**Binary Frequency Shift Keying (BFSK)**

- FSK is treated as non-linear modulation since information is put into the frequency.

**Time domain representation:**

The transmitted signal can be represented as:

$$s_i(t)=\bigg\{^{\sqrt{\dfrac{2T_b}{T_b}}\cos(2 \pi f_il), 0\lt1\le T_b} _{0,\hspace{2cm} elsewhere}$$

- S1(t) represents symbol “1”.
- S2(t) represents symbol “0”.

$$f_1=f_c+\dfrac{1}{2T_b} \ \ \ \ f_2=f_c-\dfrac{1}{2T_b}$$

The minimum frequency spacing between two adjacent frequency slots to ensure orthogonality for the continuous phase BFSK is

$\dfrac{1}{2T_b}$

**Phase Discontinuous Frequency Shift Keying**

**Generation of BFSK**

**Coherent Detection of BFSK**

**Bandwidth of FSK:**

The null to null bandwidth of FSK is

$B.W \gt 2R_b$

Power Spectral density of BFSK

We need two phasor

Two carrier are used .The frequency are selected in such a way that two carrier will be orthogonal to each other.

$∫_0^{Tb}\sqrt{2p} \cos(2πf_Ht) \sqrt{2p} \cos(2πf_Lt) = 0$