We have already presented the classical approach to generate the FSK waveform. However, as the
wireless community faces multiple standards using multiple modulation schemes, we would more
than likely use a Cartesian coordinate representation, that is, complex envelope approach.
Recall when we introduced the concept of complex envelope in Chap. 1, we already provided the
reader with a baseband FM modulator (see Fig. 2.50). Here we redraw it for sake of convenience.
[unitless] b
2fd
Rb
Above we see the input signal is integrated and multiplied by the sensitivity factor in order to
get the modulation index desired. The trigonometric functions sine and cosine are commonly
implemented in HW as LUTs; similarly, they are implemented in SW by some series expansion as
well as a LUT.
Next we aim to discuss the complex envelope signal in order to help us understand how they are
transmitted. Also, we want to be able to better understand the signal output of the receiver quadrature
demodulator for circumstances such as when a Zero IF (ZIF) Receiver or Direction Conversion
Receiver (DCR) is used.
For sake of discussion, let us consider a case without the premodulation filter present and assume
Rb 10 kbps and fd 5 kHz; then the modulation index is defined as
(2.
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