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We used Spectral Subtraction in this research as a method to remove noise from speech signals. Initially, the spectrum of the noisy speech is computed using the fast Fourier transform (FFT), then the average magnitude of the noise spectrum is subtracted from the noisy speech spectrum. We applied Spectral Subtraction to the speech signal "Hot dog" to which we digitally added vacuum cleaner noise. We implemented the noise removal algorithm 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). We had recourse to the speech to noise ratio (SNR )in order to evaluate the performance of the proposed algorithm.