FSK orthogonality - Page 1
Forum section: electronics / rf-microwave

author: Ralphy007
author_rank: Contributor
timestamp: January 28, 2020, 11:12:44 am
content: For Continuous Time FSK (CTFSK) i.e. coherent FSK, the two carriers must be at 90 degrees to one another to optimise detection. But how can this be the case if there is no difference in phase when the transmitter switches between the 2 carriers.

author: ebastler
author_rank: Super Contributor
timestamp: January 28, 2020, 02:37:03 pm
content: Not sure I understand your question correctly. But the "orthogonality" condition for optimum FSK detection does not mean that the two carriers have a 90° phase shift vs. each other. (They do not have a constant phase relationship at all, since they are different frequencies after all.)Rather, it means that integrating the product of the two carriers (over a full period) will give a zero result. E.g. f1 = 2*f2 will satisfy that condition.

author: Ralphy007
author_rank: Contributor
timestamp: January 28, 2020, 03:48:42 pm
content: Thank you for replying.My misunderstanding. I thought the description of the two carriers being orthogonal, meant they were at 90 degrees to one another.

author: ebastler
author_rank: Super Contributor
timestamp: January 28, 2020, 03:58:09 pm
content: Ah, glad that cleared it up. It's a different, but related definition of "orthogonality": The integral Int (f1(x) * f2(x)) dx can be seen as a scalar product of two functions. And, analogous to the scalar product of two vectors which are at right angles, the functions are considered "orthogonal" if their scalar product is zero.(That being said, cos(x) and sin(x)areorthogonal functions in that sense, and they do obviously have a 90° phase shift. But the 90° phase shift is not the only way to achieve orthogonality.)

author: DH1AKF_Wolfgang
author_rank: Contributor
timestamp: January 29, 2020, 05:34:37 am
content: The Wikipedia says:"To improve the immunity to demodulation interference, the individual symbol frequencies can be selected so that they are orthogonal to each otherat a certain symbol rate. In this case the intersymbol interference between individual symbols is minimized. With binary FSK and a symbol duration of T, the two frequencies are orthogonal to each other if the frequency deviation, where n is an integer and positive, meets the following condition:"delta f = 1/T * n/2 with n = 1,2,3,...Hope this helps. Wolfgang

author: T3sl4co1l
author_rank: Super Contributor
timestamp: January 29, 2020, 05:59:21 am
content: Yep, and note that the orthogonality is integrated over a symbol period, or several symbols for all possible combinations of symbols, or all possible sequences of all possible symbols, as the case may be, and to name a few examples.Tim

author: Ralphy007
author_rank: Contributor
timestamp: January 31, 2020, 03:40:27 pm
content: I believe there are 2 forms of BFSK i.e. coherent and non coherent both of which have formulae which relates the frequency shift (F1 - F0) to the bit rate.Assuming Tb is the period of 1 bit, then the bit rate is Fb = 1/Tb. F1 is the frequency for a 1 and F0 is the frequency for a 0.COHERENT F1 - F0 = n/2Tb n is an integer 1,2,3......... half the bit rate.NONCOHERENT F1 - F0 = n/Tb n is an integer 1,2,3.........Presumably these formulae are correct ? Are there any limitations to the values for F1 and F0 in either case ?