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

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels.

The quantization noise power for the quantization region between –a and +a in the figure is

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels.

If the input probability density function is divided into three regions as shown in figure, the value of 'a' in the figure is