**Instantaneous Frequency Modulation on Speech and Chirp Signals**

**Author Marwan Saad Kadhim***

__Summary Of Research__

**In this research the main idea is how to generate one signal using three different signals with three different frequencies, These signals are ; the carrier signal, the envelope signal and the phase signal, These three signals all together will generate what we called as AM – FM signal model, The main focus of this research is how to create these types of signals and using the AM – FM model to estimate the modulation components from other type of signals, like a speech signal, which is assumed to be modulation information represented by the instantaneous frequency (phase) and the instantaneous amplitude (envelope). Many example presented in this research to show the power of the AM – FM method to extract the instantaneous information from speech and chirp signals.**

** **

**Chapter One**

**Electromagnetic Waves**

**1.1 Properties of Electromagnetic Waves**

The electric and magnetic fields in an electromagnetic wave are in phase.

The electric and magnetic fields are perpendicular to each other. The electric and magnetic fields are in planes perpendicular to the direction of travel of the wave. They are transverse waves.

Electromagnetic waves travel at the speed of light the ratio of the electric to the magnetic field in electromagnetic waves carry energy. Energy can be transferred to objects placed in their path.

**1.2 Signal domains**

**Time domain**

Time domain is the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function’s value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time. An oscilloscope is a tool commonly used to visualize real-world signals in the time domain. A time – domain graph shows how a signal changes with time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies.

**2- Frequency domain**

In electronics, control systems engineering, and statistics, the frequency domain is the domain for analysis of mathematical functions or signals with respect to frequency, rather than time[1]. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.

A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called a transform. An example is the Fourier transform,

* Associate Programmer AL-Mustansiriya University – Iraq

Which decomposes a function into the sum of a (potentially infinite) number of sine wave frequency components. The ‘spectrum’ of frequency components is the frequency domain representation of the signal. The inverse Fourier transform converts the frequency domain function back to a time function. A spectrum analyzer is the tool commonly used to visualize real-world signals in the frequency domain.

Signal processing also allows representations or transforms that result in a joint time-frequency domain, with the instantaneous frequency being a key link between the time domain and the frequency domain.

**1.3 Electromagnetic waves**

Electromagnetic waves are a phenomenon of nature first observed as light. Yet light, the part of the electromagnetic spectrum we normally sense without additional instrumentation, is only a very small portion of the infinite spectrum of electromagnetic waves. In many ways, electromagnetic waves are part of the unseen realm of Creation. That is, without changing how we observe Creation, we will not perceive their existence. Through the study of physics and engineering advances humanity has come to understanding and uses these unseen waves in a variety of applications.

The light that comes from the sun or the light from a light bulb that allows us to read in an otherwise dark room is electromagnetic radiation. However, the electromagnetic vibrations that are possible extend well beyond what our eyes can perceive. Similarly, radio waves that we pick up on a radio as are the TV signals that are transmitted by our television station are also a form of this electromagnetic radiation.

A bottom line understanding from the study of electromagnetic waves is that it is by how we focus our attention and awareness is what determines what particular frequencies we experience. If we form a habit or practice a pattern of focused awareness and attention that repeats the same pattern we will continually access the same frequencies of creation. Hence we create a given experience again and again. If, however, we learn to think differently, see differently and act differently, we can access realms of Creation and possibilities that our current mind has yet to understand.

** 1.4 Type of signals**

**a**, Continuous Time Signal

**b**, Discrete Time Signal

**c**, Periodic and a periodic Signal

**d**, Even and Odd Signal

**e**, Energy and power Signals

**a, Continuous Time Signal**

A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum (e.g., a connected interval of the real’s). That is, the function’s domain is an uncountable set. The function itself need not be continuous. To contrast, a discrete time signal has a countable domain, like the natural numbers.

A signal of continuous amplitude and time is known as a continuous time signal or an analog signal. This (a signal) will have some value at every instant of time. The electrical signals derived in proportion with the physical quantities such as temperature, pressure, sound etc. are generally continuous signals. The other examples of continuous signals are sine wave, cosine wave, triangular wave etc. Some of the continuous signals.

