A hearing aid comprises at least one input unit for providing at least one stream of samples of an electric input signal in a first domain; at least one encoder configured to convert said at least one stream of samples of the electric input signal in the first domain to at least one stream of samples of the electric input signal in a second domain; a processing unit configured to process said at least one electric input signal in the second domain, to provide a compensation for the user's hearing impairment, and to provide a processed signal as a stream of samples in the second domain; a decoder configured to convert said stream of samples of the processed signal in the second domain to a stream of samples of the processed signal in the first domain. The at least one encoder is configured to convert a first number of samples from said at least one stream of samples of the electric input signal in the first domain to a second number of samples in said at least one stream of samples of the electric input signal in the second domain. The decoder is configured to convert said second number of samples from said stream of samples of the processed signal in the second domain to said first number of samples in said stream of samples of the electric input signal in the first domain. The second number of samples is larger than the first number of samples. The at least one encoder is trained, and at least a part of said processing unit providing said compensation for the user's hearing impairment is implemented as a trained neural network. A method of operating a hearing aid is further disclosed. Thereby an improved hearing aid may be provided.