## 2 The Effects on Amplitude Due to Interactions between Tones
### Analysis of Varying the Position of the Interharmonic Tone  
The amplitude variations that appear in the analysis of successive windows (and as a consequence of the spectral leakage produced by a single fixed interharmonic tone) were discussed in the previous section. Next, a similar analysis was made, but varying the frequency of the interharmonic tone of the previous example. The RMS value measured in the spectral bar corresponding to 250 Hz is represented in Figure 3, with a fixed harmonic tone of 13.2 V at the same frequency and a second interharmonic tone of 9.8 V with variable frequency. The values obtained with the DFT on four non-overlapping and consecutive windows 0.2 s long (tw1-tw4) are shown in that figure. These values were obtained using rectangular windows. When the harmonic and variable tones coincide at the origin of abscissa, 250 Hz, the RMS value of their vectorial sum is obtained. For the other variable tone positions that are synchronous with the _tw_ window (or multiples of the basic frequency: 255, 260, 265... Hz) the harmonic does not receive leakage, and therefore, its value remains stable at 13.2 V. The value obtained is different due to the generated leakage for the rest of the non-synchronous (or interharmonic) positions, with more significant variations the closer is the variable frequency interharmonic tone to the measured spectral bar, located at 250 Hz. Thus, the interaction between tones is more significant when both are closer together (Figure 3, 250-255 Hz spectral bar interval), and smaller variations occur when both tones are far apart (Figure 3, 260-265 Hz, 265-270 Hz). Therefore, in the analysis of a single window, the values obtained in all cases were different from the desired common RMS values, except in variable tone synchronous positions, where there was no leakage (see Figure 3a).  
Figure 3b shows a zoom of the area between the harmonic at 250 Hz and the following spectral bar at 255 Hz. It can be seen that the values obtained are the same as in the example in the preceding section when the position of interharmonic sweeping tone was 253.3 Hz: 9.37 V in the window tw1,  
Figure 3: RMS value measured at the 250 Hz spectral bar, with a 13.2 V harmonic fixed in the same position, as a function of the 9.8 V variable frequency tone position, in several successive windows treated individually (tw1-tw4): (**a**) variable frequency tone positions between 250 and 270 Hz, and (**b**) zoomed zone between 250 and 255 Hz.  
16.30 V in tw2, 14.78 V in tw3, 9.37 V again in the window tw4, etc. Figure 3b also highlights the position of the variable tone at 251.6 Hz. In this case, the ideal period _Tw_ is also 0.6 s, and therefore, the RMS values found repeat every three windows. Additionally, the total spectral leakage produced was the same for the positions of the variable tone at 251.6 Hz and 253.3 Hz. However, when the tone was at 251.6 Hz, the variations in the values found in each window were higher, due to its closer proximity to the 250 Hz spectral bar, where the amplitude was actually measured.  
In conclusion, in the analysis of a single window, the values obtained change depending on the position of the variable tone and are different from the ones desired, except in the synchronous positions of the tone, in which there is no leakage. Moreover, for the same position of the variable tone, the values obtained are different if they are compared along successive windows, except for the positions in which the tone does not emit leakage (and in general, the positions with distances between tones are multiples of the spectral resolution), as shown in Figure 3.