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## Agenda

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**Agenda**1. QUIZ 2. HOMEWORK LAST CLASS 3. HOMEWORK NEXT CLASS 4. TRANSMISSION MATHEMATICS a. dBs, NYQUIST & SHANNON b. NOISE 5. DIGITAL SYSTEMS 6. ANALOG AND ANALOG TO DIGITAL CONVERSIONS 7. ISDN 8. DSL**Homework**Chapter 4: 10, 11, 12, 14, 15, 16, 22, 50, 54, 63 Chapter 5: 1, 3, 6, 7, 9, 14, 17, 32**Decibells & Logarithms**Converting watts to dB (or milliwatts to dBm): 10 log10 1000 watts = 30 dBw Converting dB to watts (or dBm to milliwatts): 30 dBw = log-1, or log-1 (3) or 10 raised to the 3rd power = 103 = 1000 watts 35 dBw = 103.5 = 3162.3 watts Note: There’s a point between the 3 & 5.**Decibells & Logarithms**dBW Watts -3 .5 0 1 3 2 6 4 9 8 10 10 20 100 30 1000 40 10000**Nyquist**1. Nyquist: The maximum practical data rate (samples) per channel. Max R = 2 H log2 V Logarithmic function to the base 2: For each # V, log V = the exponent to which 2 must be raised to produce V. Then if V = 16, the log2 of V = 4. If V = 2, the log2 of V = 1. Then what is the maximum practical data rate for BPSK signal on a line with a bandwidth of 3000 Hz? What is the maximum practical data rate for a QPSK signal on a line with a bandwidth of 3000 Hz?**Shannon**Shannon: The maximum theoretical data rate per channel. Max R = CBW x log2 (1 + S/N) [CBW = H in Nyquist Theorem] Then what is the maximum practical data rate for signal with a 30 dB S/N on a line with a bandwidth of 3000 Hz?**Noise**N = Noise Power = kTB, where B is bandwidth. (Used in Shannon’s Limit) No = Noise Density = kT, where k is Boltzmann’s Constant (-228.6 dBw) (Used in Carrier to Noise ratios, i.e., C/No) T = SNT = System Noise Temperature (Used in radio and satellite link equations, e.g., G/T is a measure of quality in satellite link equations.)**Chapter 4**Signals**Figure 4-1**Comparison of Analog and Digital Signals**Figure 4-2**Example of Periodic Signal**Figure 4-3**Example of Aperiodic Signal Aperiodic signals are _____________? Inconsistant**Figure 4-4**A Sine Wave**Figure 4-5**Amplitude**Figure 4-6**Period and Frequency**Figure 4-7**Relationship between Different Phases**Figure 4-8**Amplitude Change Amplitude relates to ___________? S in S/N**Figure 4-10**Phase Change Phase shift relates to ______________? Phase shift keying**Figure 4-11**Time and Frequency Domains**Time and Frequency Domains**for Different Signals Figure 4-12**Figure 4-13**A Signal with a DC Component**Figure 4-14**Composite Waveform**Figure 4-15**Bandwidth**Figure 4-16**Example 4.8**Figure 4-17**Example 4.9**Figure 4-19**Bit Rate and Bit Interval**Figure 4-20**Harmonics of a Digital Signal**Figure 4-21**Exact and Significant Spectrum**Chapter 5**Encoding**Figure 5-3**Types of Digital to Digital Encoding**Figure 5-5**Types of Polar Encoding**Figure 5-6**NRZ-L and NRZ-I Encoding**Figure 5-7**RZ Encoding**Figure 5-8**Manchester and Diff. Manchester Encoding**Figure 5-9**Types of Bipolar Encoding**Figure 5-10**Bipolar AMI Encoding**Figure 5-15**Analog to Digital Conversion**Figure 5-16**PAM**Figure 5-17**Quantized PAM Signal**Figure 5-19**PCM**Figure 5-20**From Analog Signal to PCM Digital Code**Figure 5-21**Nyquist Theorem This assumes what?**Figure 5-27**FSK**Figure 5-28**Baud Rate and Bandwidth in FSK**Figure 5-29**PSK Why do you think PSK is better than FSK? Needs less power per bit**Figure 5-30**PSK Constellation**Figure 5-31**4-PSK**Figure 5-32**4-PSK Characteristics**Figure 5-33**8-PSK Characteristics**Figure 5-34**Baud Rate and Bandwidth in PSK**Figure 5-35**4-QAM and 8-QAM Constellations