This document discusses continuous-phase frequency-shift keying (CPFSK) modulation. CPFSK is a memory-based modulation scheme where the phase is constrained to be continuous, unlike conventional FSK which has abrupt phase shifts. This avoids large spectral side lobes outside the main signal band. CPFSK uses a voltage-controlled oscillator where the phase is determined by integrating the modulated signal. The phase trajectories form a piecewise linear phase trellis. Minimum-shift keying (MSK) is a special case of binary CPFSK with a modulation index of 1/2 and rectangular pulses.

1. BY:
MOKA DINESH
M.TECH 1ST YEAR
PONDICHERRY UNIVERSITY
DEPARTMENT OF ELECTRONICS ENGINEERING
CONTINUOUS-PHASE
FREQUENCY-SHIFTKEYING

2. MODULATION
ANALOG DIGITAL
MEMORY LESS MEMORY BASED
CPFSK CPM

3. WHY CPFSK?
In Fsk Abrupt Switching From one oscillator output to another in
successive signaling intervals results in relatively large spectral
side lobes outside of the main spectral band of the signal.
Oooscillator1
Oscillator2
digital modulated signal
Discontinues phase generate
unwanted spectrum

4. CONTINUOUS-PHASE FREQUENCY-
SHIFTKEYING
CPFSK is a memory base modulation scheme in which phase is
constrained to be continuous.
Voltage controlled
oscillator
Phase continuous fsk
CPFSK

5. Let us consider PAM signal
Where,
• {In} = sequence of amplitudes and
• g(t) =rectangular pulse of amplitude 1/2T and duration T second
The equivalent low pass waveform v(t) is expressed as
Where,
• fd = the peak frequency deviation
• ɸo = the initial phase of the carrier

6. The carrier-modulated signal expressed as
where φ(t; I) represents the time-varying phase of the carrier
Although d(t) contains discontinuities, the integral of d(t) is continuous.
The phase of the carrier is determined by integrating the above
equation(1) in the interval nT ≤ t ≤ (n+1)T
1

7. Then
• Here, θn represents the memory (accumulation of all
symbols up to time (n-1)T
• h is called the modulation index.

8. Phase diagrams
The phase diagrams are also called phase tress.
Phase tress for cpfsk is piecewise linear because the pulse g(t) is
rectangular.
Smoother phase trajectories and phase tress are obtained by using
pulses that do not contain discontinuities such as the class of raised
cosine pulses.

9. State trellis for binary cpfsk with h=1/2

10. The phase trajectories ɸ(t;I) for binary cpfsk

11. State diagram
An alternative representation to the state trellis is the state diagram which
also illustrates the state transtions at the time instants t=NT.
Only the possible phase states and their transitions are displayed in the
state diagram ,here time does not appear explicitly as a variable.
The state diagram for the cpfsk signal with h=1/2 is shown below

12. Relationship between cpm , cpfsk and msk
Cpfsk becomes a special case of a general class of continuous phase
modulated(cpm) signal in which the carrier phase is
Msk is a special form of binary cpfsk in which the modulation index h=1/2
and g(t) is a rectangular pulse of duration T.

13. Relationship between cpm ,cpfsk and msk

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