Editing Phase-shift keying (section)

===Implementation===
The general form for BPSK follows the equation:

:<math>s_n(t) =   \sqrt{\frac{2E_b}{T_b}} \cos(2 \pi f t + \pi(1-n )),\quad n = 0,1. </math>

This yields two phases, 0 and π.
In the specific form, [[binary data]] is often conveyed with the following signals:{{citation needed|date=June 2019}}

:<math>s_0(t) =   \sqrt{\frac{2E_b}{T_b}} \cos(2 \pi f t + \pi )
              = - \sqrt{\frac{2E_b}{T_b}} \cos(2 \pi f t)</math> for binary "0"
:<math>s_1(t) = \sqrt{\frac{2E_b}{T_b}} \cos(2 \pi f t) </math> for binary "1"

where ''f'' is the frequency of the base band.

Hence, the signal space can be represented by the single [[basis function]]

:<math>\phi(t) = \sqrt{\frac{2}{T_b}} \cos(2 \pi f t) </math>

where 1 is represented by <math>\sqrt{E_b} \phi(t)</math> and 0 is represented by <math>-\sqrt{E_b} \phi(t)</math>. This assignment is arbitrary.

This use of this basis function is shown at the [[#timing|end of the next section]] in a signal timing diagram. The topmost signal is a BPSK-modulated cosine wave that the BPSK modulator would produce. The bit-stream that causes this output is shown above the signal (the other parts of this figure are relevant only to QPSK). After modulation, the base band signal will be moved to the high frequency band by multiplying <math> \cos(2 \pi f_c t)</math>.