ECE 2026 Digital Signal Processing Questions & Answers

ECE 2026 Digital Signal Processing Questions & Answers "X-Point Averager" FIR Filter - CORRECT ANSWER - 3 Representations of h[n] ? - CORRECT ANSWER - Addition of Phasors - CORRECT ANSWER - The sum of multiple phasors produces another phasor. That is because the sum of sinusoids with the same frequency is also a sinusoid with that frequency A₁*cos(wt+θ₁) + A₂*cos(wt+θ₂) = Re{ A₁e^iθ₁ *e^iwt } + Re{ A₂e^iθ₂ *e^iwt } = Re{ A₁e^iθ₁ *e^iwt + A₂e^iθ₂ *e^iwt } = Re{ (A₁e^iθ₁ + A₂e^iθ₂) * e^iwt } = Re{ A₃e^iθ₃ * e^iwt } where: A₃² = [A₁cos(wt+θ₁) + A₂cos(wt+θ₂)]² + [A₁sin(wt+θ₁) + A₂sin(wt+θ₂)]² θ₃ = arctan( [A₁sin(wt+θ₁) + A₂sin(wt+θ₂)] / [A₁cos(wt+θ₁) + A₂cos(wt+θ₂)] ) Also via the law of cosines: A₃² = A₁² + A₂² + 2A₁A₂cos(θ₁-θ₂) A key point is that A₃ and θ₃ do not depend on ω or t, which is what makes phasor notation possible. The time and frequency dependence can be suppressed and re-inserted into the outcome as long as the only operations used in between are ones that produce another phasor. Aliasing: Aliasing - CORRECT ANSWER - w_hat = 2*pi * ( fo / fs ) + 2*pi*L Aliasing = w_hat: { (2*pi - 3*pi) , (4*pi - 5*pi), ... } Does not have conjugate. Aliasing: Folding - CORRECT ANSWER - w_hat = 2*pi * ( fo / fs ) + 2*pi*L..