TRANSMISSION OF VARIETY 8/6 



Ex. 6: Pass the message "314159 . . ." (the digits of tt) through the transducer 

 n' = n -{■ a — 5, starting the transducer at « = 10. 



Ex. 7: If a and b are parameters, so that the vector {a,b) defines a parameter- 

 state, and if the transducer has states defined by the vector {,x,y) and trans- 

 formation 



' x' = ax -\- by 

 y =x + (a - b)y, 



complete the trajectory in the table : 



*Ex. 8: A transducer, with parameter u, has the transformation dxldt = 

 — (m + 4)x; it is given, from initial state x = 1, the input u = cos t; 

 find the values of x as output. 



*Ex. 9: If a is input to the transducer 



dx/dt = y 



dyjdt = —X —2y + a, 



with diagram of immediate effects 



a-^y:^x, 



what is the output from x if it is started at (0,0) with input a = sin / ? 

 (Hint: Use the Laplace transform.) 



*Ex. 10: If a is input and the transducer is 



dx/dt = k{a — x) 



what characterises a;'s behaviour as k is made positive and numerically 

 larger and larger? 



INVERTING A CODED MESSAGE 



8/6. In S.8/4 it was emphasised that, for a code to be useful as a 

 message-carrier, the possibiUty of its inversion must exist. Let us 

 attempt to apply this test to the transducer of S.8/5, regarding it as 

 a coder. 



There are two transformations used, and they must be kept 

 carefully distinct. The first is that which corresponds to U of 

 S.8/4, and whose operands are the individual messages; the second 

 is that of the transducer. Suppose the transducer of S.8/5 is to 

 be given a "message" that consists of two letters, each of which 

 may be one of Q, R, S. Nine messages are possible : 



QQ, QR, QS, RQ, RR, RS, SQ, SR, SS 



10 145 



