A filter such as a Wiener filter for noise reduction in a signal, such as a speech signal, affected by background noise includes a circuit for determining values of an update function relating new value of estimated noise power to a previous value of estimated noise power, the update function being a function of said previous estimated noise power and a mean input power spectral density. The circuit includes a look-up table having values for the update function stored therein with the previous value of estimated noise power and the mean input power spectral density as a first and a second search entry, respectively. These search entries are entered via an input module and exploited by search circuitry associated with the look-up table for selectively searching values for the update function in the look-up table. The search is preferably carried out on the basis of an index computed starting from said first and second search entries.