expanded by Jozef Goetz, 2009 The McGraw-Hill Companies, Inc., 2006

1. Chapter 3 Signals PART II expanded by Jozef Goetz, 2009 The McGraw-Hill Companies, Inc., 2006 expanded by Jozef Goetz, 2009

2. Define transmission. • Describe the concept of frequency, spectrum, and • bandwidth. • Define analog and digital data transmission. • Describe the concept of data, signals, and • transmission. • List the various impairmentsto effective transmission. • Describe attenuation. • Describe delay distortion. • Describe the concept of noise & channel capacity. OBJECTIVES

3. 3-3 DIGITAL SIGNALS • In addition to being represented, information can also be represented • by an analog signal • by a digital signal • For example, • a 1 can be encoded as a positive voltage and • a 0 as zero voltage. • A digital signal can have more than 2 levels. • In this case, we can send more than 1 bit for each level.

4. 3-3 DIGITAL SIGNALS Topics discussed in this section: • Bit Rate vs Bit Length • Digital Signal as a CompositeAnalog Signal • Application Layer

5. Figure 3.16A digital signal • The bit interval (bit duration) is the time required to send 1 bit. • The bit rate is the # of bitintervalsper sec

6. Example 6 A digital signal has a bit rateof 2000 bps. What is the duration of each bit (bit interval) Solution • The bit duration (interval) is the inverse of the bit rate. • Bit interval = 1/ 2000 [bps] = 0.000500 [s/bit] = 0.000500 x [106ms/bit] = 500 [ms/bit]

7. Figure 3.16Bit rate and bit interval • The bit duration BD (interval) is the time required to send 1 bit. • The bit rateBRis the # ofbitintervalsper sec • R = 1 / D 1 s

8. Bit length and bit duration p.73 and 64 • The bit lengthBLis the distance1bitoccupies on the transmission medium. • The bit duration BD (interval) is the time required to send 1 bit. • bit length = propagation speed * bit duration • L = S * D • Remember from your elementary school formula: • D = S * T • where: D –distance, S – speed, t - Time

9. Figure 3.16 Two digital signals: one with two signal levels and the other with four signal levels

10. Note Appendix C reviews information about exponential and logarithmic functions. Appendix C reviews information about exponential and logarithmic functions.

11. Example 3.16 A digital signal has 8 levels. How many bits are needed per level? Each signal level is represented by3 bits.

12. Example 3.17 • A digital signal has 9 levels. • How many bits are needed per level? • We calculate the number of bits by using the formula. Each signal level is represented by 3.17 bits. • However, this answer is not realistic. • The number of bits sent per level needs to be an integer as well as a power of 2. • For this example, 4 bits canrepresent one level.

13. Example 3.18 • Assume we need to download text documents at the rate of 100 pages per seconds. • What is the required bit rate of the channel? • Solution • A page is an average of 24 lines with 80 characters in each line. • If we assume that one character requires 8 bits, the bit rate is • 100 x 24 [line/sec] = 100 x 24 x 80[chr/sec] = • = 100 x 24 x 80 x 8 [bit/sec] = 1, 636, 000 [bit/sec] = 1.636 Mbps

14. Example 3.19 A digitized voice channel, as we will see in Chapter 4, is made by digitizing a 4-kHzbandwidthanalog voice signal. We need tosample thesignal at twice the highest frequency (2 samples per hertz). We assume that each sample requires 8 bits. What is the required bit rate? Solution bit rate = 2 x 4000 [Hz] x 8 [bits] = 2 x 4000 [1/sec] x 8 [bits] = 64,000 [bits/sec] = 64 [kbps]

15. Example 3.20 • What is the bit rate for high-definition TV (HDTV)?Solution • HDTV uses digital signals to broadcast high quality video signals. • The HDTV screen is normally a ratio of 16 : 9. • There are 1920 by 1080 pixels per screen, and the screen is renewed30 times per second = 30 [1/sec] • 24 [bits] represents one color pixel: • 1920 x 1080 x 30 [1/sec] x 24 [bit] = • = 1,492,992,000 [bit/sec] = 1.5 Gbps • The TV stations reduce this rate to 20 to 40 Mbpsthrough compression.

16. Figure 3.17 The time and frequency domains of periodic and nonperiodic digital signals • Based on Fourier analysis, a digitalsignal is a compositeanalogsignal with an infinite bandwidthB • Theperiodicsignal has discrete frequencies • Thenonperiodicsignal has continues frequencies

17. Figure 3.18 Baseband transmission • A digital signal can be transmitted by using 2 approaches: • Baseband • Sending a digital signal without changing to an analog signal • Broadband transmission => slide 33

18. Figure 3.19 Bandwidths of two low-pass channels • Baseband transmission requires a low-pass channel with bandwidth that starts from 0

19. Figure 3.20 Baseband transmission using a dedicated medium with a. wide-bandwidth Baseband transmission of a digital signal that preservesthe shape of the digital signal is possible only if we have a low-pass channel with an infinite or very widebandwidth.

20. Example 3.21 • An example of a dedicated channel where the entirebandwidth of the medium is used as one single channel is a LAN. • Almost every wired LAN today uses a dedicated channel for 2 stations communicating with each other. • In a bus topology LAN with multipoint connections, onlytwo stations can communicate with each other at each moment in time (timesharing); • the other stations need to refrain from sending data. • In a star topology LAN, the entire channel between each station and the hub is used for communication between these two entities.

21. b. Low-pass channels with Limited Bandwidth Low-pass channels with Limited Bandwidth, we approximate the digitalsignal with an analog signal. The level of approximation depends on the bandwidth available. Assume digital bit rate = N, the worst case, max changes happens when the signalcarries. The sequence 01010101010101….or 1010101010101010. To simulate this we need an analog signal of f = N / 2.

