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 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?

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

2. If (101.01)₂=(x)₁₀, then what is the value of x?

5.25505.05101.0110.101

3. What are the lattice coefficients corresponding to the FIR filter with system function H(z)= 1+(13/24)z^-1+(5/8)z^-2+(1/3)z^-3?

(1/4,1/2,1/3)(1/2,1/4,1/3)None of these(1,1/2,1/3)

4. The structure shown below is known as ____________

Cascade structureParallel form structureDirect formNone of these

5. What does the structure given below represents?

Regular Direct form-IITransposed direct form-IIDirect form-INone of these

6. 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?

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

7. The FIR filter whose direct form structure is as shown below is a prediction error filter.

FalseMaybeTrueDon't Know

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

2M.2E(1/2<M<1)None of these2EM.2E(1/2<M<1)

9. What is the configuration of system for digital processing of an analog signal?

Analog signal|| Post-filter -> D/A Converter -> Digital Processor -> A/D Converter -> Pre-filterAnalog signal|| Pre-filter -> D/A Converter -> Digital Processor -> A/D Converter -> Post-filterNone of theseAnalog signal|| Pre-filter -> A/D Converter -> Digital Processor -> D/A Converter -> Post-filter

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

0.2*10-382*10-380.3*10-383*10-38

11. In the equation SQNR = 10 \(log_{10}⁡\frac{P_x}{P_n}\). what are the terms P_x and P_n are called ___ respectively.

Power of the Quantization noise and Signal powerSignal power and power of the quantization noiseNone of theseAll of the mentioned

12. Which of the following filters have a cascade realization as shown below?

High pass filterIIR filterComb filterFIR filter

13. What is the output of the single stage lattice filter if x(n) is the input?

x(n)+Kx(n+1)x(n)+Kx(n-1)+Kx(n+1)Kx(n-1)x(n)+Kx(n-1)

14. Which of the following is the application of lattice filter?

ElectroencephalogramAll of the mentionedDigital speech processingAdaptive filter

15. What is the value of the coefficient α₂(1) in the case of FIR filter represented in direct form structure with m=2 in terms of K₁ and K₂?

K1(K2)K1(1+K2)None of theseK1(1-K2)

16. 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-1M+N+1M+NM+N+2

17. A closed form solution of the state space equations is easily obtained when the system matrix F is?

SymmetricDiagonalTransposeIdentity

18. What is the binary equivalent of (-3/8)?

(10011)2(1101)2(1100)2(0011)2

19. What is the expression for SQNR which can be expressed in a logarithmic scale?

2 \(log_2⁡\frac{P_x}{P_n}\) 10 \(log_{10}⁡\frac{P_x}{P_n}\) 10 \(log_2⁡\frac{P_x}{P_n}\) 10 \(log_{10}⁡\frac{P_n}{P_x}\)

20. For a twos complement representation, the truncation error is ____________

None of theseZeroAlways positiveAlways negative

21. What are the mantissa and exponent required respectively to represent ‘5’ in binary floating point representation?

011,0.1100000.110000,0110.101000,011011,0.101000

22. Which of the following is an method for implementing an FIR system?

Lattice structureDirect formAll of the mentionedCascade form

23. The constants K₁ and K₂ of the lattice structure are called as reflection coefficients.

TrueDon't KnowMaybeFalse

24. We can view y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\) as the computational procedure (an algorithm) for determining the output sequence y(n) of the system from the input sequence x(n).

FalseTrueMaybeDon't Know

25. Which of the following gives the complete definition of the state of a system at time n₀?

Amount of information at n0+input signal x(n) for n≥n0 determines output signal for n≥n0Amount of information at n0 determines output signal for n≥n0Input signal x(n) for n≥0 determines output signal for n≥n0Input signal x(n) for n≥n0 determines output signal for n≥n0