A method of removing narrowband interference signals from communication signals having both data and data free intervals comprising the steps of: sampling the communication signals to generate time domain data samples thereof; transforming the time domain samples into a first series of spectral terms in the frequency domain, said samples containing data and data free intervals; generating a representation of an inverse transform of the first series of spectral terms related to respective time domain data samples; identifying spectral terms corrupted by said narrowband interference signals; reducing the representation of the inverse transform by removal of data containing entries of the representation, which are entries for time domain samples known to contain data; decomposing the representation of the inverse transform into contributions from spectral terms corrupted by said narrowband interference signals and into contributions from spectral terms not corrupted by narrowband interference signals; inserting, into non-corrupted entries of the decomposed representation, which are the entries for spectral terms not corrupted by narrowband interference signals, predetermined values for the time domain samples that are known to be data free; subtracting the contribution of the non-corrupted spectral terms from the data free entries of the representation, which are entries for time domain samples known to be data free, to provide thereby a representation that defines the contribution of the corrupted spectral terms to a predetermined time domain signal at the data free entries; estimating the value for the corrupted spectral terms that contribute to the predetermined time domain signal at the data free entries to provide a replacement value for the corrupted spectral terms; replacing only those corrupted spectral terms in the first series of spectral terms with a corresponding respective replacement value of the corrupted spectral terms to provide thereby a second series of spectral terms; and inverse transforming the second series of spectral terms to provide an essentially interference free signal. sampling the communication signals to generate time domain data samples thereof; transforming the time domain samples into a first series of spectral terms in the frequency domain, said samples containing data and data free intervals; generating a representation of an inverse transform of the first series of spectral terms related to respective time domain data samples; identifying spectral terms corrupted by said narrowband interference signals; reducing the representation of the inverse transform by removal of data containing entries of the representation, which are entries for time domain samples known to contain data; decomposing the representation of the inverse transform into contributions from spectral terms corrupted by said narrowband interference signals and into contributions from spectral terms not corrupted by narrowband interference signals; inserting, into non-corrupted entries of the decomposed representation, which are the entries for spectral terms not corrupted by narrowband interference signals, predetermined values for the time domain samples that are known to be data free; subtracting the contribution of the non-corrupted spectral terms from the data free entries of the representation, which are entries for time domain samples known to be data free, to provide thereby a representation that defines the contribution of the corrupted spectral terms to a predetermined time domain signal at the data free entries; estimating the value for the corrupted spectral terms that contribute to the predetermined time domain signal at the data free entries to provide a replacement value for the corrupted spectral terms; replacing only those corrupted spectral terms in the first series of spectral terms with a corresponding respective replacement value of the corrupted spectral terms to provide thereby a second series of spectral terms; and inverse transforming the second series of spectral terms to provide an essentially interference free signal.