A hearing aid includes an input transducer for provision of an input signal, a high pass filter configured for providing a high pass filtered part of the input signal, a low pass filter configured for providing a low pass filtered part of the input signal, a synthesizing unit configured for generating a synthetic signal from the high pass filtered part using a model based on a periodic function, wherein a phase of the synthetic signal is at least in part randomized, a combiner configured for combining the low pass filtered part with the synthetic signal for provision of a combined signal, a hearing loss processor configured for processing the combined signal for provision of a processed signal, and a receiver coupled to the hearing loss processor, wherein the receiver is configured for converting an audio output signal into an output sound signal.