Spectral subtraction is used in this research as a method to remove noise from noisy speech signals in the frequency domain. This method consists of computing the spectrum of the noisy speech using the Fast Fourier Transform (FFT) and subtracting the average magnitude of the noise spectrum from the noisy speech spectrum. We applied spectral subtraction to the speech signal “Real graph”. A digital audio recorder system embedded in a personal computer was used to sample the speech signal “Real graph” to which we digitally added vacuum cleaner noise. The noise removal algorithm was implemented using Matlab software by storing the noisy speech data into Hanning time-widowed half-overlapped data buffers, computing the corresponding spectrums using the FFT, removing the noise from the noisy speech, and reconstructing the speech back into the time domain using the inverse Fast Fourier Transform (IFFT). The performance of the algorithm was evaluated by calculating the Speech to Noise Ratio (SNR). Frame averaging was introduced as an optional technique that could improve the SNR. Seventeen different configurations with various lengths of the Hanning time windows, various degrees of data buffers overlapping, and various numbers of frames to be averaged were investigated in view of improving the SNR. Results showed that using one-fourth overlapped data buffers with 128 points Hanning windows and no frames averaging leads to the best performance in removing noise from the noisy speech.