Discrete Time Systems Implementation topics include: Realization structures for discrete time systems, FIR system structures, IIR system structures, number representation, state space system analysis, quantization error analysis and bilinear transformations. Discrete-time systems process discrete-time signals. They can be represented by a set of difference equations or a block diagram of their implementation.  The input and output of a discrete-time system are related by a linear constant coefficient difference equation. This equation defines a sequence of operations to implement the... Show more

Discrete Time Systems Implementation topics include: Realization structures for discrete time systems, FIR system structures, IIR system structures, number representation, state space system analysis, quantization error analysis and bilinear transformations.

Discrete-time systems process discrete-time signals. They can be represented by a set of difference equations or a block diagram of their implementation. 

The input and output of a discrete-time system are related by a linear constant coefficient difference equation. This equation defines a sequence of operations to implement the system. 
A discrete-time system is causal if the output is 0 when the input is 0 and there are no initial conditions. The output does not depend on future inputs. 
Discrete-time systems can be of finite impulse response (FIR) or infinite impulse response (IIR) type. A FIR filter is a filter whose impulse response is of finite duration. 
Before implementation, it is recommended to use a simulator of the system to test the importance of the value of h. 
Discrete-time signal processing (DSP) has applications in many domains, such as digital communications, medical imaging, audio and video systems, consumer electronics, and robotics

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Digital Signal Processing Practice Test: Discrete Time Systems Implementation

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25 Questions

1. If we consider a sequence of FIR filer with system function H_m(z)=A_m(z), then what is the definition of the polynomial A_m(z)?

\(1+\sum_{k=0}^m α_m (k)z^{-k}\) \(\sum_{k=0}^m α_m (k)z^{-k}\) \(1+\sum_{k=1}^m α_m (k)z^k \) \(1+\sum_{k=1}^m α_m (k)z^{-k}\)

2. The basic elements of a flow graph are branches and nodes.

Don't KnowMaybeTrueFalse

3. The binary point between the digits b₀ and b₁ exist physically in the computer.

Don't KnowFalseTrueMaybe

4. What is the condition of M, if the structure according to the direct form is as follows?

Doesn’t depend on value of MM oddAll values of MM even

5. If M and N are the orders of numerator and denominator of rational system function respectively, then how many multiplications are required in direct form-I realization of that IIR filter?

M+N+2M+N+1M+NM+N-1

6. The desired frequency response is specified at a set of equally spaced frequencies defined by the equation?

None of these\(\frac{\pi}{2M}\)(k+α)\(\frac{2\pi}{M}\)(k+α)\(\frac{\pi}{M}\)(k+α)

7. The general linear constant coefficient difference equation characterizing an LTI discrete time system is?

y(n)=-\(\sum_{k=1}^N a_k y(n)+\sum_{k=0}^N b_k x(n) \) None of thesey(n)=-\(\sum_{k=0}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k) \) y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)

8. If M and N are the orders of numerator and denominator of rational system function respectively, then how many additions are required in direct form-I realization of that IIR filter?

M+N+1M+N+2M+N-1M+N

9. A single input-single output system and its transpose have identical impulse responses and hence the same input-output relationship.

TrueFalseMaybeDon't Know

10. What is the system function of all-zero filter or comb filter?

\(\frac{1}{M}(1-z^{-M} e^{j2πα})\) \(\frac{1}{M}(1+z^{-M} e^{j2πα})\) \(\frac{1}{M}(1+z^M e^{j2πα})\) \(\frac{1}{M}(1-z^M e^{j2πα})\)

11. The direct form realization is often called a transversal or tapped-delay-line filter.

MaybeDon't KnowTrueFalse

12. The in-band quantization noise variance is given as?

\(\sigma_n^2=\int_{-B}^B |H_n (F)|^2 S_e (F)dF\) None\(\sigma_n^2=\int_{-B}^B |H_n (F)|^3 S_e (F)dF\) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^1 S_e (F)dF\)

13. What is the smallest floating point number that can be represented using a 32-bit word?

0.3*10-383*10-380.2*10-382*10-38

14. The selection of the sampling rate F_s=1/T, where T is the sampling interval, not only determines the highest frequency (F_s/2) that is preserved in the analog signal but also serves as a scale factor that influences the design specifications for digital filters.

Don't KnowMaybeFalseTrue

15. If we reverse the directions of all branch transmittances and interchange the input and output in the flow graph, then the resulting structure is called as ______________

None of theseDirect form-IITransposed formDirect form-I

16. Finite word length effects refer to the quantization effects that are inherent in any digital implementation of the system, either in hardware or software.

Don't KnowTrueFalseMaybe

17. When the frequency band is selected we can specify the sampling rate and the characteristics of the pre filter, which is also called as __________ filter.

Analog filterAnti aliasing filterNone of theseAnalog & Anti aliasing filter

18. State variables provide information about all the internal signals in the system.

Don't KnowTrueFalseMaybe

19. The zeros of the system function of comb filter are located at ______________

None of theseInside unit circleOn unit circleOutside unit circle

20. Which of the following is the correct representation of a floating point number X?

M.2E(1/2<M<1)None of these2E2M.2E(1/2<M<1)

21. The parallel form realization is also known as normal form representation.

MaybeFalseDon't KnowTrue

22. What is the system function of the second filter other than comb filter in the realization of FIR filter?

\(\sum_{k=0}^{M-1} \frac{H(k+α)}{1-e^{\frac{j2π(k+α)}{M}} z^{-1}}\) None of these\(\sum_{k=0}^{M-1} \frac{H(k+α)}{1+e^{\frac{j2π(k+α)}{M}} z^{-1}}\) \(\sum_{k=0}^M \frac{H(k+α)}{1-e^{\frac{j2π(k+α)}{M}} z^{-1}}\)

23. If a three stage lattice filter with coefficients K₁=1/4, K₂=1/2 K₃=1/3, then what are the FIR filter coefficients for the direct form structure?

(1/4,13/24,5/8,1/3)(1,5/8,13/24,1/3)(1,13/24,5/8,1/3)(1,8/24,5/8,1/3)

24. What are the nodes that replace the adders in the signal flow graphs?

Summing nodeBranch nodeSink nodeSource node

25. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-II realization of that IIR filter?

M+NMax [M,N] M+N+1Min [M,N]