17.2 : フーリエ変換の基本信号

Among the key elements of the Fourier Transform, the sinc function is unique in that it equals 1 when its argument is zero and exhibits even symmetry.

In the frequency domain, the Fourier transform of a rectangular pulse transforms into this sinc function, which exhibits symmetry with a peak at the origin and progressively smaller lobes on either side.

The exponential signal, a complex-valued function, represents a sinusoidal oscillation at a specific frequency. When subjected to a Fourier transform, its frequency content becomes a single impulse located at a particular frequency.
This indicates that a perfect square wave incorporates an infinite number of harmonic frequencies represented by the lobes of the sinc function.

The delta function is zero everywhere except at zero, where it's infinite. The Fourier transform of a delta function is a constant, signifying that a delta function contains all frequencies with equal magnitude.