MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV

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MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV JAMES S. WALKER In this article we describe how the freeware AUDACITY and FAWAVE are used for musical analysis and processing.

1 MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV JAMES S. WALKER In this article we describe how the freeware AUDACITY and FAWAVE are used for musical analysis and processing. Our discussion will provide complete details on how the examples in the paper, Music: A time-frequency approach (MTFA), were generated. There are two sections. Section 1 describes how AUDACITY can be used for displaying spectrograms and tracing those spectrograms as an audio file is played. Section 2 describes how FAWAVE can be used for computing Gabor transforms and their inverses, and for plotting scalograms, as done in MTFA. All of the sound files and FAWAVE formulas discussed in this article are available from the following webpage: which we shall refer to as the MTFA webpage. AUDACITY is freeware for audio editing, available at 1. USING AUDACITY It has a fairly intuitive interface, but it may be helpful to explain how to plot spectrograms with it. You begin by loading an audio file. To load an audio file, say the file Analysis I passage from firebird suite.wav (1) you first select File/Open from the AUDACITY menu, and then select the file. In Fig. 1 we show the result of loading the file listed in (1). FIGURE 1. Initial AUDACITY window with.wav file loaded. We have indicated on the left where to click to change the view to a spectrogram (click on Spectrum from the menu that appears). 1

2 JAMES S. WALKER FIGURE 2. Spectrogram of a.wav file, after lengthening the display to fill the screen. We have indicated the play button for playing the file and tracing out the spectrogram.

2 2 JAMES S. WALKER FIGURE 2. Spectrogram of a.wav file, after lengthening the display to fill the screen. We have indicated the play button for playing the file and tracing out the spectrogram. You then convert the display to a spectrogram. We have indicated in Fig. 1 how to convert the display of the wav file to a spectrogram. You click on the triangle indicated on the left of the figure and a menu appears. From that menu, you select the item Spectrum. In Fig. 2 we show the spectrogram that results. We have also lengthened the vertical dimension of the display by grabbing the bottom edge of its window. By pressing the play button (indicated in Fig. 2), you can trace out the spectrogram while the audio file is playing as recommended in MTFA. 2. USING FAWAVE In this section we describe how FAWAVE can be used for musical analysis and processing, with special reference to computing the examples described in MTFA. You can download FAWAVE from the following website: To compute Gabor transforms or scalograms using FAWAVE, we first load a sound file, say the Firebird Suite passage listed in (1). That can be done by either selecting Open sound file (*.wav) from the File menu, or selecting New 1-dim from the File menu and then right-clicking on the empty graph box and choosing Load/Sound file. At the top of Fig. 3 we show the loaded file in the Audio Editor window. Because of memory limitations in the programming language used to develop FAWAVE, it can only handle 1-D files of maximum length 65,536 points. Hence with this file we have to select parts of the signal to analyze. At the top of Fig. 3 we show a selected region between two vertical lines. The left line was selected first by left-clicking on the graph, followed by the right line by a second left-click. At the bottom of Fig. 3 we show the menu that appears after right-clicking on the selected region. You select the choice Clip in order to produce a clip of the signal equal to the selected region. In Fig. 4 we show the clipped signal displayed on the right of the Audio Editor window. By pressing the Analyze button you can then graph this signal in a new 1-Dim window for performing Fourier and wavelet analysis. For example, on the left of Fig. 5 we show how to perform a Gabor transform of the signal. You select Analysis/Spectrogram from the menu. On the right of Fig. 5 we show the spectrogram that is plotted for a Blackman-windowed Gabor transform (after pressing the Compute button shown in the figure). The seven-panel spectrogram in MTFA was obtained by splicing together separate spectrograms of portions of the original wav file. For example, to get the next portion s spectrogram, you right-click on the right vertical line of the previously selected region (shown on the left of Fig. 3) and then select Move clip region from the popup menu (seen

MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV 3 FIGURE 3. Top: Loaded sound file after left-clicking twice to select a region (between the two vertical lines).

3 MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV 3 FIGURE 3. Top: Loaded sound file after left-clicking twice to select a region (between the two vertical lines). Bottom: Menu that appears after right-clicking on selected region (Clip is to be chosen to clip out the selected region for analysis). FIGURE 4. Sound clip selected and displayed on the right side. By pressing the Analyze button you can graph this signal in a new 1-Dim window for further analysis. at the bottom of Fig. 3). The vertical lines then shift over, with the new left line replacing the old right line, and the clipped signal shown on the right automatically updates to the new region. You then repeat the spectrogram plotting process to get a spectrogram for this new region. In this way you can march across the signal in disjoint segments and plot spectrograms for each separate region.

4 JAMES S. WALKER FIGURE 5. Left: Selected clip displayed in 1-Dim window with Spectrogram procedure being selected.

We produced the seven panel plot in MTFA by copying each spectrogram (after dragging the right border over to show only the spectrogram itself) to the WINDOWS R clipboard.

Once the spectrogram was copied to the clipboard we then pasted it into an MS-WORD R document and resized it so that seven separate clippings could be arranged in a row.

