1. 2 nd semester 1434-1435 nalhareqi-20141 King Saud University College of Applied studies and Community Service 1301CT By: Nour Alhariqi

2.  Signals and the classification of signals  Sine wave  Time and frequency domains  Composite signals  Signal bandwidth  Digital signal  Signal operations nalhareqi-20142

3.  A communication systems involves several stages of signal manipulation:  the transmitter transforms the message into a signal that can be sent over a communication channel;  the channel distorts the signal and adds noise to it;  and the receiver processes the noisy received signal to extract the message.  Thus, studying the communication systems must be based on a sound understanding of signals. nalhareqi-20143

4.  A signal is a physical quantity by which information can be conveyed; e.g. telephone and television signals.  Mathematically, a signal is represented as a function of an independent variable : time ( t ). Thus, a signal is denoted by s (t ), x (t ),….  One way to show signals is by plotting them on a pair of perpendicular axes. The vertical axis represents the value or strength of a signal. The horizontal axis represents time. nalhareqi-20144

5.  There are several classes of signals:  Continuous-time and discrete-time signals.  Analog and digital signals.  Periodic and aperiodic signals.  Even and odd signals. nalhareqi-20145

6.  Continuous-time signal : is a signal that is specified for every value of time t. (it is defined for all time t)  Discrete-time signal : is a signal that is specified only at discrete value of t. ( it is defined only at discrete values of t) nalhareqi-20146

7.  Analog signal: is a signal whose amplitude can take on any value in a continues range.  Digital signal: is a signal whose amplitude can take on only a finite number of values. nalhareqi-20147

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9.  A periodic signal completes a pattern within a measurable time frame, called a period, and repeats that pattern over subsequent identical periods.  The completion of one full pattern is called a cycle.  A signal is periodic with period T if there is a positive nonzero value of T for which g(t+T) = g(t) for all t  An aperiodic (nonperiodic) signal changes without exhibiting a pattern or cycle that repeats over time. nalhareqi-20149

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11.  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 ). nalhareqi-201411

12.  Signals can be classified as simple or composite.  A simple signal is the signal that cannot be decomposed into simpler signals e.g. the sinusoidal signal (sine or cosine waves).  A composite signal is the signal that composed of multiple sinusoidal signals added together. nalhareqi-201412

13.  Sinusoidal signals, based on sine and cosine functions, are the most important signals you will deal with.  They are important because virtually every other signal can be thought of as being composed of many different sine and cosine signals. nalhareqi-201413

14.  A sine wave can be mathematically describe as g(t) = A sin ( ωt + φ) where A is the peak amplitude ω is the angular frequency ω = 2πf f is frequency in Hertz, and φ is the phase. nalhareqi-201414

15.  A cosine wave can be mathematically describe as g(t) = A cos ( ωt + φ) nalhareqi-201415

16.  The peak amplitude of a signal is the absolute value of its highest intensity ( the largest value it takes), proportional to the energy it carries.  For electric signals, peak amplitude is normally measured in volts. nalhareqi-201416

17.  Period refers to the amount of time, in seconds, a signal needs to complete 1 cycle.  Frequency refers to the number of periods (cycles) in 1 s.  Note that period and frequency are just one characteristic defined in two ways.  Period is the inverse of frequency, and frequency is the inverse of period nalhareqi-201417 and Hertz second

18. High frequency wave Low frequency wave nalhareqi-201418

19.  Period is formally expressed in seconds.  Frequency is formally expressed in Hertz (Hz), which is cycle per second.  Units of period and frequency are shown in the following table. nalhareqi-201419

20.  A sine wave has a frequency of 60 Hz, what is the period of this signal in ms ?  Express a period of 100 ms in microseconds?  The period of a signal is 100 ms. What is its frequency in kilohertz? nalhareqi-201420

21.  We already know that frequency is the relationship of a signal to time and that the frequency of a wave is the number of cycles it completes in 1 s.  But another way to look at frequency is as a measurement of the rate of change with respect to time.  Change in a short span of time means high frequency.  Change over a long span of time means low frequency.. nalhareqi-201421

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23.  What if a signal does not change at all? What if it maintains a constant voltage level for the entire time it is active?  In such a case, its frequency is zero.  What if a signal changes instantaneously? What if it jumps from one level to another in no time?  Then its frequency is infinite. nalhareqi-201423

24.  The term phase describes the position of the waveform relative to time 0.  If we think of the wave as something that can be shifted backward or forward along the time axis, phase describes the amount of that shift. It indicates the status of the first cycle. nalhareqi-201424

