the optimal range for alpha resides within 1<=alpha<=2. Conversely, when the sampling frequency exceeds six times the maximum signal frequency, the optimal alpha shifts to 0<=alpha<=1. This observation underscores the crucial relationship between sampling frequency and the appropriate selection of the fractional order alpha for effective OPFLP performance. In the next step, we assess the robustness of OPFLP in handling challenging signal processing tasks, particularly in hands-free speech acquisition applications. We evaluate the model's performance and robustness against environmental interferences in three scenarios: noisy environments, reverberant environments, and noisy-reverberant settings. Simulation outcomes highlight OPFLP's superior robustness compared to second-order LP in handling environmental interferences. Furthermore, our investigations elucidate that noise exerts a more detrimental impact on OPFLP performance than reverberation, emphasizing the nuanced effects of these interferences on the model's efficacy.