Find the exponential Fourier series for this periodic square wave signal with a duty cycle of 50%. The Fourier series allows us to represent any periodic signal as a sum of sinusoids (or complex exponentials), each with its own amplitude and phase. This concept is at the core of signal analysis, communications, and control systems, helping us understand how complex waveforms are built from simpler components. Let’s walk through this example step by step to see how the math translates into the si

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Japan uses piezoelectric ceramic tiles to convert electricity into electrical energy. These tiles capture the kinetic energy from your footsteps. When you walk, your weight and movements put pressure on the tiles. The ceramic tile bends slightly, resulting in mechanical stress. The piezoelectric material inside the ceramic tile converts this stress into electrical energy. Each step produces a small amount of electric charge, and millions of steps combined can produce enough electricity to drive

This Small-Cap Energy Play Could Explode… AI is creating one of the biggest electricity shortages in U.S. history — and most investors have no idea. Several brand-new data centers in Silicon Valley are literally sitting empty because the local utility doesn’t have enough power to turn them on. At the same time, America depends on foreign countries for 95% of its uranium supply, including 25% from Russia, which will be cut off by 2028. Nuclear power demand is rising fast, AI data centers are usin