Apparatus for tuning a Gm-C filter, comprising: a Gm-C filter including one or several interconnected Gm-C cells (310,311; 320,312), the Gm-C cells having a transconductance amplifier (310, 320), a tuning terminal, and a transconductance gain (g m) that is dependent from an electric value present on the tuning terminal; the Gm-C filter including one or more switching elements (510a, 510b, 510c, 510d), allowing to configure the Gm-C filter in a calibration configuration and in a filtering configuration, wherein the calibration configuration of the Gm-C filter is a free running oscillator; a digital controller, operatively arranged to measure a response of the Gm-C filter in the calibration configuration, and to generate a digital tuning value depending on the response measured, wherein the digital controller is operatively arranged to measure a period or a frequency of the oscillations of the Gm-C filter in the calibration configuration, and to generate said digital tuning value depending on the measured period or frequency; an amplitude regulation unit, operatively arranged to limit a forward gain of an output amplifier of the Gm-C filter, when the Gm-C filter is in the calibration configuration in order to maintain the oscillation amplitude in a linear operating range of the Gm-C filter, a digital-to-analogue converter, converting said digital tuning value into an analogue tuning signal, fed to the tuning terminals of the Gm-C cells; whereby the apparatus is operatively arranged to converge, in the calibration configuration, to a predefined response, and the digital-to-analogue converter is operatively arranged to maintain the resulting tuning signal in the filtering configuration, wherein the digital controller is active only during the calibration cycle and is switched off or switched to a low-power mode during the filtering configuration. a Gm-C filter including one or several interconnected Gm-C cells (310,311; 320,312), the Gm-C cells having a transconductance amplifier (310, 320), a tuning terminal, and a transconductance gain (g m) that is dependent from an electric value present on the tuning terminal; the Gm-C filter including one or more switching elements (510a, 510b, 510c, 510d), allowing to configure the Gm-C filter in a calibration configuration and in a filtering configuration, wherein the calibration configuration of the Gm-C filter is a free running oscillator; a digital controller, operatively arranged to measure a response of the Gm-C filter in the calibration configuration, and to generate a digital tuning value depending on the response measured, wherein the digital controller is operatively arranged to measure a period or a frequency of the oscillations of the Gm-C filter in the calibration configuration, and to generate said digital tuning value depending on the measured period or frequency; an amplitude regulation unit, operatively arranged to limit a forward gain of an output amplifier of the Gm-C filter, when the Gm-C filter is in the calibration configuration in order to maintain the oscillation amplitude in a linear operating range of the Gm-C filter, a digital-to-analogue converter, converting said digital tuning value into an analogue tuning signal, fed to the tuning terminals of the Gm-C cells; whereby the apparatus is operatively arranged to converge, in the calibration configuration, to a predefined response, and the digital-to-analogue converter is operatively arranged to maintain the resulting tuning signal in the filtering configuration, wherein the digital controller is active only during the calibration cycle and is switched off or switched to a low-power mode during the filtering configuration.