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Computing 'Ambiguity' Equation

1. Calculate the ambiguity function of a signal with an envelope u(t) = Bexp(-t^2)T^2). What should be the value of B that will make the signal of the unit energy?

2. Calculate the ambiguity of a signal with a complex envelope u(t) = Bexp(-t^2/T^2)exp(jpikt^2). Note that this is the same signal as above, except for the additional linear FM.

Solution Summary

Calculations apply the definition of the ambiguity function to the envelope function, factors out the B's, groups the exponents of e and algebraically manipulates the resulting exponent to "complete the square." Then they explore the characteristics of the error function. Next they change the variable of the integral and apply the results of previous calculations. More algebraic manipulation to separate the imaginary part of the exponent from the real and line 10 is the absolute value is then done. 1 and 2/3 pages of formatted calculations in word.