⚡️ Review lessons of Communication Principles released on my bilibili channel

This is the recording of the review lessons of Communication Principles released on my bilibili channel.

Bilibili:

Communication Principles Midterm Review

Universal Safety Disclaimer

1. Accuracy: Due to my knowledge limitations, there might be errors in the content. Feel free to point them out if you find any.
2. Advanced Concepts: This course may involve advanced mathematical knowledge that might be unfamiliar to most of us (myself included). It won’t prevent you from understanding the material or solving problems—just memorize for now and dive deeper later if interested.
3. Resource Scarcity: Limited resources exist for this course; please share any helpful materials you find.
4. Good Luck: Best wishes for your midterm preparation!

Fourier Transform in Communication Principles

Key Equations

1. Signal and System Context:
   

   \[ F(jw) = \int_{-\infty}^{+\infty} f(t)e^{-jwt} dt, \quad f(t) = \frac{1}{2\pi}\int_{-\infty}^{+\infty} F(jw)e^{jwt} dw \]

2. Communication Principles Context:
   

   \[ V(f) = \int_{-\infty}^{+\infty} v(t)e^{-j2\pi ft} dt, \quad v(t) = \int_{-\infty}^{+\infty} V(f)e^{j2\pi ft} df \]

Important Concepts:

1. Pulse Function:
   

   \[ \delta(t-a) \rightarrow F(j\omega) = e^{-ja\omega}, \quad V(f) = e^{-j2\pi fa} \]

2. Rectangular Function:
   

   \[ \mathrm{rect}\left(\frac{t}{T}\right) \rightarrow V(f) = T \cdot \mathrm{sinc}(Tf) \]

3. Convolution Theorem:

   • Time domain convolution corresponds to multiplication in the frequency domain (no need to divide by \( 2\pi \)).

Amplitude Modulation (AM)

Conventional AM

1. Modulation Formula:
   

   \[ x(t) = A_c[1 + k_a m(t)]\cos(2\pi f_c t) \]

2. Single Tone Modulation:

   \[ x(t) = A_c[1 + \mu \cos(2\pi f_m t)]\cos(2\pi f_c t), \quad \mu = k_a \cdot A_m \]

3. Demodulation:

   • Envelop detection is used for conventional AM demodulation.

DSBSC-AM

1. Modulation Formula:
   

   \[ x(t) = m(t) \cdot A_c \cos(2\pi f_c t) \]

2. Demodulation:

   • Local oscillator phase synchronization is critical. The output is: \[ v_o(t) = \text{constant} \cdot m(t) \]

Signal-to-Noise Ratio (SNR)

1. Noise in AWGN Channel:

   • Noise power spectrum density is uniform: \[ S_W(f) = \frac{\eta}{2}, \quad \text{Bandwidth: } B \]

2. SNR Improvement:

   • Conventional AM: \[ \frac{SNR_o}{SNR_i} = \frac{2k_a^2 \overline{m^2(t)}}{1 + k_a^2 \overline{m^2(t)}} \]
   • DSBSC-AM: \[ \frac{SNR_o}{SNR_i} = 2 \]

Example Problems and Practice

• Illustrated examples and diagrams to explain modulation, demodulation, and SNR calculations in real scenarios.