Reconstruction: Sampling Theorem Conclusion

This lecture concludes with a fascinating and powerful result that has revolutionized global communication, shifting from analog to digital communication without loss. By respecting a threshold rule of twice the bandwidth, we can perfectly reconstruct a continuous signal from a discrete set of samples. The crucial role of bandwidth in this technique is highlighted, where sampling beyond twice the maximum frequency allows for perfect reconstruction, while sampling below this threshold leads to dramatic effects like signal distortion and the appearance of negative frequencies. To avoid these issues, it is essential to apply a low-pass filter before sampling, a fundamental concept emphasized by the instructor.