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Let’s integrate sin(x) / x from 0 to infinity, known as the Dirichlet integral. The integrand, sin(x) / x, is the unnormalized sinc function sinc(x) that is crucial in electrical engineering, particularly in signal processing. In the frequency domain, an ideal “brick-wall” low-pass filter is a rectangular pulse. Taking the inverse Fourier transform of this rectangular pulse gives you a sinc function in the time domain. If you integrate the sinc function up to a variable t (which gives the Sine I
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