Assesment on unit-1 & 2

If x₁(n) and x₂(n) are two real valued sequences of length N, and let x(n) be a complex valued sequence defined as x(n)=x₁(n)+jx₂(n), 0≤n≤N-1, then what is the value of x₁(n)?

• [x(n)-x^*(n)]/2

• [x(n)+x^*(n)]/2

• [x(n)+x^*(n)]/2j

• [x(n)-x^*(n)]/2j

If x₁(n) and x₂(n) are two real valued sequences of length N, and let x(n) be a complex valued sequence defined as x(n)=x₁(n)+jx₂(n), 0≤ n≤ N-1, then what is the value of x₂(n)?

• [x(n)+x^*(n)]/2

• [x(n)-x^*(n)]/2

• [x(n)+x^*(n)]/2j

• [x(n)-x^*(n)]/2j

How many complex multiplications are need to be performed for each FFT algorithm?

• N/2 log N

• Nlog₂N

• NlogN

• N/2 log₂N

How many complex additions are required to be performed in linear filtering of a sequence using FFT algorithm?

• N/2 log N

• 2Nlog₂N

• NlogN

• N/2 log₂N

If the system is initially relaxed at time n=0 and memory equals to zero, then the response of such state is called as

• Zero-state response

• Zero-input response

• Zero-condition response

• None of the mentioned

The total solution of the difference equation is given as

• y_p(n)-y_h(n)

• y_p(n)+y_h(n)

• y_h(n)-y_p(n)

• None of the mentioned

What is the impulse response of the system described by the second order difference equation y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1)?

• [-1/5 (-1)ⁿ–6/5 (4)ⁿ]u(n)

• [1/5 (-1)ⁿ–6/5 (4)ⁿ]u(n)

• [1/5 (-1)ⁿ+6/5 (4)ⁿ]u(n)

• [-1/5 (-1)ⁿ+6/5 (4)ⁿ]u(n)

If x(n) and X(k) are an N-point DFT pair, then X(k+N)=?

• X(-k)

• -X(k)

• X(k)

• None of the mentioned

What is the order of the four operations that are needed to be done on h(k) in order to convolute x(k) and h(k)?Step-1:Folding, Step-2:Multiplication with x(k), Step-3:Shifting, Step-4:Summation

• 1-2-3-4

• 1-2-4-3

• 2-1-3-4

• 1-3-2-4

Zero-state response is also known as

• Forced Response

• Natural response

• free response

• Total response