22. Low-pass channels with Limited Bandwidth Figure 3.21Rough approximation of a digital signal using the first harmonic N/2 and N/4 for worst case • 1 is represented by positive amplitude, • 0 is represented by negative amplitude • Here is a sequence of • all 3-bit combinations: Where: bit rate = N <= after analyzing, we need A channel with f = 0 , N/4, N/2. p = phase

23. Low-pass channels with Limited Bandwidth To make the shape of the analog signal look more like that of a digital signal, we need to add more harmonics to the first harmonics N/4, N/2.

24. Figure 3.22 Simulating a digital signal with first three harmonics for all scenarios

25. Digital versus analog The best case when we use a singlef signal to send it Worst case: the most # of changes, Others are between 0 Hz and 3 Hz. So, to send 6 bits per sec we need a bandwidth of 3 Hz

26. Relationship between the bit rates and bandwidth • To send n bps (bit rate) through analogchannel using the aboveapproximation, we need bandwidth B such that B = bit rate / 2 B = n / 2 Note: B represents f = 3 Hz of a single sine ( with only one frequency which is the first harmonic) The required bandwidth is proportional to the bit rate ! • Using a single sine analog signal per each pattern as a “kind of digital signal” cannot be recognized on the receiver site correctly. • So we need to improve the shape of the signal by using a composite signals (i.e. adding more harmonics)

27. Note: A digitalsignal is a composite signal with an infinite bandwidth.

28. Table 3.2 Bandwidth Requirement How is it calculated: B = n / 2 is related to the first harmonic B = 3 n / 2 is related to the 2nd column etc. B = 5 n / 2 is related to the 3rd column etc. So B >= n / 2 => n <= 2B Adding more oddharmonics gives us better shape of the signal

29. Note • The bit rate and the bandwidth are proportional to each other • and • B >= n / 2 from the previous slide • A typical voice signal has a bandwidth of approximately 4 kHz, so we should be able send about 8000 bps if we use a single sine (with the 1st harmonic) In baseband transmission, the required bandwidth is proportional to the bit rate; if we need to send bits faster, we need more bandwidth.

30. Example 3.22 What is the required bandwidth of a low-pass channel if we need to send 1 Mbps by using baseband transmission? Solution The answer depends on the accuracy desired. a. The minimum bandwidth, is B = bit rate /2, or 500 kHz. b. A better solution is to use the first and the third harmonics with B = 3 × 500 kHz = 1.5 MHz. c. Still a better solution is to use the first, third, and fifth harmonics with B = 5 × 500 kHz = 2.5 MHz.

31. Example 3.23 We have a low-pass channel with bandwidth100 kHz. What is the maximum bit rate of this channel? Solution See note under table 3.2 From B >= bit rate / 2 => bit rate <= 2 x B The maximum bit rate can be achieved if we use the first harmonic. The bit rate is 2 times the available bandwidth, or 200 kbps.

32. Figure 3.23 Bandwidth of a bandpass channel • If the available channel is a bandpass channel, we cannot send the digital signaldirectly to the channel; • we need to convert the digital signal to an analog signal before transmission.

33. Figure3.24Modulation of a digital signal for transmission on a bandpass channel

34. Low-pass and band-pass Used for digital bandwidth, though it can be used by analog one too Used for analog bandwidth

35. Note: The analog bandwidth of a mediumis the range of frequencies that medium can pass and it is expressedin hertz; the digital bandwidth of a medium is the maximum bit rate that medium can pass and itis expressedin bitspersecond.

36. Note: • Digital transmission needs a low-pass channel (theoretically between 0 and infinity). • the upper limit can be relaxed if we lowerour standards by accepting a limited # of harmonics Analogtransmission canuse a band-pass channel.

37. analog bandwidth • The analog bandwidth can always be shifted • The bandwidth of a medium can be divided into several band-passchannel to carryseveralanalog transmission

38. ANALOG AND DIGITAL DATA TRANSMISSION Speech bandwidth ~ 300 Hz - 3.4 kHz

39. ANALOG AND DIGITAL DATA TRANSMISSION Data (information) can be analog or digital. The data can be transmitted using analog transmission or digital transmission. This gives us 4 possibilities: Analog Data, Analog Transmission Analog Data, Digital Transmission Digital Data, Analog Transmission Digital Data, Digital Transmission

40. ANALOG AND DIGITAL DATA TRANSMISSION TRANSMISSION DATA

41. ANALOG AND DIGITAL DATA TRANSMISSION TRANSMISSION DATA

42. EFFECT OF BANDWIDTH ON A DIGITAL SIGNAL

43. Example 3.24 • An example of broadband transmission using modulation is the sending of computer data through a telephone subscriber line, the line connecting a resident to the central telephone office. • These lines are designed to carry voice with a limited bandwidth (0 – 4 kHz), so the max bit rate is only 8 kbps • The channel is considered a bandpass channel. • We convert the digital signal from the computer to an analog signal, and send the analog signal. • We can install two converters to change the digital signal to analog and vice versa at the receiving end. • The converter, in this case, is called a modem (modulator/demodulator)

44. Example 3.25 • A second example is the digital cellular telephone. • For better reception, digitalcellular phones convert the analog voice signal to a digital signal (see Chapter 16). • Although the bandwidth allocated to a company providing digital cellular phone service is very wide, we still cannot send the digital signalwithout conversion. • The reason is that we only have a bandpass channel available between caller and callee. • We need to convert the digitized voice to a composite analog signal before sending.