Noise reduction for periodic signals using high-resolution frequency analysis

The spectrum subtraction method is one of the most common methods by which to remove noise from a spectrum. Like many noise reduction methods, the spectrum subtraction method uses discrete Fourier transform (DFT) for frequency analysis. There is generally a trade-off between frequency and time resolution in DFT. If the frequency resolution is low, then the noise spectrum can overlap with the signal source spectrum, which makes it difficult to extract the latter signal. Similarly, if the time resolution is low, rapid frequency variations cannot be detected. In order to solve this problem, as a frequency analysis method, we have applied non-harmonic analysis (NHA), which has high accuracy for detached frequency components and is only slightly affected by the frame length. Therefore, we examined the effect of the frequency resolution on noise reduction using NHA rather than DFT as the preprocessing step of the noise reduction process. The accuracy in extracting single sinusoidal waves from a noisy environment was first investigated. The accuracy of NHA was found to be higher than the theoretical upper limit of DFT. The effectiveness of NHA and DFT in extracting music from a noisy environment was then investigated. In this case, NHA was found to be superior to DFT, providing an approximately 2 dB improvement in SNR.