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Main Lobe Peak: Width and Zero Crossings

Explore how the main lobe peak height and width of the sinc function arise from the Discrete Fourier Transform of a rectangular signal. Understand how to calculate the amplitude at zero frequency, representing the DC value, and determine the first zero crossings which define the main lobe width in the frequency domain.

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The DFT of a rectangular signal x[n]x[n] is found to be a sinc signal.

X[k]=sin(πkNL)πkNX[k]=\frac{\sin\left( \pi\frac{k}{N}L\right)}{\pi\frac{k}{N}} ...