The signal is defined over a domain, which may or may not be finite, and there is a functional mapping from the domain to the value of the signal. The continuity of the time variable, in connection with the law of density of real numbers, means that the signal value can be found at any arbitrary point in time.

**Discrete Time Signal**

A discrete signal or discrete-time signal is a time series consisting of a sequence of qualities. In other words, it is a type series that is a function over a domain of discrete integral.

Unlike a continuous-time signal, a discrete-time signal is a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal, and then each value in the sequence is called a sample. When a discrete-time signal obtained by sampling a sequence corresponding to uniformly spaced times, it has an associated sampling rate; the sampling rate is not apparent in the data sequence, and so needs to be associated as a separate data item

**Periodic and a periodic Signal**

A signal is a periodic signal if it completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods. The completion of a full pattern is called a cycle. A period is defined as the amount of time (expressed in seconds) required completing one full cycle. The duration of a period represented by T, may be different for each signal but it is constant for any given periodic signal.

**Even and Odd Signal**

An even signal is any signal f such that f (t) = f (t). Even signals can be easily spotted as they are symmetric around the vertical axis. An odd signal, on the other hand, is a signal f such that f (t) = (f (t)).

**Energy and power Signals**

**Signal Energy**

Since we often think of signal as a function of varying Amplitude through time, it seems to reason that a good Measurement of the strength of a signal would be the area under the curve. However, this area may have a negative part. This negative part does not have less strength than a positive Signal of the same size (reversing your grip on the paper clip In the socket is not going to make you any livelier). This Suggests squaring the signal or taking its absolute Value, then finding the area under that curve. It turns out that what we call the energy of a signal is the Area under the squared signal.

**Signal Power**

Our definition of energy seems reasonable, and it is. However, what if the signal does not decay? In this case we have infinite energy for any such signal. Does this mean that? A sixty hertz sine wave feeding into your headphones is as Strong as the sixty hertz sine wave coming out of your outlet? Obviously not. This is what leads us to the idea of Signal power.

** **

**Chapter Two**

*Speech Modulation Components*

Almost all current speaker recognition systems are basically composed of two main parts: speech parameterization and statistical modeling. These two parts are responsible for the production of a machine readable parameterization of the speech samples and the computation of a statistical model from the parameters *(Bimbot et al., 2004).*

For many speech processing techniques, spectral analysis is the key point in

speech parameter extraction such as linear predictive coding (LPC), mel-frequency cepstral coefficients (MFCCs), perceptual linear prediction (PLP) coefficients *(Chen et al., 1997).*

These procedures, in one way or another, adopt the source-filter model of speech generation in computing spectral templates (feature vectors) to use in the recognition process. Unfortunately, these parameters are highly sensitive to changes in speaking conditions such as changing channels and speaking style *(Reynolds, 2002).*

Also, source-filter model techniques are known to discard all phase information in the signal’s spectrum.

In recent years, new ways of modeling and characterizing speech have been

proposed in a number of different works.

*(Jankowski et al., 1996), (Potamianos and Maragos, 2001),*

Among all the methods that are presented to deal with speech signal processing AM-FM signal modeling is of particular interest. It can be justified for two major reasons,

**first,** the phase information, which is in this case represents the phase parameter

of the speech in time domain, carried by the speech signal will be preserved in

this model (while it is ignored by other models).

**Second,** the model views the speech signal as a product of elementary signals (envelope and phase) which is quite different from other models.

The ** AM-FM** signal model aims at generating a new set of parameters that

represent a new direction in describing each individual in speaker identification

system. These parameters need to be robust against channels changing, changes

in speaking style, and minimize within-speaker variability and (at the same time)

maximize between-speaker variability. Towards this goal, this chapter will focus on techniques for estimating and modeling the speech signal modulation components, namely the signal’s envelope (instantaneous amplitude) and phase **(instantaneous frequency).**

This chapter will present a technical review of the signal modulation procedure

and the development of AM-FM model in the context of speech signal processing.

