Digital signal processing lab viva questions on Z transforms and DFT, FFT

Home/ lab viva questions/ DSP Part-II& III

Part-II : Z Transforms
1. Define one-sided and two-sided Z-transform.

2. What is region of convergence (ROC)?
The region of Z magnitude (|Z|) for which  x(n).|Z|^-n is absolutely summable

3. State the  Initial value and final value theorem with regard to Z-transform.

4. Define Z-transform of unit step signal.
                  Z/(Z-1)        ROC |z|>1

5. What are the different methods available for inverse Zs-transform?
Residue method, Partial fractions method, Long division method, Convolution integral method

6. When the z-domain transfer function of the system can be directly obtained from s-domain transfer function?
When input is an Impulse sampled signal.

7. Define the transfer function of an LTI system.
For Discrete time systems: Z transform of impulse response of system
For Continuous time systems: Laplace transform of impulse response

8. Write the transfer function of Nth order LTI system.

9. Give the importance of convolution and deconvolution operations using Z-transform.

10. Give the conditions for stability of an LTI discrete time system in z-plane.

The ROC should contain unit circle with in it.
11. Explain when an LTI dicrete time system will be causal.

The ROC should contain infinite. i.e system impulse response is a right sided signal.

12. State the convolution property of Z-transform.
  -------------> 
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13. state the properties of Z transform?
            click here
14. Z-transform  of various signals?
            click here

Part-III: DFT & FFT

1. Define DFT of a discrete time sequence?

2. Define inverse DFT.

3. What is the relation between DTFT and DFT?

4. What is the drawback in Fourier transform and how is it overcome?

Fourier transform is that it is not truly realizable in practice but we can get closer, it is not applicable to all signals, so we go for Laplace in continuous , Z in discrete. 
5. List any four properties of DFT .
linearity Property :  ax1(n)+bx2(n)→aX1(ω)+bX2(ω)







Duality Property:  X(N)⟷Nx[((−k))N]

Complex conjugate property:  x∗(n)⟷X∗((K))N=X∗(N−K)

Circular shift property: x(n)exp(j2ΠKn/N)⟷X((K−L)

6. What is FFT, What it's importance?

FFT stands for Fast Fourier Transform, this is same as DFT but algorithm is different by FFT with in lees time we can compute Fourier transform compared to DFT.
7. compare FFT and DFT?

DFT and FFT both are used to represent a discrete time signal in frequency domain, But DFT procedure is formula based where FFT is algorithm based, FFT is more efficient and faster than DFT, i.e if a sequence contains N samples then to calculate 
DFT  no. of multiplications and additions  required are:   N² ,  N(N-1) 
FFT no. of multiplications and additions required are : (N/2) log₂(N), N log₂(N)

8. What are the various algorithms to calculate FFT?

Decimation In Time (DIT), Decimation In frequency (DIF)
9. Draw the DIT FFT structure with the length of 8?

10. Draw the DIF FFT structure with the length of 8?

11. What is phase factor or twiddle factor?
It is defined as W_N = e^-j2π/N

12. What are the phase factors involved in all stages of computation in the 8-point DIT radix-2 FFT?

First stage: W₈⁰

Second stage: W₈⁰_, W₈²

Third stage: W₈⁰_, W₈¹_, W₈², W₈³

13. Draw the basic butterfly diagram or flow graph of DIT radix-2 FFT?

14. Draw the basic butterfly diagram or flow graph of DIF radix-2 FFT?

15. What are the phase factors involved in all stages of computation in 8-point DIF radix-2 FFT?

First stage: W₈⁰_, W₈¹_, W₈², W₈³

Second stage: W₈⁰_, W₈²

Third stage: W₈⁰

16. What is magnitude and phase spectrum? 
Magnitude spectrum is the graph between Fourier transform magnitudes and frequency. Phase spectrum is the graph between Fourier transform phases and frequency.

                                                                                                             

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