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==Chapter 8== | ==Chapter 8== | ||
| − | #Complex Exponential and Sinusoidal Amplitude Modulation ( | + | #'''Complex Exponential and Sinusoidal Amplitude Modulation''' (You Can Hear the Music on the Amplitude Modulation Radio -''Everclear'') Systems with the general form <math> y(t) = x(t)c(t) </math> where <math>c(t)</math> is the ''carrier signal'' and <math>x(t)</math> is the ''modulating signal''. The ''carrier signal'' has its amplitude multiplied (modulated) by the information-bearing ''modulating signal''. |
| − | ##<math>c(t) = e^{\omega_c t + \theta_c}</math> | + | ##Complex exponential ''carrier signal'': <math>c(t) = e^{\omega_c t + \theta_c}</math> |
| − | ##<math>c(t) = cos(\omega_c t + \theta_c )</math> | + | ##Sinusoidal ''carrier signal'': <math>c(t) = cos(\omega_c t + \theta_c )</math> |
| − | #Recovering the Information Signal <math>x(t)</math> Through Demodulation | + | #'''Recovering the Information Signal''' <math>x(t)</math> '''Through Demodulation''' |
##Synchronous | ##Synchronous | ||
##Asynchronous | ##Asynchronous | ||
| − | #Frequency-Division Multiplexing | + | #'''Frequency-Division Multiplexing''' (Use the Entire Width of that Frequency Band!) |
| − | #Single-Sideband Sinusoidal Amplitude Modulation | + | #'''Single-Sideband Sinusoidal Amplitude Modulation''' (Save the Bandwidth, Save the World!) |
| − | #AM with | + | #'''AM with a Pulse-Train Carrier''' Digital Airwaves |
| − | + | ##<math>c(t) = \sum_{k=-\infty}^{+\infty}\frac{sin(k\omega_c \Delta /2)}{\pi k}e^{jk\omega_c t}</math> | |
| + | ##Time-Division Multiplexing "Dost thou love life? Then do not squander time; for that's the stuff life is made of." -''Benjamin Franklin'') | ||
| + | Recommended Exercises: | ||
8.1, 8.2, 8.3, 8.5, 8.8, 8.10, 8.11, 8.12, 8.21, 8.23 | 8.1, 8.2, 8.3, 8.5, 8.8, 8.10, 8.11, 8.12, 8.21, 8.23 | ||
Revision as of 02:05, 5 December 2008
Suggested problems from Oppenheim and Willsky
Contents
Chapter 7
- Sampling
- Impulse Train Sampling
- The Sampling Theorem and the Nyquist
- Signal Reconstruction Using Interpolation: the fitting of a continuous signal to a set of sample values
- Sampling with a Zero-Order Hold (Horizontal Plateaus)
- Linear Interpolation (Connect the Samples)
- Undersampling: Aliasing
- Processing CT Signals Using DT Systems (Vinyl to CD)
- Analog vs. Digital: The Show-down (A to D conversion -> Discrete-Time Processing System -> D to A conversion
- Sampling DT Signals (CD to MP3 albeit a complicated sampling algorithm, MP3 is less dense signal)
7.1, 7.2, 7.3, 7.4, 7.5, 7.7, 7.10, 7.22, 7.29, 7.31, 7.33
Chapter 8
- Complex Exponential and Sinusoidal Amplitude Modulation (You Can Hear the Music on the Amplitude Modulation Radio -Everclear) Systems with the general form $ y(t) = x(t)c(t) $ where $ c(t) $ is the carrier signal and $ x(t) $ is the modulating signal. The carrier signal has its amplitude multiplied (modulated) by the information-bearing modulating signal.
- Complex exponential carrier signal: $ c(t) = e^{\omega_c t + \theta_c} $
- Sinusoidal carrier signal: $ c(t) = cos(\omega_c t + \theta_c ) $
- Recovering the Information Signal $ x(t) $ Through Demodulation
- Synchronous
- Asynchronous
- Frequency-Division Multiplexing (Use the Entire Width of that Frequency Band!)
- Single-Sideband Sinusoidal Amplitude Modulation (Save the Bandwidth, Save the World!)
- AM with a Pulse-Train Carrier Digital Airwaves
- $ c(t) = \sum_{k=-\infty}^{+\infty}\frac{sin(k\omega_c \Delta /2)}{\pi k}e^{jk\omega_c t} $
- Time-Division Multiplexing "Dost thou love life? Then do not squander time; for that's the stuff life is made of." -Benjamin Franklin)
Recommended Exercises: 8.1, 8.2, 8.3, 8.5, 8.8, 8.10, 8.11, 8.12, 8.21, 8.23
Chapter 9
9.2, 9.3, 9.4, 9.6, 9.8, 9.9, 9.21, 9.22
Chapter 10
10.1, 10.2, 10.3, 10.4, 10.6, 10.7, 10.8, 10.9, 10.10, 10.11, 10.13, 10.15, 10.21, 10.22, 10.23, 10.24, 10.25, 10.26, 10.27, 10.30, 10.31, 10.32, 10.33, 10.43, 10.44.
Note: If a problem states that you should use “long division”, feel free to use the geometric series formula instead.
