List of top Signals and Systems Questions on Signals asked in GATE EC

Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is . 
 

In the circuit shown in the figure, the transistors M1 and M2 are operating in saturation. The channel length modulation coefficients of both the transistors are non-zero. The transconductance of the MOSFETs M1 and M2 are \( g_{m1} \) and \( g_{m2} \), respectively, and the internal resistance of the MOSFETs M1 and M2 are \( r_{o1} \) and \( r_{o2} \), respectively. Ignoring the body effect, the ac small signal voltage gain \( \frac{\partial V_{\text{out}}}{\partial V_{\text{in}}} \) of the circuit is 

A speech signal, band limited to 4 kHz, is sampled at 1.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range \( -5 \, \text{V} \) to \( +5 \, \text{V} \), are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is kHz.
A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is V.
Consider a real-valued base-band signal \( x(t) \), band limited to 10 kHz. The Nyquist rate for the signal \( y(t) = x(t) \cdot \left( 1 + \frac{t}{2} \right) \) is