1. Presented by: Class Presentation of Custom DSP Implementation Course on: This is a class presentation. All data are copy rights of their respective authors as listed in the references and have been used here for educational purpose only. ECE Department – University of Tehran May 2005 m.Khafaji Digital FM Demodulator

2. Outline Introduction to FM Modulation FM signal demodulation Quadrature-Mixer Digital Limiter Baseband Delay Demodulator Phase-Adapter Demodulator Direct Digital Synthesizers

3. Introduction to FM Modulation Information signal encoded in carrier frequency (or phase) Modulated signal is s(t)=A c cos(q(t)) q(t)=2pf c t+2pk f  m(t)dt Benefits: –Instantaneous frequency: f i =f c +k f m(t) –Signal robust to amplitude variations –Robust to signal reflections and refractions

4. Spectral Analysis of FM s(t)=A c cos(2pf c t+2pk f  m(t)dt) –Very hard to analyze for general m(t). Let m(t)=cos(2pf m t): Bandwidth f m Using Fourier Series analysis : –Df 1  B  2f m =2B m –If Df >>f m, significant components up to f c ±Df. fcfc f c +f m f c +2f m f c +3f m f c + 4f m f c -4f m f c -3f m f c -2f m f c -f m f NBFM B  2B m AcAc -.5A c .5A c  …….5A c J n (  ) WBFM B2fB2f.5A c J n (  )

5. FM signal demodulation filtering and Limiting the transmitted signal. Differentiation to obtain the phase information in the modulated signal. There are four ways to implement differentiation: Differentiator and Envelope Detector Zero Crossing Detector –Uses rate of zero crossings to estimate f i Phase Lock Loop (PLL) –Uses VCO and feedback to extract m(t) Phase-Shift or Quadrature Detection

6. Quadrature-Mixer The mixing to the baseband is carried out by the multiplication of the FM signal and a complex oscillator e j  Tn and a low pass filter The input signal is: S FM (n) = A. cos (  T n +  FM (n)) And the output signal of the mixer is: S basis (n) = = A/2. cos (  FM (n)) + jA/2. sin (  FM (n))

7. Real quadrature-mixer S real (n) = A/2. cos (  FM  (n)) S imag (n)= A/2. sin (  FM  (n)) The mixer can also be realized with real signals by multiplying the FM signal with a sine and cosine oscillation signal

8. Digital Limiter The received FM signal due to distortion in the channel is not known However demodulators need a constant amplitude which is achieved by normalizing the magnitude of the signal

9. Baseband Delay Demodulator Delay demodulator needs the FM-Signal in the baseband For this a quadrature mixing has to be done first

10. Real Baseband Delay Demodulator

11. Continued An approximation of the actual phase angle is sufficient for computing arcsine function Several popular methods include: Table look up, Taylor- series approximation, and polynomial fitting The signal after the arcsine must be limited between −  2 and  2 to be clearly defined ( )

12. Phase-Adapter Demodulator The signal after the arc tangent function g (n) =  FM (n) must be limited between −  2 and  2 to be clearly defined For very low message frequencies, the maximal derivation will be very low and not practicable for most applications. Therefore this demodulator is only useful for narrowband FM.

13. Mixed Demodulator A combination of the delay demodulator and the phase adapter demodulator.

14. Direct Digital Synthesizers DDSs also called Numerically Controlled Oscillators Directly Synthesize a Selectable Output Frequency from a Clock Using Digital Techniques Types of DDSs –Pulse Output –Sine Output –Fractional Divider –Fractional Divider Phase Interpolation –Other

15. Sine Output DDS

16. Typical Sine Output DDS Spectrums

17. DDS with modulation capabilities

18. Quadrature Outout of DDS

19. Summery Review of FM modulation and demodulation Implementation of digital mixer, limiter, demodulator Produce of quadrature signal with direct digital synthesizer

20. References Franz Schnyder-Christoph Haller, “Implementation of FM Demodulator Algorithms on a High Performance Digital Signal Processor”, Diploma Thesis-2002 James Micheal Shima, “FM Demodulation Using A Digital Radio And Digital Signal Processing”, Master of Science Thesis University of Florida 1995 Jouko Vankka,” Direct Digital Synthesizers: Theory, Design and Applications”, PhD Thesis Helsinki University of Technology November 2000