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 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 side bands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) 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 V to +5 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 .

Consider a polar non-return to Zero (NRZ) waveform, using +2 V and -2 V for representing binary ' 1 ' and ' 0 ' respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance $0.4 \mathrm{~V}^2$. If the a priori probability of transmission of a binary ' 1 ' is 0.4 , the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is $\_\_\_\_$ V.