*2.1 ,***Basic Communications System**

The basic communications system ** (as shown in Figure 1)** has:

** Transmitter:** The sub-system that takes the information signal and processes it prior to transmission. The transmitter modulates the information On to a carrier signal, amplifies the signal and broadcasts it over the channel,

** Channel:** The medium which transports the modulated signal to the receiver. Air acts as the channel for broadcasts like radio. May also be a wiring system like cable TV or the Internet.

*Receiver**:* The sub-system that takes in the transmitted signal from the channel and processes it to retrieve the information signal. The receiver must be able to discriminate the signal from other signals which may using the same channel (called tuning), amplify the signal for processing and demodulate (remove the carrier) to retrieve the information. It also then processes the information for reception (for example, broadcast on a loudspeaker).

** **

**Fig. 1: Basic communication system.**

**2.2, Signal Modulation Models**

In the digital signal processing literature, the most utilized techniques to modulate the signal are:

**Amplitude Modulation (AM),**

**Frequency Modulation (FM),and **

**Phase Modulation (PM).**

These are actually methods that are usually adopted tosystematically vary one of the three parameters of the signal depending on the modulating signal. The

parameters are: the signal amplitude, the frequency, and the phase; which are processed within the AM, FM, and PM respectively. **This section** will give a brief review of AM and FM modulation only. Since the PM modulation characteristics are quite similar to FM, it will not be covered. For more information about the modulation technique, the reader can refer to **(Lathi,1998, Ch. 4,5)**,

*2.3 Amplitude Modulation*

**The Aim**

Usually we apply such application in order to know some information about the base signal as well as the carrier signal. Two reasons for using a carrier frequency

Be able to use a Power Density Spectrum to find: **efficiency** and **bandwidth**.

Know the relationship of carrier frequency, modulation frequency and modulation index to efficiency and the bandwidth. Finally, to be able to explain why AM is limited to **33%** efficiency and the consequence of trying to exceed that in to the normal speech signal.

**AM**

- Amplitude modulation is the simplest of the three to understand. The transmitter just uses the information signal,
**Vm(t)**to vary the amplitude of the carrier, Vco to produce a modulated signal, VAM(t). Here are the three signals in mathematical form:

**Information,****Vm(t)****Carrier**:**V**_{c}(t) = V_{co}sin (2**f**_{c}t +^{ϕ}**)****AM**,**V**_{AM}(t) = { V_{co}+ V_{m}(t) }sin (2**f**_{c}t +^{ϕ}**)**

Here, we see that the amplitude term has been replaced with the combination of the original amplitude plus the information signal. The amount of modulation depends on the amplitude of the information signal. This is usually expressed as a ratio of the maximum information signal to the amplitude of the carrier.

**Modulation Index**

**m** **= MAX(V _{m}(t))/ V_{co}.**

If the information signal is also a simple sine wave the modulation index has a simple form:

**m = V _{mo}/V_{co}**

** **

The interpretation of the modulation index, m, may be expressed as: The fraction (percentage if multiplied by 100) of the carrier amplitude that it varies by. If m = 0.5, the carrier amplitude varies by 50 % above and below its original value. If m= 1.0 then it varies by 100%.

Here is a typical AM signal, showing the parts. Note that the information modulates the envelope of the carrier signal.

**Fig. 2, show modulation index**

In this example, the modulation index is **< 1.0,**

**Example: AM Radio**

**AM radio** is the most common example of this type of modulation. The frequency band used for **AM radio** is about **550** to **1720** kHz. This is the range of carrier frequencies available. The information transmitted is music and talk which falls in the audio spectrum. The full audio spectrum ranges up to **20** kHz, but AM radio limits the upper modulating frequency to **5 **kHz. This results in a maximum bandwidth of **10** kHz. Therefore, the FCC can assign stations frequencies that are **10** kHz apart without fear of overlap (in reality, there still can be some overlap because the spectrum doesn’t just end at the side-band, it actual kind of tapers off slowly. These “tails” can overlap if the signal is strong enough. You can make your receiver more selective by changing from the “distant” to the “local” setting to eliminate this at the expense of sensitivity). So if we fill up the AM band, assigning stations every 10 kHz, there are 107 available transmitter frequencies.

