Wavelet Denoising Results

Initial Denoising Results

We added random white noise to three songs (one electronic, one classical, and one folk) and used several wavelet types to denoise the signal. To simplify the procedure, we only analyzed the first ten seconds of each song.

After trying different kinds of thresholding procedures, we concluded that SureShrink threshold calculation and soft thresholding application provided the best results. We used a level 5 decomposition for all cases.

The original audio files and noisy audio files are included below for comparison:

Comparison to Moving Average

Moving Average Results:

Comparing this set of the plots to the ones shown above for wavelet-based techniques, we see that the moving average, while simple to implement, does not have the same capabilities as wavelet based denoising. Thus, although wavelet based denoising requires more computational effort, it is worth that price because it can remove white noise from musical signals. Just listen to the difference between Jason Shaw's Acoustic Blues for Daubechie 4 Wavelet and Moving Average denoising!

Results from Subsequent Algorithms

We used the cross-correlation key signature detection algorithm to test results before and after denoising. Please find below a list of tabulated results.

As we can see from above, even with 50% noise added, the cross correlation key identification algorithm is robust to noise. The interesting result here is that after using wavelet denoising, in certain cases denoted in red, the algorithm no longer gives the correct result. For these cases, when Daubechie 4 wavelet denoising did not return the correct result, we tried using other wavelet types. We are not sure why this happens. Upon inspection of the resulting audio files, it seems that the song audio becomes corrupted by the noise when the wavelet denoising technique doesn't work properly.

Conclusions

We see that wavelet denoising can be used to denoise music files with white noise, but it doesn't do the best job possible. That being said, compared to the moving average technique, wavelet denoising is a much better strategy in this case.

When used with our key detection algorithm, wavelet denoising did not improve the results from noisy signals. In fact, the wavelet-denoised signals made results worse in some cases. Thus, it is not recommended to use this simplified version of wavelet based denoising in conjunction with further analysis.