CPFSK and GFSK

CPFSK and GFSK

Continuous Phase Frequency Shift Keying (CPFSK) and Gaussian Frequency Shift Keying (GFSK) are advanced forms of FSK designed to improve spectral efficiency and reduce interference.

1. CPFSK (Continuous Phase FSK)

In standard FSK, phase may abruptly change between symbols. CPFSK ensures that the phase remains continuous, avoiding sudden jumps.

s(t) = A cos(2π f_c t + θ(t))

Where the phase is:

θ(t) = 2π h ∫ m(τ) dτ

• A = constant amplitude
• f_c = carrier frequency
• h = modulation index
• m(t) = input data signal (±1)

Because phase is an integral of the data, it changes smoothly → no discontinuities.

Why CPFSK is Better

• Continuous phase → reduced bandwidth
• No sharp transitions → less spectral splatter
• Maintains constant envelope

2. GFSK (Gaussian FSK)

GFSK improves CPFSK further by passing the data through a Gaussian filter before modulation.

m_g(t) = m(t) * g(t)

Where:

• g(t) = Gaussian filter impulse response
• * = convolution

The transmitted signal becomes:

s(t) = A cos(2π f_c t + 2π h ∫ m_g(τ) dτ)

Gaussian Filter

g(t) = (1 / √(2πσ²)) e^{-t² / (2σ²)}

The filter smooths transitions between bits, reducing high-frequency components.

Why GFSK is Used in Bluetooth

• Better spectral efficiency
• Reduced adjacent channel interference
• Constant envelope → efficient RF amplification
• Low power consumption

BT Product

GFSK uses a bandwidth-time product:

BT = Bandwidth × Symbol Time

In Bluetooth:
BT ≈ 0.3 – 0.5

Lower BT → narrower bandwidth but more intersymbol interference (ISI).

Summary

• FSK → frequency changes only
• CPFSK → smooth phase transitions
• GFSK → filtered CPFSK for compact spectrum

GFSK = “Smooth frequency changes with no sharp edges”