In this example we compute the Fourier transform of the right-sided decaying exponential signal f(t) = exp(-at)u(t) using the definition of the Fourier Transform.

In this example we compute the Fourier transform of the left-sided decaying exponential signal x(t) = exp(bt)u(-t) using the definition of the Fourier Transform. The signal x(t) is commonly referred to as the left-sided decaying exponential signal.

x(t)=exp(-a|t|) using the definition of the Fourier Transform. The signal x(t) is commonly referred to as the two-sided or double-sided decaying exponential signal.

This example computes the Fourier Transform of the complex exponential x(t) = exp(j\omega0 *t) using the definition of the inverse Fourier Transform and the sifting property of the delta function.

This example computes the Fourier Transform of the time-domain impulse function x(t) = delta(t) using the definition of the Fourier Transform, and the Fourier Transform of the constant function x(t) = A using the definition of the Inverse Fourier Transform. The sifting property of the delta function is used in both examples to help work the integral equations.