Further Examples/Topics on Fourier Transform

Abstract

With the basic introductory material about the Fourier transform covered in the last two chapters, this chapter drills into some heavy-duty examples including the stair signum function, odd negative exponential, sines/cosines times negative exponential, cropped cosine, cosine squared, cropped t, |t|, t ², and t ⁴ functions, functions of the form f(t)/g(t), arctan function, hat function, tapered pulse, asymmetric triangular function, 3-step stair, truncated pulse train, and the ramped unit step function. Heavy use of applications to drill the idea of the Fourier transform in ones mind and get plenty practice and experience in carrying on the transform. In the chapter we rely heavily on using the Fourier transform properties, developed in the last chapter. We wrap the chapter by demonstrating the flexibility of the Fourier transform by deriving the FT of the unit step function using at least seven methods.