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26.  Phase is measured in degrees or radians.  A phase shift of 360° corresponds to a shift of a complete period.  A phase shift of 180° corresponds to a shift of one-half of a period.  A phase shift of 90° corresponds to a shift of one-quarter of a period. nalhareqi-201426

27.  Wavelength is another characteristic of a signal traveling through a transmission medium.  Wavelength depends on both the frequency and the medium.  The wavelength is the distance a simple signal can travel in one period.  The wavelength is normally measured in micrometers (microns) instead of meters. nalhareqi-201427

28.  Wavelength can be calculated if one is given the propagation speed (the speed of light) and the period (or frequency) of the signal where λ is the w avelength and c is the propagation speed. nalhareqi-201428

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30.  The time-domain plot shows changes in signal amplitude with respect to time (it is an amplitude-versus-time plot).  To show the relationship between amplitude and frequency, we can use what is called a frequency-domain plot.  A frequency-domain plot is concerned with only the peak value and the frequency. Changes of amplitude during one period are not shown. nalhareqi-201430

31. nalhareqi-201431 A complete sine wave is represented by one spike. The position of the spike shows the frequency and its height shows the peak amplitude.

32.  It is obvious that the frequency domain is easy to plot and conveys the information that one can find in a time domain plot.  The advantage of the frequency domain is that we can immediately see the values of the frequency and peak amplitude. nalhareqi-201432

33. nalhareqi-201433 The frequency domain is more compact and useful when we are dealing with more than one sine wave.

34.  According to Fourier analysis, any composite signal is a combination of simple sinusoidal signals with different frequencies, amplitudes, and phases.  A composite signal can be periodic or nonperiodic. nalhareqi-201434

35.  A periodic composite signal can be decomposed into a series of simple sinusoidal signals with discrete frequencies (that have integer values 1, 2, 3, and so on) in the frequency domain. (Fourier series)  A nonperiodic composite signal can be decomposed into a combination of an infinite number of simple sinusoidal signals with continuous frequencies in the frequency domain. (Fourier transform) nalhareqi-201435

36. nalhareqi-201436 A composite periodic signal

37. nalhareqi-201437 A nonperiodic composite signal Frequency domain

38.  The range of frequencies contained in a composite signal is its bandwidth.  The bandwidth is normally a difference between two numbers. nalhareqi-201438

39. nalhareqi-201439 Bandwidth of a periodic signal Bandwidth of a nonperiodic signal

40.  If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V.  A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? nalhareqi-201440

41.  Information can be represented by a digital signal. Amplitude Time A digital signal with two levels A digital signal with four levels nalhareqi-201441

42.  The bit interval is the time required to send one single bit.  The bit rate is the number of bits sent in 1 s, expressed in bits per second (bps). nalhareqi-201442 1 s Bit interval Bit rate = 8 bps Bit rate = 16 bps 1 s

43.  It should be know that a digital signal with all its sudden changes is actually a composite signal having an infinite number of frequencies. In other word, the bandwidth of a digital signal is infinite.  Fourier analysis can be used to decompose a digital signal. nalhareqi-201443

44.  We discuss here three useful signal operations: shifting, scaling, and inversion.  Since the independent variable in our signal description is time, these operations are discussed as time shifting, time scaling, and time reversal (inversion).  However, this discussion is valid for functions having independent variables other than time (e.g., frequency). nalhareqi-201444

45.  Shifts the signal left or right  Let x(t) denote a continues time signal.  If y(t) = x(t – a)  y(t) is a time shifted signal of x(t) by a seconds,  If a > 0  y(t) is a delayed version of x(t) (i.e. shift x(t) relative to the time axis towards the right by a )  If a < 0  y(t) is an advanced version of x(t) shift to left (i.e. shift x(t) relative to the time axis towards the left by a ) nalhareqi-201445

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48.  The compression or expansion of a signal in time.  Let x(t) denote a continues time signal.  If y(t) = x(at)  y(t) is a time scaling version of x(t).  |a| > 1  compression x(t) by a factor of “a”  |a| < 1  expansion x(t) by a factor of “a”  Also, we can look to scaling as speed up or slow down a signal  |a| > 1  speed up x(t) by a factor of “a”  |a| < 1  slow down x(t) by a factor of “a” nalhareqi-201448

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51.  Reflecting the signal about t=0.  Let x(t) denote a continues time signal.  If y(t) = x(-t)  y(t) is a time reversal version of x(t). nalhareqi-201451

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