Let $$g\left( t \right){\mkern 1mu} {\mkern 1mu} \,\,\,\,\,{\mkern 1mu} = {\mkern 1mu} {\mkern 1mu} p\left( t \right){}^ * p\left( t \right)$$ where $$ * $$ denotes convolution and $$p(t) = u(t) - u(t-1)$$ with $$u(t)$$ being the unit step function

The impulse response of filter matched to the signal $$s(t) = g(t)$$ $$ - \delta {\left( {t - 2} \right)^ * }\,\,g\left( t \right)$$ is given as:

In the following figure the minimum value of the constant “C”, which is to be added to y₁(t) such that y₁(t) and y₂(t) are different, is

The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the unit-step function)

x(t) = 125t(u(t) - u (t - 1) + (250 - 125t) (u (t - 1) - u (t - 2 )) so that slope - overload is avoided, would be

The following question refer to wide sense stationary stochastic process:

The parameters of the system obtained in Q. 12 would be