where the fundamental frequency w_o is 2p /T rad/sec, the amplitude coefficients a₁, ..., a_N are non-negative, and the radian phase angles satisfy 0 £ q₁ , ..., q_N < 2p. To explore the Fourier series approximation, select a labeled signal, use the mouse to sketch one period of a signal, or use the mouse to modify a selected signal. Specify the number of harmonics, N, and click "Calculate." The approximation will be shown in red. In addition, the magnitude spectrum (a plot of a_n vs. n) and phase spectrum (a plot of q_n vs. n) are shown. (If the dc-component is negative, a₀ < 0, then |a₀| is shown in the magnitude spectrum and an angle of p radians is shown in the phase spectrum.) To see a table of the coefficients, click "Table."