JNTU B.Tech II SIGNALS AND SYSTEMS Previous Question Paper (August/September - 2022 - R15)

Elementary continuous-time signals are the fundamental building blocks used to represent and analyze complex signals. The primary signals include:

• Unit Impulse Signal (δ(t)): Defined as δ(t) = 0 for t ≠ 0 and the integral from -∞ to +∞ of δ(t)dt = 1. Graphically, it is represented as an arrow at the origin with height 1.
• Unit Step Signal (u(t)): Defined as u(t) = 1 for t ≥ 0 and 0 for t < 0. Graphically, it is a horizontal line at 0 for t < 0 and a horizontal line at 1 for t ≥ 0.
• Unit Ramp Signal (r(t)): Defined as r(t) = t for t ≥ 0 and 0 for t < 0. Graphically, it is a straight line passing through the origin with a slope of 1 for t ≥ 0.
• Exponential Signal (x(t) = Ae^at): These signals grow or decay exponentially depending on the constant 'a'. If 'a' is real and positive, it is a growing exponential; if negative, it is a decaying exponential.
• Sinusoidal Signal (x(t) = A cos(ωt + φ)): These are periodic signals characterized by amplitude A, angular frequency ω, and phase φ.

Any signal x(t) can be decomposed into its even component x_e(t) and odd component x_o(t) using the formulas:

Given x(t) = e^j2t, we know x(-t) = e^-j2t. Applying Euler's identity, e^jθ = cos(θ) + j sin(θ):

The even component is:

The odd component is: