Bandwidth of BPSK is lower than that of BFSK

BPSK (Binary Phase Shift Keying) and BFSK (Binary Frequency Shift Keying) are two common digital modulation schemes used in communication systems. Both these modulation techniques are used to transmit binary data over a communication channel. The bandwidth of a modulation scheme refers to the range of frequencies required to transmit the signal.

BPSK (Binary Phase Shift Keying)
In BPSK, the carrier signal is phase-shifted to represent binary data. It uses two phases: 0° and 180°. When the binary input is '0', the carrier phase remains unchanged, and when the binary input is '1', the carrier phase is inverted. BPSK can be represented mathematically as:

s(t) = A * cos(2πfct + φ)

where A is the amplitude of the carrier, fc is the carrier frequency, and φ is the phase shift.

BFSK (Binary Frequency Shift Keying)
In BFSK, two different carrier frequencies are used to represent binary data. When the binary input is '0', one carrier frequency is used, and when the binary input is '1', a different carrier frequency is used. BFSK can be represented mathematically as:

s(t) = A * cos(2πf1t) for binary '0'
s(t) = A * cos(2πf2t) for binary '1'

where A is the amplitude of the carrier, f1 and f2 are the two carrier frequencies.

Bandwidth Comparison
The bandwidth of a modulation scheme is determined by the highest frequency component in the signal. In the case of BPSK, the phase shift between the carrier signals is the only factor that changes, while the carrier frequency remains the same. Therefore, the bandwidth required for BPSK is equal to the bandwidth of the carrier signal.

On the other hand, BFSK uses two different carrier frequencies to represent binary data. This means that the bandwidth required for BFSK is equal to the difference between the two carrier frequencies. Since BFSK uses two carrier frequencies, its bandwidth is higher compared to BPSK.

Therefore, the statement "Bandwidth of BPSK is lower than that of BFSK" is correct. BPSK requires a lower bandwidth as it uses a single carrier frequency, while BFSK requires a higher bandwidth as it uses two carrier frequencies.