Advanced Noise Reduction Module

Theoretical Background

Noise Reduction Filters are designed to attenuate unwanted components in an audio signal while preserving the desired content. Each method operates on the signal in a specific domain and uses assumptions about signal and noise characteristics.

1. Wiener Filter

The Wiener filter is optimal in the mean-square-error sense. It uses the estimated power spectra of the signal and noise to compute a frequency-dependent gain H(f):

H(f) = S_xx(f) / [S_xx(f) + S_nn(f)]

where S_xx and S_nn are the signal and noise power spectral densities, respectively. In practice, it attenuates frequencies dominated by noise.

2. Spectral Subtraction

Spectral subtraction estimates noise by averaging silent segments and subtracts this from the noisy spectrum. The result is:

|Y(f)| = max(|X(f)| - |N(f)|, β·|N(f)|)

where |X(f)| is the noisy magnitude spectrum, |N(f)| the noise estimate, and β a small floor to avoid negative values.

3. Wavelet Denoising

Wavelet denoising transforms the signal into the wavelet domain, where noise often concentrates in small coefficients. By applying a threshold θ to coefficients:

w' = sign(w)·max(|w| - θ, 0)

and then inverting the transform, noise is reduced while preserving signal features.

Interpreting the Plots

• Time Domain: shows the waveform amplitude over time before and after filtering.
• Frequency Domain: illustrates the magnitude spectrum; filters appear as frequency‑dependent gains.
• Effective Gain (dB): plots the filter’s attenuation (in dB) across frequencies—a gain of 0 dB means no attenuation, negative values indicate suppression of noise bands.