A pulse-shape estimator calculates an impulse response for the transmit and receive pulse-shaping filters in a mobile wireless terminal. The pulse-shape estimator receives a training signal that has passed through the pulse-shaping filters and known training symbols. Based on the actual received signal containing the training symbols and the expected received signal, the pulse-shape estimator estimates the impulse response of the pulse-shaping filters. The calculated impulse response may be used to improve signal demodulation or to calculate the coefficients for a digital filter applied before demodulation to compensate for pulse-shape distortion.