A sometimes annoying problem in the most internationally widespread cellular telephone system, the GSM system, is an interfering signal generated by the switching nature of TDMA cellular telephone system. A humming noise originating from the speech frames, equivalent to 160 samples of data corresponding to 20 ms at 8 kHz sampling rate is sometimes clearly audible. This paper describes a study of two different software solutions designed to suppress such interference internally in the mobile handset. The methods are Notch Filtering, which is performed on a sample-per-sample basis, and Speech Frame Noise Cancellation, which is an alternative method employing correlators and subtraction, similar to Active Noise Control.