GATE IN 2014 Question Paper (02-Feb-2014) (Shift 2)

An N-bit ADC has an analog reference voltage V. Assuming zero mean and uniform distribution of the quantization error, the quantization noise power will be:

A microprocessor accepts external interrupts (Ext INT) through a Programmable Interrupt Controller as shown in the figure.



Assuming vectored interrupt, a correct sequence of operations when a single external interrupt (Ext INT1) is received will be :

The circuit in the figure represents a counter-based unipolar ADC. When SOC is asserted the counter is reset and clock is enabled so that the counter counts up and the DAC output grows. When the DAC output exceeds the input sample value, the comparator switches from logic 0 to logic 1, disabling the clock and enabling the output buffer by asserting EOC. Assuming all components to be ideal, 𝑉${}_{ref}$, DAC output and input to be positive, the maximum error in conversion of the analog sample value is:

𝑋(𝑘)is the Discrete Fourier Transform of a 6-point real sequence 𝑥(𝑛).

If 𝑋(0) = 9 + 𝑗0, 𝑋(2) = 2 + 𝑗2, 𝑋(3) = 3 – 𝑗0, 𝑋(5) = 1 – 𝑗1, 𝑥(0) is

The transfer function of a digital system is given by $\frac{b_0}{1-z^{-1}+a_2{z}^{-2}}$ where a₂ is real.

The transfer function is BIBO stable if the value of a₂ is