5.6. MAGNITUDE SPECTRA OF DIAL AND RINGBACK TONES
Amplitude
(a)
115
(aa)
0.04
0.03
0.02
0.02 0.01
0 0 −0.02
−0.01
−0.04
−0.02
−0.06 0
2
4 Time (s)
6
8
−0.03
2
2.01
Magnitude
(b) 0.04
0.03
0.03
0.02
0.02
0.01
0.01
0
1000 2000 3000 Frequency (Hz)
2.04
2.05
(bb)
0.04
0
2.02 2.03 Time (s)
4000
0 200
300 400 500 Frequency (Hz)
600
Figure 5.15: (a) A dial tone over 6.5 seconds. (aa) Its small segment. (b) Magnitude spectrum of (a). (bb) Its segment between [200, 600]. Then it will generate the solid dots and the solid line in Figure 5.14(b). Note that the solid dots are generated by plot(mp*D,abs(X(mp+1)),’.’) and the solid line by plot(mp*D,abs(X(mp+1))). See Problem 3.29. Note that two or more plot functions can be combined as in the fifth line of the program. We plot in Figure 5.14(b) with dotted line also the exact magnitude spectrum for comparison. Program 5.10 uses Nb=2xN or adds 200 trailing zeros, thus it has a frequency resolution half of the one in Program 5.8. Consequently Program 5.10 generates one extra point between any two immediate points in Figure 5.14(a) as shown in Figure 5.14(b). We see that the exact and computed spectra become closer. If we use Nb=20xN, then the program generates extra 19 points between any two immediate points in Figure 5.14(a) and the computed magnitude spectrum (solid lines) is indistinguishable from the exact one (dotted lines) as shown in Figure 5.14(c). In conclusion, the exact magnitude spectrum in Figure 5.13(a) can also be obtained using FFT by introducing trailing zeros.
5.6
Magnitude spectra of dial and ringback tones
Our telephones use dual-tone multi-frequency signals to carry out all functions. When we pick up a handset, the dial tone will indicate that the telephone exchange is working and ready to accept a telephone number. We use an MS sound recorder (with audio format: PCM, 8.000 kHz, 8 Bit, and Mono) to record a dial tone over 6.5 seconds as shown in Figure 5.15(a). We plot in Figure 5.15(aa) its small segment for t in [2, 2.05]. We then use a program similar to Program 5.5 to plot the magnitude spectrum of the dial tone in Figure 5.15(b) for the entire positive Nyquist frequency range and in Figure 5.15(bb) its small segment for frequency in [200, 600] (Hz). It verifies that the dial tone is generated by two frequencies 350 and 440 Hz. We repeat the process by recording a ringback tone. Figure 5.16(a) shows a ringback tone for about 8 seconds. We plot in Figure 5.16(aa) its small segment for t in [4, 4.1]. We
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