The practice of limiting the upper frequency to 5 kHz removes some of the original information (that which falls in the 5-20 kHz) range. Since the ability to exactly reproduce the signal is called fidelity, there is a loss of fidelity in AM broadcasts. This is one of the reasons that AM radio doesn’t sound that good (compared to FM radio, as we will see later). Talk radio is relatively unaffected because conversation has very little of its signal above 5 kHz anyway. This might explain why talk radio is much more common on AM than FM.

**AM Performance**

**Bandwidth**

Now that the tools are in place, we can begin to make some evaluations of the performance of AM signals. The first example is bandwidth.

The bandwidth of a signal is always of significance for many reasons, but predominately, it determines how many channels (or stations) are available in a specific band. We saw that there could be a maximum of 107 AM radio stations. If you improved the fidelity of AM radio by making the upper modulating frequency 10 kHz, you would double the signal bandwidth, and as a result only be allowed 53 radio stations. If you tried to increase the AM band, you would lose some other band, like amateur radio.

The bandwidth of AM signals can be easily predicted using the now familiar formula: BW = 2 f_{m}.

# 2.4 Frequency Modulation

**The Aim**

**Usually the reasons of using such application can de as follow: **

- Know the relationship of carrier frequency, modulation frequency and modulation index to efficiency and bandwidth
- Compare FM systems to AM systems with regard to efficiency, bandwidth and noise.

**FM**

**Frequency modulation** uses the information signal, **V _{m}(t)** to vary the carrier frequency within some small range about its original value. Here are the three signals in mathematical form:

**Information: V**_{m}(t)**Carrier: V**_{c}(t) = V_{co}sin (2**f**_{c}t +^{ϕ}**)****FM: V**_{FM}(t) = V_{co}sin (2**{ f**_{c}+ (∆f/V_{mo}) V_{m}(t)}t +^{ϕ}**)**

We have replaced the carrier frequency term, with a time-varying frequency. We have also introduced a new term: **∆**f, *the peak frequency deviation*. In this form, you should be able to see that the carrier frequency term: f_{c}+ (**∆**f/V_{mo}) V_{m} (t) now varies between the extremes of f_{c }– **∆**f and f_{c }+ **∆**f. The interpretation of **∆**f becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the “swing” in the frequency.

**We can also define a modulation index for FM, analogous to AM:**

β = **∆**f/f_{m,} where f_{m} is the maximum modulating frequency used.

The simplest interpretation of the modulation index, β, is as a measure of the peak frequency deviation, **∆**f. In other words, β, represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, f_{m}, i.e. **∆**f = β f_{m}.

**Example:** suppose in FM radio that the audio signal to be transmitted ranges from **20 **to **15,000** Hz (it does). If the FM system used a maximum modulating index, β, of 5.0, then the frequency would “swing” by a maximum of 5 x 15 kHz = 75 kHz above and below the carrier frequency.

Here is a simple FM signal:

**Fig. 3 , simple FM signal**

Here, the carrier is at **30** Hz, and the modulating frequency is **5** Hz. The modulation index is about** 3**, making the peak frequency deviation about **15** Hz. That means the frequency will vary somewhere between **15** and **45** Hz. How fast the cycle is completed is a function of the modulating frequency.

