Professor Patrick J. Wolfe's Harvard Home Page

Harvard University > Division of Engineering and Applied Sciences > Electrical Engineering > Patrick J. Wolfe

Examples of Short-Time Spectral Attenuation

Patrick J. Wolfe and Simon Godsill

Here are some examples of short-time spectral attenuation in the case of narrowband speech:

This speech example is taken from the RWTH Aachen Institute of Communication Systems and Data Processing.

Noisy Signal (SNR 25 dB)
Restored Signal (SNR 25 dB) Using MMSE criterion due to Ephraim and Malah, with smoothing parameter alpha = 0.97
Restored Signal (SNR 25 dB) Using approximate MAP criterion due to Wolfe and Godsill, with smoothing parameter = 0.97

Noisy Signal (SNR 0 dB)
Restored Signal (SNR 0 dB) Using MMSE criterion due to Ephraim and Malah, with smoothing parameter 0.97
Restored Signal (SNR 0 dB) Using approximate MAP criterion due to Wolfe and Godsill, with smoothing parameter 0.97

In both of the above cases, the approximate MAP solution yields a slightly lower level of musical residual noise.

Below, a comparison of 11 different methods is given for an input SNR of 10 dB:

Software

Download the latest version of the STSA Matlab Toolbox as STSA-Toolbox-0-03.zip. Installation instructions may be found here.

With this Matlab toolbox you can reproduce the results shown here as well as in the EURASIP journal paper submission, and experiment with different short-time spectral attenuation algorithms.

Written by Patrick J. Wolfe and distributed under the terms of the GNU General Public License.

SNR Results

To view some results obtained using narrowband speech as well as wideband speech and music, you can download this zipped .mat file which contains SNR measurements for the three different audio examples discussed in the paper, for both smoothed and unsmoothed estimation versions, as well as Wiener filtering and magnitude spectral subtraction.

You'll have to take a look at the file eurasip.m contained in the /demos directory of the STSA Matlab Toolbox to understand how these data were generated (in the above .mat file, struct E corresponds to the wideband speech example; struct F to the narrowband speech example; and struct G to the wideband music example).

To reproduce these results, you'll need the source files in eurasip_audio.zip You can then, for example, reproduce the SNR results reported in the paper.

Spectrogram Results

Below is a comparison of spectrograms corresponding to the sound examples given above (moving from left to right, and then by rows), for degradations yielding an SNR of 25, 10, and 0 dB, respectively:

[Matlab diagram]

In the 25 dB case (above), it can be seen that the decision-directed approach for a priori SNR estimation (first row of figures) reduces the resultant level of residual noise. However, this smoothing is noticeably audible.

[Matlab diagram]

At an SNR of 10 dB (above), the musical residual noise is quite visible in the non-decision-directed approaches to a priori SNR estimation (second and third row of figures).

[Matlab diagram]

At an SNR of 0 dB (above), even the decision-directed approaches (first row of figures) result in noticeable musical noise.