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52 lines
2.3 KiB
52 lines
2.3 KiB
From text to speech: The MITalk system
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12.1.5 Parameter update rate
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Control parameter values are updated every 5 msec. This is frequent enough to
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mimic even the most rapid formant transitions and brief plosive bursts. If desired,
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the program can be modified to update parameter values only every 10 msec with
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relatively little decrease in output quality.
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12.1.6 Digital resonators
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The basic building block of the synthesizer is a digital resonator having the
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properties illustrated in Figure 12-5. Two parameters are used to specify the input-
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output characteristics of a resonator, the resonant (formant) frequency F and the
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resonance bandwidth BW. In Figure 12-5, these values are 1000 Hz and 50 Hz,
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respectively. Samples of the output of a digital resonator, y(nT), are computed
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from the input sequence, x(nT), by the equation:
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y(nT)=Ax(nT)+By (nT-T)+Cy (nT-2T) (1)
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where y(nT-T) and y(nT-2T) are the previous two sample values of the output
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sequence y(nT). The constants A, B, and C are related to the resonant frequency F
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and the bandwidth BW of a resonator by the impulse-invariant transformation
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(Gold and Rabiner, 1968):
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C=—e2"BWT
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B=2¢"™8WTcos(2nfT) )
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A=1-B-C
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The constant T is the reciprocal of the sampling rate and equals 0.0001 seconds in
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the present 5-kHz simulation.
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The values of the resonator control parameters F and BW are updated every 5
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msec, causing the difference equation constants to change discretely in small steps
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every 5 msec as an utterance is synthesized. Large, sudden changes to these con-
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stants may introduce clicks and burps in the synthesizer output. Fortunately,
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acoustic theory indicates that formant frequencies must always change slowly and
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continuously, relative to the 5-msec update interval for control parameters.
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A digital resonator is a second-order difference equation. The transfer func-
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tion of a digital resonator has a sampled frequency response given by:
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A
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T(f)=————— 3)
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1-Bz-1-Cz2
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where z=62™7 j is the square root of —1, and f is frequency in Hz which ranges
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from 0 to 5000 Hz. The transfer function has a (sampled) impulse response iden-
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tical to a corresponding analog resonator circuit at sample times nT (Gold and
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Rabiner, 1968). But the frequency responses of an analog and digital resonator are
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not exactly the same, as seen in Figure 12-5.
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128
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