The proposed method applies genetic algorithms (GA) to optimize the weight coefficients of the power spectrum of the Fourier-transformed signal of lateral acceleration of a moving car. The evolved weighted power spectrum detects the steering oscillations caused by the delayed steering response of a human driver in normal, routine driving situations - traffic-less driving on straight and curved roads. Delayed steering response is often a result of drivers having an inadequate cognitive load due to either distraction or cognitive overload. The experimental results, conducted on a realistically simulated car and its environment, indicate that, compared to the power spectrum featuring equal (flat) weight coefficients, the evolved weighted power spectrum facilitates improved discrimination between (i) signals of the lateral acceleration of the car driven by cognitively impaired (i.e., distracted by texting on a mobile phone while driving) drivers and (ii) analog signals of the car, driven by fully attentive drivers. Moreover, for all human drivers who participated in the experiments, the weighted power spectrum of the lateral acceleration of the car driven with distraction, even on a straight section of the road (i.e., inherently featuring lower values of the power spectrum) is even higher than that of the car driven by attentive drivers along curved roads (inherently, featuring higher values of the power spectrum). These results suggest that the proposed method would be applicable for discriminating between subtle driver-induced steering oscillations on straight roads and well-manifested, yet normal steering behavior of drivers when cornering.