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# BU EECE 359 - Data and Signals

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EECE 359 1st Edition Lecture 4 Outline of Last Lecture I. Asynchronous CommunicationOutline of Current LectureA. Data and SignalsB. Transmission of Digital SignalsC. Transmission ImpairmentsD. Transmission Performance Current LectureData Transmission (Introduction to the Physical Layer) 2 Computer Communications and Networking EECE 359  Data and Signals  Transmission of Digital Signals  Transmission Impairments  Transmission Performance3 Data and Signals analog signal – continuous • signal intensity varies smoothly with no breaks digital signal – discrete • signal intensity maintains a constant level and then abruptly changes to another level periodic signal • signal pattern repeats over time aperiodic signal • pattern not repeated over time Time Domain Concepts4 Analog and Digital Signals5 Periodic Signals S ( t + T ) = s ( t ) − ∞ < t < + ∞6 Sine Wave • peak amplitude (A) – maximum strength of signal – typically measured in volts • frequency (f) – rate at which the signal repeats – Hertz (Hz) or cycles per second – period (T) is the amount of time for one repetition – T = 1/f • phase () – relative position in time within a single period of signal (periodic continuous signal)7 Sine Waves s(t) = A sin(2ft +) A=1, f=1, ɸ=0 A=0.5, f=1, ɸ=0 A=1, f=2, ɸ=0 A=1, f=1, ɸ=π/48 Wavelength () the wavelength of a signal is the distance occupied by a single cycle can also be stated as the distance between two points of corresponding phase of two consecutive cycles assuming signal velocity v, then the wavelength is related to the period as  = vT or equivalently f = v f = c or f = Kc • c = 3*108 ms-1 (speed of light in free space) • K = fractional factor These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Relationship between sine wave in time and sine wave in spaceWavelength and period Direction of propagation 912 • signals are made up of many frequencies • components are sine waves • Fourier analysis can show that any signal is made up of components at various frequencies, in which each component is a sinusoid • can plot frequency domain functions Frequency, Spectrum, and Bandwidth Frequency Domain Concepts13 Spectrum & Bandwidth14 Composite Signal (T=1/f) sin(2πft) (1/3)sin(2π(3f)t) (4/π)[sin(2πft)+(1/3)sin(2π(3f)t)]15 Frequency Domain Representations a. frequency domain of composite signal – BW = 2f b. frequency domain function of single square pulse – s(t) = 1, -T/2≤ t ≤ T/2 – BW = ∞ 0 1/T 2/T 3/T 4/T 5/T 0 1f 2f 3f 4f 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.2T 1.0T 0.8T 0.6T 0.4T 0.2T 0.0T -0.2T -0.4T S(f) S(f) a b16 Signal with DC Component Composite Signal with DC componentadded – BW = 3f s(t)=1+(4/π)[sin(2πft)+(1/3)sin(2π(3f)t)] s(f)The time and frequency domains of periodicand aperiodic digital signals 17Data Transmission (Introduction to the Physical Layer) 18 Computer Communications and Networking EECE 359  Data and Signals  Transmission of Digital Signals  Transmission Impairments  Transmission Performance19 Analog and Digital Data Transmission • data – entities that convey meaning or information • signals – electric or electromagnetic representations of data • signaling – physical propagation of a signal along a medium • transmission – communication of data by propagation and processing of signals DIGITAL SIGNALS • Can have two discrete levels: N 1 encoded as a positive voltage N 0 encoded as zero voltage. • Can have more than two levels N Each value representing the values of more than one bit N � = log2 � 20Bit Rate or Data Rate Digital signals in communications are aperiodic • period/frequency are not appropriate characteristics. Bit rate • used instead of frequency • number of bits sent in 1 second (bits per second (bps) Example 1: What bit rate is required to download a 100 page document in 1 second, given the average page has 24 lines of 80 characters (8 bits each) of text? ��� ���� = 100 ����� × 24 ����� ���� × 80 �ℎ�� ���� × 8 ��� � �ℎ�� /������ = 1,536,000 ��� = 1.536 ���� Example 2: A digitized analog voice signal with BW = 4 kHz needs to be sampled at twice the BW (Nyquist). If samples are 8 bits, what bit rate is required? ��� ���� = 2 ������� ×4000 �� × 8 ��� ������ = 64,000 ��� = 64 ���� 2122 Data Rate and Bandwidth .  Any transmission system is able to accommodate only a limited band of frequencies • This limits the data rate that can be carried on the transmission medium  Consider a square wave • Represents a digital signal of alternating 0’s and 1’s ─ Data rate is 2f bits per second • Square waves have infinite frequency components and hence an infinite bandwidth • Most energy contained in first few components ─ kth component has frequency of kf with peak amplitude of 1/k • Consider limiting the bandwidth Data Rate and Bandwidth 23 Consider a binary bit stream – alternating 1’s and 0’s (square wave) f = frequency of the square wave “data rate” is 2f bpsData Rate and Bandwidth 24 a: frequency components f, 3f, 5f b: frequency components f, 3f, 5f, 7f c: all odd frequency components Bandwidth of square wave is infinite. However, peak amplitude of each kf frequency component is 1/k. Can limit bandwidth to first 3 components and still have a reasonably square signal.Examples 25 3 sine -wave frequency components •f = 1 MHz (1 x 106 Hz) • BW = 5 MHz - 1 MHz = 4 MHz • T = 1/f = 1 μS • Duration of Data Bit = T/2 = 0.5 μ S • Data Rate = 1/0.5 = 2 Mbps 3 sine -wave frequency components • f = 2 MHz • BW = 10 MHz - 2 MHz = 8 MHz • T = 1/f = 0.5 μ S • Duration of Data Bit = T/2 = 0.25 μ S • Data Rate = 1/0.25 = 4 Mbps 2 sine -wave frequency components • f = 2 MHz • BW = 6 MHz - 2 MHz = 4 MHz • T = 1/f = 0.5 μ S • Duration ofData Bit = T/2 = 0.25 μ S • Data Rate = 1/0.25 = 4 Mbps Data Rate and Bandwidth 26 Conclusions 1. Any purely digital waveform will have infinite bandwidth 2. The transmission system media will limit the bandwidth that can be transmitted 3. For a given media, the greater the bandwidth transmitted, the greater the cost 4. Economic and practical reasons force the limiting

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