Discrete Time Signals and Systems topics include: Discrete time systems, their analysis and implementation, discrete time signals, differential equations and the correlation of discrete time signals. A discrete-time signal is a sequence of values that correspond to specific moments in time. A discrete-time system is a system that takes a discrete-time signal as input and generates a discrete-time signal as output.  Discrete-time signals can be classified as either periodic or aperiodic, which refers to whether the signal repeats itself.  Discrete-time systems are signal processing entities... Show more

Discrete Time Signals and Systems topics include: Discrete time systems, their analysis and implementation, discrete time signals, differential equations and the correlation of discrete time signals.

A discrete-time signal is a sequence of values that correspond to specific moments in time. A discrete-time system is a system that takes a discrete-time signal as input and generates a discrete-time signal as output. 

Discrete-time signals can be classified as either periodic or aperiodic, which refers to whether the signal repeats itself. 
Discrete-time systems are signal processing entities that process discrete-time signals. Discrete-time signals are generally obtained as equidistant samples of continuous-time waveforms along the time axis. 
A system is defined mathematically as a unique operator or transformation that maps an input signal into an output signal. This is defined as y(n) = T[x(n)] where x(n) is input signal, y(n) is output signal, T[] is transformation that characterizes the system behavior. 

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Digital Signal Processing Practice Test: Discrete Time Signals and Systems

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25 Questions

1. The odd part of a signal x(t) is?

(1/2)*(x(t)+x(-t))x(t)-x(-t)(1/2)*(x(t)-x(-t))x(t)+x(-t)

2. An LTI system is said to be causal if and only if?

Impulse response is zero for negative values of nImpulse response is non-zero for positive values of nImpulse response is zero for positive values of nImpulse response is non-zero for negative values of n

3. The discrete time function defined as u(n)=n for n≥0;u(n)=0 for n<0 is an _____________

Unit step signalNone of theseUnit ramp signalUnit sample signal

4. Which of the following is the auto correlation of x(n)?

rxy(l)=x(l)+x(-l)rxy(l)=x(l)*x(-l)rxy(l)=x(l)*x(l)None of these

5. What is the system does the following direct form structure represents?

FIR systemPurely recursive systemNone of theseGeneral second order system

6. Which of the following linear time invariant system is a purely recursive system?

y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)+b_0x(n)\) y(n) = \(\sum_{k=1}^{N} a_k y(n-k)+\sum_{k=0}^{M} b_k x(n-k)\) y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)+\sum_{k=0}^{M} b_k x(n-k)\) y(n) = \(-\sum_{k=1}^{N} a_k y(n-k)-\sum_{k=0}^{M} b_k x(n-k)\)

7. x(n)*δ(n-n₀)=?

x(-n-n0)x(n+n0)x(n-n0)x(-n+n0)

8. x(n)*[h₁(n)+h₂(n)]=x(n)*h₁(n)+x(n)*h₂(n).

FalseTrueDon't KnowMaybe

9. What is the particular solution of the first order difference equation y(n)+ay(n-1)=x(n) where |a|<1, when the input of the system x(n)=u(n)?

\(\frac{1}{1-a}\) u(n)\(\frac{1}{1+a}\) \(\frac{1}{1+a}\) u(n)\(\frac{1}{1-a}\)

10. Resolve the sequence into a sum of weighted impulse sequences.

None of these2δ(n)+4δ(n-1)+3δ(n-2)2δ(n+1)+4δ(n)+3δ(n-2)2δ(n)+4δ(n-1)+3δ(n-3)

11. What is the homogenous solution of the system described by the first order difference equation y(n)+ay(n-1)=x(n)?

c(a)n(where ‘c’ is a constant)c(-a)-nc(a)-nc(-a)n

12. What is the particular solution of the difference equation y(n)=\(\frac{5}{6}y(n-1)-\frac{1}{6}\)y(n-2)+x(n) when the forcing function x(n)=2ⁿ, n≥0 and zero elsewhere?

\(\frac{5}{8}\) 2n\(\frac{5}{8}\) 2-n\(\frac{1}{5}\) 2n\(\frac{8}{5}\) 2n

13. What is the impulse response of the system described by the second order difference equation y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1)?

[-\(\frac{1}{5}\) (-1)n+\(\frac{6}{5}\) (4)n]u(n)[-\(\frac{1}{5}\) (-1)n–\(\frac{6}{5}\) (4)n]u(n)[\(\frac{1}{5}\) (-1)n+\(\frac{6}{5}\) (4)n]u(n)[\(\frac{1}{5}\) (-1)n–\(\frac{6}{5}\) (4)n]u(n)

14. If the output of the system is \(y(n)=\sum_{k=-\infty}^nx(y)\) with an input of x(n) then the system will work as ___________

SubtractorMultiplierAccumulatorAdder

15. If a system do not have a bounded output for bounded input, then the system is said to be __________

CausalNon-causalStableNon-stable

16. If the output of the system of the system at any ‘n’ depends only the present or the past values of the inputs then the system is said to be __________

Non-causalCausalNon-LinearLinear

17. The phase function of a discrete time signal x(n)=aⁿ, where a=r.e^jθ is?

none of the mentionedtan-1(nθ)nθtan(nθ)

18. If x(n) is the input signal of a system with impulse response h(n) and y(n) is the output signal, then the auto correlation of the signal y(n) is?

rhh(l)*rxx(l)rxx(l)*rhh(l)rxy(l)*rhh(l)ryx(l)*rhh(l)

19. What is the relation between cross correlation and auto correlation?

|rxy(l)|=\(\sqrt{r_{xx}(0).r_{yy}(0)}\) |rxy(l)|≥\(\sqrt{r_{xx}(0).r_{yy}(0)}\) |rxy(l)|≠\(\sqrt{r_{xx}(0).r_{yy}(0)}\) |rxy(l)|≤\(\sqrt{r_{xx}(0).r_{yy}(0)}\)

20. The impulse response of a LTI system is h(n)={1,1,1}. What is the response of the signal to the input x(n)={1,2,3}?

{1,3,6,5,3}{1,3,6,3,1}{1,1,1,0,0}{1,2,3,2,1}

21. The block denoted as follows is known as __________

Delay blockMultiplier blockAdder blockAdvance block

22. What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?

(-1)n+1 + (4)n+2(-1)n-1 + (4)n-2(-1)n+1 + (4)n-2None of these

23. What is the condition for a signal x(n)=Brⁿ where r=e^αT to be called as an decaying exponential signal?

0<r<∞r<0r>10<r<1

24. What is the order of the four operations that are needed to be done on h(k) in order to convolute x(k) and h(k)?
Step-1:Folding
Step-2:Multiplication with x(k)
Step-3:Shifting
Step-4:Summation

1-2-3-41-3-2-41-2-4-32-1-3-4

25. Zero-state response is also known as ____________

Forced responseFree responseNatural responseNone of these