4 4 JAMES S. WALKER FIGURE 5. Left: Selected clip displayed in 1-Dim window with Spectrogram procedure being selected. Right: Graph of spectrogram obtained from a Blackman windowed Gabor transform after pressing Compute button. FIGURE 6. Copying a spectrogram plot to the Clipboard (after selecting File/Print). We produced the seven panel plot in MTFA by copying each spectrogram (after dragging the right border over to show only the spectrogram itself) to the WINDOWS R clipboard. This copying to the clipboard was done by selecting File/Print, producing the window shown in Fig. 6. Once the spectrogram was copied to the clipboard we then pasted it into an MS-WORD R document and resized it so that seven separate clippings could be arranged in a row. To produce the seven-panel scalogram in Fig. 3 of MTFA we proceeded in the same way. The only difference was that we computed scalograms rather than spectrograms. To compute a scalogram you choose the Scalogram option from the menu shown on the left of Fig. 5. For example, we show a scalogram in Fig. 7 (using the parameters from Analysis I in MTFA). To enhance the appearance of the scalogram we changed the viewing style by selecting View/Display style

MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV 5 FIGURE 7. Left: Gabor scalogram. Right: Enhanced view of Gabor scalogram. FIGURE 8.

and then replotted the scalogram as shown on the right of Fig. 7.

Buenos Aires.wav (2) To compute the percussion scalogram shown in MTFA, we proceeded as follows.

5 MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV 5 FIGURE 7. Left: Gabor scalogram. Right: Enhanced view of Gabor scalogram. FIGURE 8. Left: Selecting Percussion scalogram for a modified spectrogram. Right: Percussion scalogram. and then replotted the scalogram as shown on the right of Fig. 7. Plotting seven separate scalograms and piecing them together, in the same way as we did for the spectrograms, we produced the seven-panel scalogram in MTFA. The spectrograms for Analysis II in MTFA were computed by the procedure described above, except that we used the sound file Analysis II passage from Buenos Aires.wav (2) To compute the percussion scalogram shown in MTFA, we proceeded as follows. We loaded the sound file Analysis II clip from Buenos Aires percussion plotted its spectrogram, selected Graph/Plot and plotted the function g1(2000 < y < 3000) and then selected Percussion scalogram (see the left of Fig. 8). We then calculated a Gabor wavelet scalogram of the resulting signal (see the right of Fig. 8). The spectrograms and scalograms in the remainder of MTFA were computed by the methods described above. We now turn to the syntheses described in Section 3 of MTFA.

6 6 JAMES S. WALKER FIGURE 9. Left: Plotting a boxcar windowed Gabor transform. Right: Plotting a hard threshold denoising of Gabor transform on left. To produce the denoisings described in subsection 3.2 of MTFA you do the following. First, select File/New 1-dim from the menu and then load (by right-clicking on the empty graph area and selecting Load/Sound file from the popup menu) the sound file Synthesis I noisy warbler song.wav Second, you plot its spectrogram (selecting None from the Filter list 1 ). See the left of Fig. 9. Fourth, you select Graph/Plot from the spectrogram menu, and plot the following function: g1(abs(g1)>c)\c= See the right of Fig. 9. [In this formula g1 is replaced at each point in the time-frequency plane by the Gabor transform magnitude at that point, while the phase is left unchanged. The quantity (abs(g1)>c) returns the value 1 if the Gabor transform magnitude is larger than c, and returns the value 0 otherwise. Hence this formula performs hard thresholding with threshold c.] Fifth, you select Graph/Invert and that will produce the first denoising described in MTFA. To produce the second denoising you do the same steps, except the function you plot is (g1-c)(abs(g1)>c)\c= To perform the selected amplification described in subsection 3.3 of MTFA, you do the following. First, load the sound file Synthesis II original clip from Firebird Suite.wav Second, compute a Blackman windowed spectrogram. Third, you select Graph/Plot from the spectrogram menu and then press the Load button (see the left of Fig. 10) to load the formula in the following file firebird_clipping_amplification.uf2 This formula file can be obtained from the archive formulas.zip at the MTFA website. This archive is located by clicking on the link Document on using FAWAVE and AUDACITY (3) You can extract all of its files to the Formulas subdirectory of your FAWAVE directory. We show on the left of Fig. 10 the result of plotting this formula. To obtain the artificial bird chirp in subsection 3.5 of MTFA you do the following. First, load the sound file Synthesis IV oriole chirp.wav 1 In FAWAVE a boxcar windowed spectrogram is plotted using this None option.

MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV 7 FIGURE 10. Left: Modified spectrogram. Right: 16-bit option checked for playing sound file. Second, compute its Blackman windowed spectrogram.

uf2 Fourth, plot this formula and choose Graph/Invert from the spectrogram menu. The graph that results from this last step is an artificial bird chirp.

7 MUSIC ANALYSIS AND PROCESSING WITH AUDACITY AND FAWAV 7 FIGURE 10. Left: Modified spectrogram. Right: 16-bit option checked for playing sound file. Second, compute its Blackman windowed spectrogram. Third, choose Graph/Plot from the spectrogram menu and load the following formula file (from formulas.zip): new_bird_chirp (Synthesis IV).uf2 Fourth, plot this formula and choose Graph/Invert from the spectrogram menu. The graph that results from this last step is an artificial bird chirp. You can listen to it by selecting Graph/Audio from the menu. To obtain the artificial bird song, you repeat the steps just described but use the following formula: new_bird_sound (Synthesis IV).uf2 Note: When playing the resulting artificial bird song, be sure that you check the option 16-bit (see the right of Fig. 10). JAMES S. WALKER, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF WISCONSIN EAU CLAIRE, W A L K E R J S@U W E C.E D U

Examples and Exercises for A Primer on Wavelets

Examples and Exercises for A Primer on Wavelets James S. Walker Department of Mathematics University of Wisconsin Eau Claire Eau Claire, WI 5472 44 e-mail: walkerjs@uwec.edu 1 Examples and Exercises for