components and no frequency contents at the other DFT values If we are considering a periodic signal with period 64,then our signal is the sum of two pure sinusoidal sequences,and thus the clean appearance of the DFT correctly shows the expected spectrum.However,since we are considering a finite-length sequence,the DFT figure can lead to an illusion resulting from the sampling of the spectrum.As shown in OSB Figure 10.6(c),the Fourier transform of vn]has significant content at almost all frequencies but is exactly zero at the frequencies that are sampled by the DFT.Therefore,interpreting the spectrum based only on the 64-point DFT figure is quite misleading. In order to avoid the above illusion we can take finer sampling of the DTFT.First,we extend vn]by zero-padding to obtain a 128-point sequence,and then take a 128-point DFT,which is shown in OSB Figure 10.7.Now it becomes apparent that the spectrum has significant content at other frequencies. OSB Example 10.6 illustrates the effect of different choices for the window.If we reduce the length of a window,the main-lobe width is increased,as illustrated in OSB Figure 10.4(c).This means that frequency resolution is reduced,which is apparent from OSB Figure 10.8(b)and (d).The two frequency components clearly resolved in (b)overlap each other in (d)and we do not see two distinct peaks. A common misconception is that more zero padding results in better spectral resolution.How- ever,zero padding and increasing the size of the DFT does not lead to better resolution,as illustrated in OSB Example 10.7.Notice that increasing the DFT size by zero-padding results in finer frequency spacing but does not change the ability to resolve the two frequency components. In order to achieve better frequency resolution,we need to change the length and shape of the window.OSB Example 10.8 illustrates this.In OSB Figure 10.10,as the window length increases,we see improvements in our ability to distinguish the two frequency components,and the relative amplitude of the two components becomes closer to the correct value. 3components and no frequency contents at the other DFT values. If we are considering a periodic signal with period 64, then our signal is the sum of two pure sinusoidal sequences, and thus the clean appearance of the DFT correctly shows the expected spectrum. However, since we are considering a finite-length sequence, the DFT figure can lead to an illusion resulting from the sampling of the spectrum. As shown in OSB Figure 10.6(c), the Fourier transform of v[n] has significant content at almost all frequencies but is exactly zero at the frequencies that are sampled by the DFT. Therefore, interpreting the spectrum based only on the 64-point DFT figure is quite misleading. In order to avoid the above illusion we can take finer sampling of the DTFT. First, we extend v[n] by zero-padding to obtain a 128-point sequence, and then take a 128-point DFT, which is shown in OSB Figure 10.7. Now it becomes apparent that the spectrum has significant content at other frequencies. OSB Example 10.6 illustrates the effect of different choices for the window. If we reduce the length of a window, the main-lobe width is increased, as illustrated in OSB Figure 10.4(c). This means that frequency resolution is reduced, which is apparent from OSB Figure 10.8(b) and (d). The two frequency components clearly resolved in (b) overlap each other in (d) and we do not see two distinct peaks. A common misconception is that more zero padding results in better spectral resolution. How￾ever, zero padding and increasing the size of the DFT does not lead to better resolution, as illustrated in OSB Example 10.7. Notice that increasing the DFT size by zero-padding results in finer frequency spacing but does not change the ability to resolve the two frequency components. In order to achieve better frequency resolution, we need to change the length and shape of the window. OSB Example 10.8 illustrates this. In OSB Figure 10.10, as the window length increases, we see improvements in our ability to distinguish the two frequency components, and the relative amplitude of the two components becomes closer to the correct value. 3