Question

A band pass signal has a complex baseband envelope defined as gz (t)=5e−ʲ²π⁶ᵗ +2e−ʲ²π⁴ᵗ +1e−ʲ²π²ᵗ +3eʲ²π²ᵗ +8eʲ²π⁴ᵗ +9eʲ²π⁶ᵗ

Determine the in-phase and quadrature-phase components of the signal in trignometric form such that the amplitude of all the terms are even integers.

Answer 1

The in-phase component consists of terms with even exponents, while the quadrature-phase component consists of terms with odd exponents.

Step-by-step explanation:

The in-phase and quadrature-phase components of the given band pass signal can be determined by separating the real and imaginary parts of the signal. In the given complex baseband envelope, the in-phase component, also known as the real part, is obtained by adding the terms with even exponents: 5e^(-j2π^6t) + 1e^(-j2π^2t) + 8e^(j2π^4t). The quadrature-phase component, also known as the imaginary part, is obtained by adding the terms with odd exponents: 2e^(-j2π^4t) + 3e^(j2π^2t) + 9e^(j2π^6t).