Determine the lowpass signal with energy, Electrical Engineering

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Determine the lowpass signal with energy

Solve the following problem:

Consider the equivalent lowpass (complex-valued) signal s₁(t), 0 ≤ t ≤ T , with energy ε = ∫₀^T |s₁(t)|² dt

Suppose that this signal is corrupted by AWGN, which is represented by its equivalent lowpass form z(t). Hence, the observed signal is

r_l(t) = s₁(t) + z(t) , 0≤t≤T

The received signal is passed through a filter that has an (equivalent lowpass) impulse response h₁(t). Determine h₁(t) so that the filter maximizes the SNR at its output (at t = T ).

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Electrical Engineering: Determine the lowpass signal with energy

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Electrical Engineering: Determine the lowpass signal with energy

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