**Example: FM Radio**

**FM radio** uses frequency modulation, of course. The frequency band for FM radio is about **88** to **108** MHz. The information signal is music and voice which falls in the audio spectrum. The full audio spectrum ranges form **20** to **20,000** kHz, but FM radio limits the upper modulating frequency to **15** kHz (cf. AM radio which limits the upper frequency to **5** kHz). Although, some of the signal may be lost above 15 kHz, most people can’t hear it anyway, so there is little loss of fidelity. FM radio may be appropriately referred to as **“high-fidelity”.**

If FM transmitters use a maximum modulation index of about 5.0, so the resulting bandwidth is 180 kHz (roughly 0.2 MHz). The FCC assigns stations) 0.2 MHz apart to prevent overlapping signals (coincidence? I think not!). If you were to fill up the FM band with stations, you could get 108 – 88 /,2 = 100 stations, about the same number as AM radio (107). This sounds convincing, but is actually more complicated (agh!).

FM radio is broadcast in stereo, meaning two channels of information. In practice, they generate three signals prior to applying the modulation:

**the L + R (left + right) signal in the range of 50 to 15,000 Hz.****a 19 kHz pilot carrier.****the L-R signal centered on a 38 kHz pilot carrier (which is suppressed) that ranges from 23 to 53 kHz,**

So, the information signal actually has a maximum modulating frequency of 53 kHz, requiring a reduction in the modulation index to about 1.0 to keep the total signal bandwidth about 200 kHz.

**FM Performance**

As we have already shown, the bandwidth of a FM signal may be predicted using:

**BW = 2 (β + 1) f _{m}**

where β is the modulation index and f_{m }is the maximum modulating frequency used.

**FM radio** has a significantly larger bandwidth than AM radio, but the FM radio band is also larger. The combination keeps the number of available channels about the same.

The bandwidth of an FM signal has a more complicated dependency than in the AM case (recall, the bandwidth of AM signals depend only on the maximum modulation frequency). In FM, both the modulation index and the modulating frequency affect the bandwidth. As the information is made stronger, the bandwidth also grows.

**2.5 Noise**

FM systems are far better at rejecting noise than AM systems. Noise generally is spread uniformly across the spectrum (the so-called white noise, meaning wide spectrum). The amplitude of the noise varies randomly at these frequencies. The change in amplitude can actually modulate the signal and be picked up in the AM system. As a result, AM systems are very sensitive to random noise. An example might be ignition system noise in your car. Special filters need to be installed to keep the interference out of your car radio.

FM systems are inherently immune to random noise. In order for the noise to interfere, it would have to modulate the frequency somehow. But the noise is distributed uniformly in frequency and varies mostly in amplitude. As a result, there is virtually no interference picked up in the FM receiver. FM is sometimes called “static free, ” referring to its superior immunity to random noise.

** 2.6 Summary**

- In FM signals, the efficiency and bandwidth both depend on both the maximum modulating frequency and the modulation index.
- Compared to AM, the FM signal has a higher efficiency, a larger bandwidth and better immunity to noise.

**Chapter Three**

**The Proposed System **

**Introduction**

In this chapter we are going to show some example about the AM-FM modulation model and the main algorithms that used for features extraction and modulation components separation.

**AM – FM Demodulation Techniques**

Multi component **AM – FM **models can be described in discrete form as:

X[ᶯ]= ᴹ∑ᵐAị[ᶯ] cos [Ωcn + Ω ᵐ ʃ q (t) dt +ϴ ]

Where M is the number of signal components (formant frequencies in comparing with a speech signal), Ω is the Centre value of the formant frequency (or the frequency of the carrier), Omega is the modulation index (or the maximum frequency deviation from), and q(t) is the modulation signal. this model forms the basis for the general modeling of non-stationary signals as superposition’s around its its carrier frequency (Cohen, 1992). Such a model is quite proper for applications in speech processing where speech signals can be represented as a superposition of tine-varying acoustic resonances and each AM-FM component of the signal models a single resonance.

The essential of the AM-FM model is to estimate the modulation information in the forms of instantaneous amplitude (IA) and instantaneous frequency (IF) that the given signals are composed of many Been suggested in the last few years. Although they have done a great job in modulation parameter estimation, no one of them can give a general solution for multi component AM-FM signals,(Santhanam and Maragos, 2000).

