V.I. Nefedov, O.I. Pugachev, E.V. Egorova, A.V. Gerasimov
Real sound signals basically are the continuous functions (if don’t take into consideration the quantum effect). For computer treatment of such signals it is necessary to convert the signals into the digital form. One of the available ways to perform this is to make the uniform measurement of the signal values in a definite period of time and then enter the obtained amplitude values into a computer. Making rather frequent measurements and achieving the discrete signals it is possible to regenerate the shape of the source continuous signal rather accurately. It should be noted that a sound signal being recorded in a real acoustical condition very often contains undesirable noises, which can be produced by the environment or the recording equipment. One of the noise classes is the additive stationary noises. There is an algorithm of spectral subtraction for additive stationary noises attenuation. This article presents the concise algorithm of spectral calculation used for elimination of the stationary noises. Briefly the algorithm consists of the next stages:
1. Signal decomposition by means of short-time Fourier transformation (STFT) or other transformation, that compactly localize the signal energy.
2. Noise spectrum estimation.
3. Noise amplitude spectrum subtraction from signal amplitude spectrum.
4. STFT reverse transformation - synthesis of the resulting signal.
STFT factors of the noise signals are statistically random, that lead to their nonuniform attenuation and this involves one of the spectral subtraction method problems which is called the «musical noise». As a result the refined signal contains the short-time and limited in frequency energy impulses, which can be heard as «handbells» or «running water». In some cases this effect even is less desirable, then the source attenuating noise. One of the most widen method for the «musical noise» attenuation uses the spectrum smoothing in time. More qualitative attenuation can be reached by applying for a spectrogram the adaptive two-dimensional algorithm of filtration, such as nonlocal averaging algorithm or bilateral filter used in noise attenuation during work with images.