Z-Transform and Discrete Fourier Transform — MCQs – EE

1. The Z-Transform is used to analyze:
(A) Continuous-time systems
(B) Discrete-time systems
(C) Nonlinear systems
(D) Analog systems

2. The Z-Transform converts a signal from:
(A) Time domain to frequency domain
(B) Time domain to Z-domain
(C) Frequency domain to time domain
(D) Continuous domain to discrete domain

3. The inverse Z-Transform converts a signal from:
(A) Frequency domain to time domain
(B) Z-domain to time domain
(C) Analog to digital
(D) Continuous to discrete

4. The Z-Transform is particularly useful for:
(A) Solving differential equations
(B) Solving difference equations
(C) Solving algebraic equations
(D) Solving integral equations

5. The Z-Transform of a shifted signal corresponds to:
(A) Time shifting property
(B) Scaling property
(C) Convolution property
(D) Differentiation property

6. The Region of Convergence (ROC) in Z-Transform determines:
(A) Frequency of signal
(B) Stability and causality
(C) Sampling frequency
(D) Amplitude response

7. A causal system’s ROC lies:
(A) Inside the outermost pole
(B) Outside the outermost pole
(C) Between poles
(D) On the unit circle

8. The Discrete-Time Fourier Transform (DTFT) is a special case of:
(A) Laplace Transform
(B) Z-Transform
(C) Fourier Series
(D) Wavelet Transform

9. The Z-Transform reduces to DTFT when:
(A) |z| = 1
(B) |z| = 0
(C) z → ∞
(D) z → 0

10. The Discrete Fourier Transform (DFT) is used to analyze:
(A) Infinite-duration signals
(B) Finite-duration signals
(C) Continuous-time signals
(D) Analog waveforms

11. The DFT converts a discrete-time signal from:
(A) Time domain to frequency domain
(B) Frequency domain to time domain
(C) Time domain to Z-domain
(D) Z-domain to s-domain

12. The inverse DFT converts a signal from:
(A) Frequency domain to time domain
(B) Z-domain to frequency domain
(C) Continuous to discrete
(D) Time domain to Z-domain

13. The DFT is a discrete version of the:
(A) Laplace Transform
(B) Fourier Transform
(C) Hilbert Transform
(D) Wavelet Transform

14. The computationally efficient algorithm to compute DFT is known as:
(A) Fast Fourier Transform (FFT)
(B) Z-Algorithm
(C) Laplace Reduction
(D) Sampling Theorem

15. The DFT is periodic in:
(A) Time domain
(B) Frequency domain
(C) Both time and frequency domains
(D) Neither

16. Circular convolution in time domain corresponds to:
(A) Multiplication in frequency domain
(B) Addition in frequency domain
(C) Subtraction in frequency domain
(D) Convolution in frequency domain

17. The FFT algorithm reduces computational complexity from:
(A) N² to NlogN
(B) N³ to N
(C) N to logN
(D) N² to N²/2

18. The DFT assumes the input signal to be:
(A) Periodic
(B) Aperiodic
(C) Random
(D) Constant

19. The number of points in DFT is equal to:
(A) Number of frequency samples
(B) Sampling rate
(C) Time duration
(D) Nyquist frequency

20. Zero-padding in DFT increases:
(A) Frequency resolution
(B) Time duration
(C) Sampling rate
(D) Quantization error

21. Leakage effect in DFT occurs when:
(A) Signal is not periodic in the observation window
(B) Sampling rate is too high
(C) Quantization levels are few
(D) Windowing is applied

22. The main use of windowing in DFT is to:
(A) Reduce spectral leakage
(B) Increase aliasing
(C) Decrease signal amplitude
(D) Add distortion

23. In DFT, the term “bin” refers to:
(A) A frequency sample
(B) A time sample
(C) A quantization level
(D) A filter output

24. The magnitude of the DFT represents:
(A) Frequency content of the signal
(B) Phase response of the signal
(C) Amplitude distortion
(D) Time delay

25. The phase of the DFT represents:
(A) Time shift information
(B) Amplitude information
(C) Sampling rate
(D) Signal duration

26. The relationship between DFT and IDFT is:
(A) Inverse operations
(B) Same operation
(C) Independent
(D) Both are Laplace transforms

27. In digital signal processing, the Z-Transform helps in:
(A) System analysis and stability
(B) Quantization
(C) Filtering analog signals
(D) Increasing resolution

28. The poles of the system in the Z-plane determine:
(A) System stability
(B) System causality
(C) Sampling rate
(D) Frequency content

29. A system is stable if all its poles lie:
(A) Inside the unit circle
(B) Outside the unit circle
(C) On the real axis
(D) On the imaginary axis

30. The Z-Transform and DFT are both widely used in:
(A) Digital filters and spectral analysis
(B) Power electronics
(C) Analog amplifiers
(D) Mechanical systems