A binary transmission is constructed from two orthogonal signals )( 1 ts and )( 2 ts , 0 ≤≤ Tt , with energies E1 = 1 and E2 = 5.0 , respectively. The additive noise is white Gaussian with mean zero and power spectral density 0.5. )( 1 ts and )( 2 ts are transmitted with equal a priori probabilities.

(a) Determine the achievable probability of error.

(b) Determine the minimum signal energy to achieve the same error performance.