Modulator systems

Speech source signals can be modelled, with some idealisation, as a basic, fundamentally static carrier signal with a superimposed modulation signal. The sinusoid speech signal has three basic properties: amplitude, frequency, and phase. Each of these properties can be modulated in time in order to superimpose information on the signal.

The source system function for a sinusoid carrier signal is given by the following equation:

In some sources, , lower case theta, is rendered as , lower case p hi, and may is often replaced by (a phase shift). The expression is generally abbreviated as , lower case omega. Thu s another possible formulation of this basic function is:

The source system for the speech carrier signal is the glottis, where phonation takes place. Although the speech carrier signal is not a sinusoid but a harmonic series of sinusoids, it is convenient to think of the basic modulation functions in terms of the modulation of a sinusoid carrier signal. The three kinds of modulation are related to the three defining components of the carrier signal as follows:

1. Amplitude modulation, AM: Multiplication with A, the amplitude of the signal, by means of variable filters in the supraglottal area (pharyngeal, oral and nasal cavitities. Amplitude modulation uses the lower frequency modulating signal to change the pe ak to peak amplitude of the carrier signal. The relation of amplitude modulation to speech is varied:
   1. Consonant and vowel amplitude is a conspicuous property of the spectrum, a nd differences in amplitude are often used to segment the signal into segments f or further processing.
   2. Stressed and unstressed syllables involve a number of factors, in particul ar changes in frequency and in syllable length, but also changes in intensity, a function of amplitude.
   3. Frequency and frequency bandwidth variation in the spectrum determines the difference between one vowel and another in terms of their formants, but also between one fricative and another: some are `sharper' and some are `plainer'.

   A variety of amplitude modulation is pulse code modulation, PCM. Pulse code modulation can be seen as a specific form of amplitude modulation, in whic h the carrier signal is modulated by a rectangular pulse signal. In speech, the following features may be modelled by pulse modulation (though the transitions a t the pulse flanks may be `softer' than for a true pulse). Pulse code modulation can be seen as a possible model for the following aspects of sp eech:

   1. Consonants, in particular stops, cause very abrupt, pulse-like changes in the amplitude of the signal.
   2. Pauses involve quite abrupt changes between non-zero and zero signal stret ches, which are also pulse-like.
   3. Accents represent frequency modulation by a pulse signal, and are modelled as such in the intonation model of Fujisaki (see []). The polarity of the pulses may be important in distinguishing between `upward' and `downward ' frequency pulses.
2. Frequency modulation, FM: Multiplication with F, the frequency of the carrier signal, at the glottis, as in tone, accent and intonation. In frequency modulation, the frequency of the carrier signal is changed in proportion to the amplitude of the modulation signal. Frequency modulation relates to the following aspects of speech:
   1. Segmental perturbations are the sudden (imperceptible) modulations of frequency caused by sudden changes in air pressure associated with obstruents, particularly stop consonants.
   2. Tone, pitch accent involve step or pulse modulation of the frequency of the signal for register tones and for accents.
   3. Intonation patterns such as initial and terminal boundaries, and the global melody, are modelled by frequency modulations of the carrier signal by damped pulses. The most well-known model of this type is that of Fujisaki (see []).
3. Phase modulation, PM: Multiplication with , the phase of the carrier signal (closely related to frequency modulation), at the glottis, as in tone and accent displacement. In phase modulation, the phase of the carrier signal is changed in proportion to the amplitude of the modulation signal.
   1. Secondary phase modulation of LF pattern: Pitch accent delay relative to l exical or focal ictus is an important feature in many languages; the delay can be modelled as a phase shift in the rhythmic pattern.