Unit 3 quiz 1

What is the periodicity property of DFT?

• Periodicity property of DFT states that a signal's DFT is periodic with a period equal to the length of the signal.

• Periodicity property of DFT states that a signal's DFT is only valid for odd-length signals

• Periodicity property of DFT states that a signal's DFT is periodic with a period equal to half the length of the signal

• Periodicity property of DFT states that a signal's DFT is aperiodic

State the linearity property of DFT.

• DFT(ax[n] - by[n]) = aX[k] - bY[k]

• DFT(ax[n] * by[n]) = aX[k] * bY[k]

• DFT(ax[n] / by[n]) = aX[k] / bY[k]

• DFT(ax[n] + by[n]) = aX[k] + bY[k]

Explain the symmetry property of DFT.

• If x(n) is real-valued, then X(k) = X(N-k)* for all k.

• The symmetry property of DFT is not related to the real or imaginary parts of the signal.

• The symmetry property of DFT only applies to even-length sequences.

• If x(n) is imaginary-valued, then X(k) = X(N-k)* for all k.

What is the time shifting property of DFT?

• x(n - m) corresponds to X(k) multiplied by exp(j2πmk/N)

• x(n - m) corresponds to X(k) multiplied by exp(-j2πmk)

• x(n - m) corresponds to X(k) multiplied by exp(-j2πmk/N)

• x(n + m) corresponds to X(k) multiplied by exp(-j2πmk/N)

Describe the conjugate symmetry property of DFT.

• For a real-valued input signal, the DFT coefficients satisfy the property X[k] = X[N-k]* for k = 1, 2, ..., N-1.

• The conjugate symmetry property of DFT is not related to the symmetry of the input signal.

• For a real-valued input signal, the DFT coefficients satisfy the property X[k] = X[N-k]+ for k = 1, 2, ..., N-1.

• The conjugate symmetry property of DFT only applies to complex-valued input signals.

How does the DFT behave under frequency shifting?

• The DFT behaves by dividing the original DFT by a complex exponential in the frequency domain.

• The DFT behaves by multiplying the original DFT by a complex exponential in the frequency domain.

• The DFT behaves by adding a constant value to the original DFT in the frequency domain.

• The DFT behaves by taking the square root of the original DFT in the frequency domain.

What is the difference between circular convolution and linear convolution in DFT?

• Circular convolution in DFT results in a shorter output sequence compared to linear convolution in DFT.

• Circular convolution in DFT is equivalent to linear convolution in DFT when the input sequences are zero-padded to the sum of their lengths minus 1.

• Circular convolution in DFT is always longer than linear convolution in DFT.

• Linear convolution in DFT requires zero-padding while circular convolution does not.

Discuss the magnitude and phase properties of DFT.

• The magnitude of DFT represents the time domain signal, while the phase represents the frequency domain signal.

• The magnitude of DFT is constant for all frequency components, while the phase varies.

• The magnitude of DFT shows the strength of frequency components, while the phase of DFT shows the shift or delay of each frequency component.

• The magnitude of DFT is inversely proportional to the frequency components, while the phase is directly proportional.

Explain the energy conservation property of DFT.

• DFT does not consider energy conservation

• The energy of a signal increases in the transformation process

• The total energy of a signal is conserved in the transformation process from time domain to frequency domain.

• Energy conservation in DFT is only applicable to specific signals

How does the DFT handle time reversal of a signal?

• Divide the input signal by 2 before applying the DFT

• Negate the input signal before applying the DFT

• Apply the DFT without any changes

• Conjugate the input signal before applying the DFT.