Govt. Exams
Entrance Exams
For real signals, Fourier transform exhibits conjugate symmetry: X(-f) = X*(f)
IFT of δ(f-f₀) = e^(j2πf₀t) using sifting property of delta function
Energy signal has 0 < E < ∞ and P = 0. Power signal has P > 0 and E = ∞
For a causal system, ROC is outside the outermost pole. Pole at z=0.5, so |z| > 0.5
Time reversal is linear (satisfies superposition) but time-variant (violates shift invariance)
The Laplace transform does not preserve periodicity of signals in the frequency domain
E = ∫₀^∞ e^(-4t)dt = [-e^(-4t)/4]₀^∞ = 1/4 = 0.25 J
Bounded Input Bounded Output stability requires the impulse response to be absolutely summable: ∑|h[n]| < ∞
The Fourier transform of rect(t/T) is T·sinc(πfT) where sinc(x) = sin(x)/x
PSRR (in dB or V/V) measures how much power supply voltage variations appear at output. Higher PSRR (more negative in dB) = better rejection. PSRR varies with frequency and is crucial for low-noise applications.