The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillations, respectively, are

In the circuit shown, assume that the opamp is ideal. The bridge output voltage V₀ (in mV) for $$\delta = 0.05$$ 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

A source emits bit 0 with probability $${1 \over 3}$$ and bit 1 with probability $${2 \over 3}$$. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as
$${f_{\left. R \right|o}}\,(r) = \left\{ {\matrix{ {{1 \over 4},} & { - \,3\,\, \le \,\,x\,\, \le \,\,1,\,} \cr 0 & {otherwise,} \cr } } \right.and$$
$${f_{R/o}}\,(r) = \left\{ {\matrix{ {{1 \over 6},} & { - \,1\,\, \le \,\,x\,\, \le \,\,5\,,} \cr 0 & {otherwise.} \cr } } \right.$$

The minimum decision error orobability is