The derivative of the symmetric function drawn in Fig .1 will look like

The function x(t) is shown in Fig. Even and odd parts of a unit-step function u(t) are respectively.

A signal x(n)$$ = \sin ({\omega _0}\,n + \phi )$$ is the input to a linear time-invariant system having a frequency response $$H({e^{j\omega }})$$.If the output of the system is $$Ax(n - {n_0})$$, then the most general form of $$\angle H({e^{j\omega }})$$ will be

For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by