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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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Young mum Amber Curragh is determined to warn others about the devastating effects of ketamine use after being left with such severe bladder damage, she has to spend two hours a day in the bath and wear incontinence pads just to cope. Experts have been warning about the dangers of the drug for years - and now new research shows deaths linked to it have risen twenty-fold in the last decade. For more information and support around drug addiction, call the Frank helpline on 0300 123 6600 or visit t