For example, Maragos et al. (1993) adapts the Teager Energy Operator (TEO) and its demodulation capabilities to develop a demodulation algorithm and calls it the Discrete Energy Separation Algorithm (DESA). The behavior of TEO, particularly with regard to its positivity, has proved its effectiveness in estimating the modulation parameters. Santhanam and Maragos (2000) presented an innovative approach, called Periodic Algorithm Separation and Energy Demodulation (PASED) that is able, in some cases, to outperform the demodulation capabilities of methods suggested by Maragos et al. (1993), especially regarding the proper filter bank parameter selecting.

Recently, Gianfelici et al. (2007) developed the Hilbert Transform Demodulation (HTD) that allows an asymptotically exact reconstruction of non-stationary signals as multi component AM-FM representation. This approach does not need the complex filter optimizations required by the other techniques and has higher performance than that obtained by current best practices. For this reason, we use HTD throughout this work.

This section will review the main steps and the general structures of both discrete energy separations algorithm (DESA) and Hilbert Transform Demodulation (HTD) techniques.

**Energy separation scheme**

Maragos et al. (1993) have shown that the energy-tracking signal operator can approximately estimate the envelope (instantaneous amplitude) and the phase (instantaneous frequency) of AM-FM modulated signals.

This energy operator can track the energy of a linear oscillator, i.e., it essentially tracks the energy needed by a source to produce the oscillatory signal.

**Hilbert Transform Demodulation Scheme**

Based on Gabor theory, presented in Gabor (1946), the complex signal can be generated from the real one through the FT of the real signal. His method for doing so is first to find the FT of the real signal and then to suppress the amplitudes belonging to negative frequencies and multiply the amplitudes of positive frequencies by two. It is equivalent to the following time-domain procedure:

Z (t) = x (t) + j H [ x(t) ]

where x(t) is the real signal, and z(t) is Gabor’s complex signal, also referred to as the analytic signal. Analytic signals are the main concept in Hilbert AM-FM demodulation techniques. These signals are adopted because it permits the characterization of the real input in terms of instantaneous amplitude and frequency (Rao and Kumaresan, 2000).

Because the analytic signal is complex, it can be presented in amplitude/phase (polar) notation of the form:

Z (t) = a (t) e ^{j ϕ (t)}

** **

where a(t) is the time-varying amplitude (the envelope of the analytic signal), and ϕ(t) is the time-varying frequency (the phase of the analytic signal). These modulation components can be easily extracted from the analytic signals. The instantaneous amplitude of the analytic signal is computed as:

(t) = ……. (3.1)

** **

where represents an estimated envelope component, and represents the imaginary counterpart of analytic signal. The instantaneous frequency (IF) of the analytic signal is computed by finding the phase ϕ(t) argument by

(t) = arc tan

then taking the first time derivative of the phase we will get the values of the instantaneous frequency:

……..(3.2)

**The main steps of the Grimaldi and Cummins modulation feature estimation are as follow:**

- Take the whole speech signal x(t) and filter through a bank of N band pass Gabor filters.
- For each waveform (t) generated by Step 1, calculate the analytic signal (t) using the Hilbert transform.
- Using the following equation, find the instantaneous amplitude:
- Calculate the phase of the complex (analytic) signal using:
- The instantaneous frequency is estimated using:
- The two modulation values, the instantaneous amplitude and frequency, are combined together to produce the mean squared amplitude-weighted short-time instantaneous frequency, which represents the actual modulation parameters of the signal. It is calculated as:

Where represents the length of the modulation parameter segment.

(Note that for simplicity of notation the above assumes continuous time t, but in reality the processing will be based on sampled signals).

**The code,-**

**We use the MATLAB program to apply how algorithm on a speech signal is as follow,-**

**The modulation components of sin/cos signal,****AM signal generating and envelope estimation**

Fs=1000;

L=1000;

t=(0:L-1)/Fs;

a = cos (2 * pi *3 * t) ;

ex = exp (i * 2 * pi * 200 * t) ;

am = a. *ex ;

This code is used to generate the AM signal with information signal of frequency 3Hz and the carrier frequency 200Hz.

