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FSK has several advantages over ASK due to the fact that the carrier has a constant amplitude. hence, its immunity to non-linearities, immunity to rapid fading, immunity to adjacent channel interference, and the ability to work in small SNR environments due to the effect of exchanging SNR for bandwidth.
I think you should look for a good communication book, in there they will give a good foundation but still some things can't be expressed in math simply because the way the signal is detected is more robust. The best you can find is a Math representation which is very close to the real world and most books do give this.
yes , FSK is better than ASK in the cases that the carrier has a constant amplitude and hence are used in the communication systems wher security reasons are considered .... but it cannot be said that it fades less as over long distance communication its SNR decreases and hence quality of signals ... thats why , PSK ( BPSK , QPSK , DPSK ) were introduced to overlook this disadvantage too ....
HERE IS WHY FSK IS BETTER
1. LESS COMPLEXITY RECEIVER CAN BE USED
2. NO POLARITY INVERSION ERROR
3. WAVEFORM CAN BE GENERATED WITHOUT EDGES SO LESS INTERCHANNEL INTERFERENCE
4. PROBABILITY OF ERROR IS LESS
DISADVANTAGE
LARGE BANDWIDTH
APPLICATION: IT IS PREFERRED IN SATELLITE COMMUNICATION BECAUSE OF BETTER RECEPTION. REGARDS
JOE1986
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