## 5 Measurement Improvements by Window Overlapping  
### Appearance of Local Peaks  
In previous sections, the interactions between two frequency components--such as a harmonic (that does not emit leakage) and an interharmonic whose leakage was vectorially added in the position of the harmonic, generating a variable amplitude in the total vector--were analyzed. However, this situation also extends to other frequency components, which interact when added together in the same spectral bar. Examples of these frequency components that interact on the spectral bars of a frequency group are leakage generated by interharmonic tones present within a group being measured; leakage received from other tones located outside the group; or even, if HW is used, sidebands (located within the measured group) of all types of tones, both harmonic and interharmonic, internal and external to the group.  
Thus, when several frequency components interact in the same spectral bar, they are vectorially added in that position, generating a total vector whose amplitude depends on their phase angles and frequencies. If these components occupy synchronous positions (therefore, they do not emit spectral leakage), the vector amplitude remains stable. If, on the other hand, the phase angles change and differ at the beginning of each acquisition window, the vector amplitude will also change, and time aggregation will be necessary to find the result closest to the desired common RMS value. This is the case for several tones whose frequency difference (or relative rotation speed) is not a multiple of the frequency resolution, as may occur between a harmonic and an interharmonic, or between several interharmonics (and even harmonics, when there are synchronism errors).  
However, if the frequency differences between the spectral components that interact in the same spectral bar are multiples of the frequency resolution, \(D\!f\), the relative phase between these components do not change between successive windows, and therefore, its total sum vector does not change either. Therefore, time aggregation does not solve these cases, but this may result in inadequate or singular values at the positions of these components, creating local peaks. These peaks may come closer or move away from the correct amplitude value, depending on the phase angle between the tones that cause them. However, most of the time the local peaks move away from the correct common RMS value obtained for other sweep tones, close to each singularity (except for the case of a 90\({}^{\circ}\) phase angle between all leakage vectors, in which case the correct RMS value is always obtained).  
Figure 7a,b shows an example of these local peaks at distances multiples of 5 Hz between the variable tone and the interharmonic located at 752.5 Hz. Figure 7a illustrates the result using RW, and Figure 7b using HW. Note how the largest local peaks are due to the sidebands of both tones and obtained when HW is used. However, HW generates more local peaks of much smaller amplitude, also at distances multiples of _Df_. These other peaks are not observed in the figure because this window significantly attenuates the leakage of more distant tones.