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Ferran Perez i Marc Peig. Grup 21. Marc Peig Noms: Ferran Perez Lloc treball: Grup: 21 1. Fixing the values of A1=1, A2=1, F1=0.125 and F2=0.148, repeat the MATLAB code above and represent the DFT of 512 samples of the two windowed tones xr[n] and xh[n] (using a rectangular window and a hamming window respectively). Try to distinguish the two tones in the DFT representation. Can you easily distinguish the two tones F1 and F2 using both windows? From this result, which window has better resolution in frequency? No, it’s diffi ult to distinguish the two tones with oth windows. The figure 1 has a higher resolution. 2. Now, using the values F1=0.125, F2=0.25, A1=1 and A2=0.1 represent again the DFT of the two tones using the rectangular and the Hamming window and try to distinguish the two tones F1 and F2. Observing the resulting figures, which window has the better sensitivity? 1 Ferran Perez i Marc Peig. Grup 21. The figure 2 has more sensibility. 3. Explain the differences between Fig. 3.7 and 3.4 and justify why there are 'spectral lines' in the DFT of y[n]. Relate the distance between the spectral lines in Fig. 3.7 with some feature of the signal e[n] (note that the DFT of y[n] in Fig. 3.7 has N=1024 samples). Explain which is the effect of the window.. In figure 3.7 we see the result of the convolution between an impulse train and a filter, whereas in the figure 3.4 we see the DFT of the filter h[n]. There are spectral lines because of the windowed effect. The relation between the digital frequency, the number of samples is the following, and the number of samples taken when we do the DFT: F=k/N *In our case: N=1024. 4. Select an approximate version of the impulse response of the vocal tract for the vowel a and also estimate the fundamental frequency of the vocal chords. Estimation of the fundamental frequency: f0=75 Hz. 5. Explain the spectral lines that appear in Fig. 3.10 and relate them to the fundamental frequency of the voice (similarly to question 3). The spectral lines in fig 3.10 are a consequence of the convolution between a periodic signal (the speech) and the filter (As we saw in question 3). 6. Identify the two most important formants and calculate their analogue frequencies. Do they have the expected alues for a o el a as explained in the o el triangle of Figure 2.5? Frequency of the first formant: f1=80 Hz Frequency of the second formant: f2=946Hz Yes, they have the expected values relating to the fig 2.5. 2 Ferran Perez i Marc Peig. Grup 21. 7. Load any of the WAV files unknown_x. a and, following a similar procedure as in the last two questions, relate the formants observed in the DFT plot to the vowels diagram of Figure 2.5 and try to guess which vowel it is. In the part relating to exercise five, the explanation is the same one given both on exercise 3 and 5. Approximately the frequencies are: First formant: F1=218.15 Hz Second formant: F2: 2,0468.75 Hz Looking at the ta le we guess that is an I . 3