In binary frequency shift keying (FSK), the given signal wave forms are
$$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ and
$${u_o}(t) = 5\,\cos \,(22000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$

where T is the bit-duration interval and t is in seconds. Both $${u_o}(t)$$ and $${u_1}(t)$$ are zero output the interval $$0 \le \,\,t\, \le \,T$$. With a matched filter (correlator ) based receiver, the smallest positive value of T (in milliseconds) required to have $${u_o}(t)$$ and $${u_1}(t)$$ uncorrelated is

An ideal band-pass channel 500Hz-2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is____________________

The bit error probability of a memoryless binary symmetric channel is $${10^{ - 5}}$$. If $${10^{ - 5}}$$ bits are sent over this channel, then the probability that not more than one bit will be in error is ________________

A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size $$\Delta $$ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is