Figure (1) show and example of the AM modulated signal that represent the combination of information signal and the carrier.

** **

** **

** **

**Figure (1) , simple AM modulation**

In order to estimate the envelope of the AM signal, we used the follow code that apply the Hilbert Transform (HT) in the modulation components estimation.

hs = Hilbert (am) ;

amp = sqrt (real (hs).^2+ imag (hs).^2) ;

This code is for AM envelope estimation. Figure (1) show and example of the modulated signal and its envelope.

**FM signal generating and envelope estimation**

fc =150 ; % [ the carrier freq ]

cx = cos (2 * pi * fc * t) ;

ffm = 10 ; % [ the freq of FM information signal the modulating freq ]

q = cos (2 * pi * ffm * t) ; %[ the information signal for FM signal modulating signal ]

B = 20 ; % [ the modulation index ]

Fm = cos (2 * pi * fc * t+B * q) ;

This code is to generate the FM signal with carrier frequency =150Hz and information signal with frequency = 10. Figure (2) show an example of the FM signal.

**Figure (2) , simple FM modulation**

**The Modulation Components estimation (Demodulation)**

In this section we will present the main functions (procedures) that we used in order to estimate the modulation components presented in the manmade and speech signal.

**Chirp signal components estimation**

The code that we adopt in this section will used to estimate the instantaneous amplitude (envelop) and the instantaneous frequency (phase) of the signal that have many time-variable frequencies. The code will be as follow:

fc=150;

a = cos (2 * pi *5 * t) ; % the information signal

Chirp = cos (2 * pi * fc * t.^2) ; %the chirp signal

hs = Hilbert (Chirp);

phase = unwrap (angle (hs)) ;

ifreq = Fs * diff (phase) / (2 * pi) ;

iamp = sqrt (real (hs).^2+ imag (hs).^2) ;

This code is to extract the Amplitude and Frequency components form the Chirp signal that have time-varying envelop and phase. Figure (3) show an example of the time-varying chirp signal.

**Figure (3), time-varying chirp signal**

**Real signal components estimation**

The code is to used the real speech signal and estimate the modulation component presented with the speech. The idea is to figure out to what extent that the speech signal can carry the modulation components during speaking. Figure (4) show an example of a real speech with it amplitude and frequency modulation parameters.

**Figure(4), real speech with it amplitude and frequency modulation parameters**

The figure (4) show us what are the modulation components that can be converted with the speech signal. This will help us to predict the most effective parameters that can change the behavior and the style of speech during the speaking.

**Chapter Four **

**Conclusion and Future Work**

Two points have to be the main focus of this research; first, how to create the signal that can hold the information comes from important signal (the information signal) and the values of the carrier signal. Second, what is the methods that used to estimate the modulation components from the modulated signals such as, the chirp signal and the speech signal.

In the first case, we simply used two type of signal modulation, namely, the Amplitude modulation (AM) and the frequency modulation (FM). These two types of modulation represent the most effect methods that used in shaping some features of one signal (carrier) based on the values of another signal (information signal) in a way that make both signals to keep their properties. For example, in the AM modulation, the envelope of the carrier signal will take the shape of the information signal. In the FM modulation, the phase of the carrier signal will changed based on the information signal.

For some signals, such as the speech signal, the modulated components are already impeded inside the signal, what we need is to estimate the modulation parameters and separate them from each other. Generally, we need to extract the modulation information from the speech signal and used them in some applications such as, speech and speaker recognition. In this research we present some methods to extract those parameters such as, HT and EST. In our proposed system we present the demodulation method based on the Hilbert Transform (HT)to extract the modulation information from the chirp and speech signal. The results show how these information can be extracted from the signal and estimated based on the signal type that we adopt.

In the future work, we suggest using the modulation information with some applications related to the speech signals. Also, we suggest a combination between more than one method to used more affected parameters that carry more information about the speech signal.

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