Explore topological data analysis and signal processing in this comprehensive lecture by Harish Chintakunta. Delve into Takens' embedding, trigonometric polynomials, and the effects of embedding dimensions. Examine experimental results, including the impact of higher-order harmonics and sample sizes. Investigate sampling noise and compare classification performance of Short-Time Fourier Transform (STFT) versus other methods. Learn about predicting epileptic seizures using sample time signals and cyclicity response. Discover applications in detecting oscillations in power grids and conduct comparative studies on synthetic signals. Gain insights into Prony analysis and its relevance to signal processing techniques.