Extraction of the Instantaneous Frequency of a Speech Signal
Abstract Generated abstract
This paper examines how the instantaneous frequency of a speech signal can be extracted when speech is represented as an oscillation with slowly varying amplitude and phase. Building on the intelligibility of clipped and compressed speech, it applies amplitude limiting, pulse generation through a monostable multivibrator, and low-pass filtering to obtain an envelope corresponding to changes in instantaneous frequency. An experimental analyzer was constructed and tested with speech signals, including the vowel “a,” showing that the extracted instantaneous frequency varies with the fundamental tone. The author reports an observed proportionality between the amplitude envelope and the instantaneous-frequency envelope, suggesting a compact representation of the speech signal in terms of instantaneous frequency.
Full Text
EXTRACTION OF THE INSTANTANEOUS FREQUENCY OF A SPEECH SIGNAL
N. F. KUCHER
(Presented by the scientific seminar of the Department of Computer Engineering)
Let us represent a speech signal as a function of time
\[ u(t)=A(t)\operatorname{Cos}\varphi(t), \tag{1} \]
that is, as an oscillation with slowly varying amplitude \(A(t)\) and phase \(\varphi(t)\), where
\(\varphi'(t)=\omega(t)\) is the instantaneous frequency of the signal \(\operatorname{Cos}\varphi(t)\).
In works [1] and [2] it is shown that a speech signal preserves intelligibility under such transformations as a result of which the original signal (1) is converted into signals of the form:
\[ u_1(t)=\operatorname{sign}\operatorname{Cos}\omega(t) \]
\[ u_2(t)=\operatorname{Cos}\varphi(t). \tag{2} \]
The signal \(u_1(t)\) is called a clipped signal, and \(u_2(t)\) a compressed speech signal.
The preservation of the intelligibility of signals of the form (2) shows that the most significant part of the information is concentrated in the envelope \(\varphi(t)\) of the change in phase of signal (1), and consequently also in the envelope of the instantaneous frequency \(\omega(t)=\varphi'(t)\).
Therefore, in order to extract the envelope \(\varphi(t)\), or \(\omega(t)\), the original signal (1) must be brought to the form (2) and detected by means of a frequency detector. Since in signal (2) there is no carrier frequency, which is usually taken into account in constructing frequency detectors, the method of frequency detection described in work [3] was applied.
The essence of this method consists in converting the frequency-modulated signal \(u_2(t)=\operatorname{Cos}\varphi(t)\) into the signal \(u_1(t)=\operatorname{sign}\operatorname{Cos}\varphi(t)\) by means of amplitude limiting (clipping), and subsequently differentiating the signal in order to obtain pulse-duration modulation (PDM). The PDM oscillations are passed through a low-pass filter, at the output of which we obtain the envelope of the change in instantaneous frequency.
An analyzer of the instantaneous frequency of a speech signal was constructed according to this principle.
The block diagram of the analyzer is given in Fig. 1.
Fig. 1. Analyzer of the instantaneous frequency of a speech signal
The speech signal from the microphone is subjected to limiting in amplitude—clipping—by means of a clipper. The clipped speech signal of the form (2) triggers a monostable multivibrator, which generates pulses of duration 20 μsec and amplitude 7 V, corresponding to the PIM signal. When the PIM speech signal is listened to, it retains its intelligibility. The PIM signal is fed to a transistor low-pass filter, the frequency response of which is shown in Fig. 2. The cutoff frequency of the filter, equal to 500 Hz, was chosen purely intuitively. The steepness of the falloff of the frequency response is approximately 40 dB per octave. The output signal of the filter, representing the envelope of the instantaneous frequency \(\omega(t)\) of the speech signal, was displayed on an oscilloscope. An oscillogram of the function \(\omega(t)\) for the vowel sound “a” is shown in Fig. 3.
Fig. 2. Frequency response of the low-pass filter
Fig. 3. Function \(\omega(t)\) for the vowel “a”
As can be seen from the oscillogram, the instantaneous frequency of the speech signal changes in step with the fundamental tone of speech.
A comparison of the original speech signal with the envelope of the instantaneous frequency, made from oscillograms, is shown in Fig. 4.
In doing so, it was possible to discover a very interesting regularity. As can be seen from Figs. 3 and 4, the speech signal, represented in the form
Fig. 4. Comparison of the functions \(A(t)\) and \(\omega(t)\) for the vowel “a”
\(u(t)=A(t)\cos\varphi(t)\), has the property that the envelope amplitude \(A(t)\) and the envelope of the instantaneous frequency \(\omega(t)\) vary according to the same law, that is, \(A(t)=k\omega(t)\) (\(k\) is the proportionality coefficient), and, consequently, the speech signal can be described by a function of the form:
\[ u(t)=k\omega(t)\cos\int \omega(t)\,dt. \tag{3} \]
The experiment was carried out with an MD-44 microphone.
REFERENCES
- Yu. G. Rostovtsev. On the possibilities of application in communication systems of amplitude limiting of speech signals. Elektrosvyaz’, No. 6, 1958.
- P. Marku, J. Dage. New methods of speech transmission. In the collection Information Transmission Theory, edited by V. I. Siforov, IL, Moscow, 1957.
- V. V. Palshkov. Radio receiving devices. Svyaz’, Moscow, p. 456, 1965.