Govt. Exams
Entrance Exams
For sinusoidal input, steady-state output is |H(jω)|×A at angle ∠H(jω). Here ω=2, so output amplitude = |H(j2)|×10.
Frequency resolution = fs/N = 8000/1000 = 8 Hz. This is the minimum frequency spacing in DFT.
Linear phase FIR filters have constant group delay = (N-1)/2 samples, which is why they're preferred for applications requiring minimal distortion.
Group delay τ_g(ω) = -dθ(ω)/dω represents dispersion in filter's phase response
DC gain = H(z=1) = 1/(1-0.5) = 1/0.5 = 2
Parseval's theorem for discrete-time: ∑|x[n]|² = (1/2π)∫|X(e^jω)|²dω over 2π
Rectangular window has narrowest main lobe (best resolution) but highest sidelobe (worst leakage)
For sustained oscillation: (1) Barkhausen condition: |Aβ| = 1 (unity loop gain), (2) Phase condition: ∠Aβ = 0° or 360°. In Wien bridge, gain needed ≈ 3 to compensate losses.
Bootstrapping increases input impedance by reducing effective base current drawn from source through capacitive feedback. This minimizes loading effects on high-impedance sources.
Log amplifier uses diode in feedback. Temperature changes cause Is (reverse saturation current) to vary exponentially, directly affecting the logarithmic transfer function. This is the dominant non-ideal effect.
