For the operational amplifier circuit shown, the output saturation voltages are $$ \pm \,\,15V$$. The upper and lower threshold voltages for the circuit are, respectively.

In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is inter symbol interference zero?

Which one of the following statements about differential pulse code modulation (DPCM) is true?

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