Subjects signal processing

Aliasing Visualization C2Ddf8

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1. **Problem Statement:** We need to visualize two graphs of a signal: one sampled above the Nyquist rate (which allows correct reconstruction) and one sampled below the Nyquist rate (which causes aliasing). 2. **Key Concept - Nyquist Rate:** The Nyquist rate is twice the highest frequency present in the signal. Sampling above this rate prevents aliasing, allowing perfect reconstruction. 3. **Graph 1 - Sampling Above Nyquist Rate:** - Let the original signal be $y = \sin(2\pi f t)$ with frequency $f$. - Sample at a rate $f_s > 2f$. - The sampled points accurately represent the original signal. 4. **Graph 2 - Sampling Below Nyquist Rate:** - Sample at a rate $f_s < 2f$. - The sampled points misrepresent the original frequency, creating a lower frequency alias. 5. **Labeling:** - X-axis: Time $t$ - Y-axis: Amplitude - Indicate the original continuous signal and the sampled points. - Show reconstructed signals from samples. 6. **Summary:** Sampling above Nyquist rate preserves the signal frequency; sampling below causes aliasing, distorting the signal.