In order to convert a complex analog signal into a complex digital signal in an analog-digital conversion device having two channels, I and Q respectively, in quadrature, each comprising an input and an associated output, each output being fed back onto said associated input so as to form a first and a second feedback loops each comprising a digital-analog converter, the device comprising a complex filter with a first stage and a last stage, after sampling (508), a signal integration is performed in a first stage (501) of the filter without introducing any substantial delay. Then, an integration is performed in the last stage (502) of the filter. A substantial delay (507) is then introduced and the output signal of the last stage is converted into a digital signal over several bits. The digital signal is injected into the feedback loop (108) of said channel and the digital signal is converted into a feedback signal.