Fourier Representations in Signals and Systems

Yo, skibidi vibes in the lecture about Fourier representations, lowkey dank knowledge drop. We got the linear and symmetric properties, plus the convolution property, all essential for the goons in Signals and Systems. Do not sleep on differentiation in both time and frequency, it is straight sigma energy. Also, time-shift and frequency-shift are key, like ships sailing through the edge of understanding. Multiplication and scaling properties are where it gets spicy, especially with Parseval relationships linking energy in time and frequency. Time-Bandwidth product is the real MVP, showing that as T shrinks, frequency expands, keeping it all balanced. Questions? Time to dive deeper!