The goal of this project was to compare the two methods in their ability to remove unwanted noise from a signal. For this purpose we needed signals that were ‘clean’ (that did not have noise added to them) and the same signals after noise corruption. By having both the noisy and clean signals, it was possible for us to see how well our filtering methods did, based on a comparison of the filtered signal with the original clean signal.
Available Data
The data we worked with was available at http://www.ee.columbia.edu/~dpwe/sounds/sents/. This source basically had 3 male and 3 female clean speech signals, all about 3 seconds long. For each of these clean signals, there were 6 different kinds of noise added to them. Thus we essentially had 36 different speech signals of about 3 seconds each. For the implementations we used for both spectral subtraction and Wiener filtering, it was necessary to have a short segment of noise-only signal so that the characteristics of noise could be estimated. These signals were chosen because in addition to providing us with both the clean and corrupted version of a signal, these signals had initial short segments that were noise only.
Filtering Process
For both Spectral Subtraction and Wiener Filtering, we used MATLAB implementations that were available online (can be found in the ADDENDUM section).
Both of these methods work by iterating over a noisy signal in terms of small overlapping windows and performing the algorithm. The inputs to these methods were: 1) the noisy input signal, 2) the sampling frequency and 3) the length of the initial noise-only signal.
How to compare the results of the two methods?
The two methods were compared in 3 manners.
1.The most crude method was listening to the clean signal, the noisy signal and then the filtered signal. Since humans are accustomed to listening and understanding speech signals, this was an intuitive way to understand the effects of filtering.
2.The second method was plotting the time domain and frequency domain versions of the clean, noisy and filtered signal and comparing them for the two denoising methods. This allowed a relatively more empirical differentiation of the two methods.
3.Both of these methods, even though were intuitive and gave a good understanding of the workings of the two methods in the first approximation, were not quantitative enough to draw any conclusions.Since the clean signals were also available, we took advantage of that by finding the correlation of the filtered signal and the clean signal. A correlation of 1 would thus translate to perfect noise removal.