A hearing aid with wireless signal transmission is provided which includes a radio reception unit for wireless reception of modulated and/or coded audio signals, a device to estimate the reception quality of the received audio signal, a device to generate an acoustic limit signal whose level increases when the estimated reception quality of the received audio signal decreases, a device to heterodyne a demodulated and/or decoded audio signal with the limit signal, and a device to output the audio signal heterodyned with the limit signal to a hearing aid wearer. To generate a limit signal, the hearing aid includes a device to generate an impulse response and a device to perform the operation of convolving the demodulated and/or decoded audio signal with the impulse response. This convolution produces a desired signal which appears closer to the hearing aid wearer when the estimated reception quality is better.