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Physical Layer: Data and Signals Outline Analog and digital data/signals Time and frequency domain views of signals Bandwidth and bit rate Transmitting digital signals as analog Theoretical data rate Signal impairment Analog vs Digital Data Analog data Data take on continuous values E.g., human voice, temperature reading Digital data Data take on discrete values E.g., text, integers Analog vs Digital Signals To To be be transmitted, transmitted,data data must must be be transformed transformed to to electromagnetic electromagneticsignals signals Analog signals have an infinite number of values in a range Digital signals value Have a limited number of values time value time Data and Signals Analog Data Analog Signal Telephone Digital Data Analog Signal Modem Analog Data Digital Signal Codec Digital Data Digital Signal Digital transmitter Periodic Signals A periodic signal completes a pattern within a timeframe, called a period A signal x(t) is periodic if and only if x(t) = x(t+T) - < t < value period time Sine Waves Simplest form of periodic signal signal strength period T = 1/f peak amplitude time General form: x(t) = A×sin(2ft + ) phase / phase shift Varying Sine Waves 3 2 1 0 0.5 1.5 2.5 -1 -1 -2 -2 A = 1, f = 1, = -3 2 1 1.5 2.5 A = 2, f = 1, = 0 0.5 1.5 2.5 -1 -1 -2 -2 -3 -3 0.5 A = 1, f = 2, = -3 0.5 1.5 2.5 A = 1, f = 1, = /4 Time vs Frequency Domains Consider the signal x(t ) sin(2 t ) sin(2 3t ) 1.5 1.5 1.5 1 0.5 0.5 0.5 0 0.5 1.5 2.5 + 0 0.5 1.5 2.5 = 0 -0.5 -0.5 -0.5 -1 -1 -1 -1.5 -1.5 -1.5 0.5 1.5 2.5 Demo: sine.py Time vs Frequency Domains signal strength signal strength 1 time -1 Time Domain Representation plots amplitude as a function of time frequency -1 Frequency Domain Representation plots each sine wave’s peak amplitude against its frequency Demo: Equalizer 10 Noise Types of noise (cont’d) Crosstalk Signal from one line picked up by another Wire Wire Impulse Irregular pulses or spikes E.g., lightning Short duration High amplitude 43 Signal-to-Noise Ratio Signal-to-Noise Ratio (SNR) SNR Powersignal Powernoise 44 Example The power of a signal is 10 mW and the power of the noise is μW; what are the values of SNR and SNRdB ? Solution The values of SNR and SNRdB can be calculated as follows: 45 Data Rate: Noiseless Channels Nyquist Theorem Bit BitRate Rate==22××Bandwidth Bandwidth××log log22LL Harry Nyquist (1889-1976) Bit rate in bps Bandwidth in Hz L – number of signal levels 46 Example We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz How many signal levels we need? Solution We can use the Nyquist formula as shown: Since this result is not a power of 2, we need to either increase the number of levels or reduce the bit rate If we have 128 levels, the bit rate is 280 kbps If we have 64 levels, the bit rate is 240 kbps 47 Data Rate: Noisy Channels Shannon Capacity Capacity Capacity==Bandwidth Bandwidth××log log22(1+SNR) (1+SNR) Capacity (maximum bit rate) in bps Bandwidth in Hz Elwood Shannon SNR – Signal-to-Noise Ratio Claude(1916-2001) 48 Example A telephone line normally has a bandwidth of 3000 The signal-to-noise ratio is usually 3162 Calculate the theoretical highest bit rate of a regular telephone line This means that the highest bit rate for a telephone line is 34.860 kbps If we want to send data faster than this, we can either increase the bandwidth of the line or improve the signal-to-noise ratio 49 Example We have a channel with a 1-MHz bandwidth The SNR for this channel is 63 What are the appropriate bit rate and signal level? Solution First, use the Shannon capacity followed by the Nyquist formula 50 Note The Shannon capacity gives us the upper limit; the Nyquist formula tells us how many signal levels we need 51 Network Performance Bandwidth Throughput Hertz Bits per second (bps) Actual data rate Latency (delay) Time it takes for an entire message to completely arrive at the destination 52 Latency Composed of Propagation time Transmission time Queuing time Processing time Entire message propagation time transmission time 53 Latency Receiver Sender First bit leaves First bit arrives Propagation time Data bits Last bit leaves Transmission time Last bit arrives Time Time 54 Bandwidth-Delay Product The link is seen as a pipe Cross section = bandwidth Length = delay Bandwidth-delay product defines the number of bits that can fill the link 55 Figure Filling the link with bits for case 56 Summary Data need to take form of signal to be transmitted Frequency domain representation of signal allows easier analysis Fourier analysis Medium's bandwidth limits certain frequencies to pass Bit rate is proportional to bandwidth Signals get impaired by attenuation, distortion, and noise 57 ... Analog vs Digital Signals To To be be transmitted, transmitted,data data must must be be transformed transformed to to electromagnetic electromagneticsignals signals Analog signals have...Outline Analog and digital data /signals Time and frequency domain views of signals Bandwidth and bit rate Transmitting digital signals as analog Theoretical data rate Signal impairment... signals have an infinite number of values in a range Digital signals value Have a limited number of values time value time Data and Signals Analog Data Analog Signal Telephone Digital Data Analog
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