1. To implement the linear time invariant recursive system described by the difference equation y(n)=[latex]\displaystyle\sum_{k=1}^{N} a_k y(n-k)+\displaystyle\sum_{k=0}^{M}b_kx(n-k)[/latex]
in Direct form-I, how many number of delay elements and multipliers are required respectively?
a) M+N+1,M+N
b) M+N-1,M+N
c) M+N,M+N+1
d) None of the mentioned
Answer: Option (c)
Explanation:
Explanation: From the given equation, there are M+N delays, so it requires M+N number of delay elements and it has to perform M+N+1 multiplications, so it require that many number of multipliers.
2. The system represented by the following direct form structure is:
a) General second order system
b) Purely recursive system
c) Partial recursive system
d) FIR system
Answer: Option (d)
Explanation:
The output of the system according to the direct form given is
y(n)= b0x(n)+b1x(n-1)+b2x(n-2)
Since the output of the system is purely dependent on the present and past values of the input, the system is called as FIR system.
3. Which of the following should be done in order to convert a continuous-time signal to a discrete-time signal?
a) Sampling
b) Differentiating
c) Integrating
d) None of the mentioned
Answer: Option (a)
Explanation:
The process of converting a continuous-time signal into a discrete-time signal by taking samples of continuous time signal at discrete time instants is known as ‘sampling’.
4. The process of converting discrete-time continuous valued signal into discrete-time discrete valued(digital) signal is known as:
a) Sampling
b) Quantization
c) Coding
d) None of the mentioned
Answer: Option (b)
Explanation:
In this process, the value of each signal sample is represented by a value selected from a finite set of possible values. Hence this process is known as ‘quantization’
5. The difference between the unquantized x(n) and quantized xq(n) is known as:
a) Quantization coefficient
b) Quantization ratio
c) Quantization factor
d) Quantization error
Answer: Option (d)
Explanation:
Quantization error is the difference in the signal obtained after sampling i.e., x(n) and the signal obtained after quantization i.e., xq(n) at any instant of time.
6. Which bit coder is required to code a signal with 16 levels?
a) 8 bit
b) 4 bit
c) 2 bit
d) 1 bit
Answer: Option (b)
Explanation:
To code a signal with L number of levels, we require a coder with (log L/log 2) number of bits. So, log16/log2=4 bit coder is required.
7. What is the spectrum that is obtained when we plot |ck| as a function of frequency?
a) Magnitude voltage spectrum
b) Phase spectrum
c) Power spectrum
d) None of the mentioned
Answer: Option (a)
Explanation:
We know that, Fourier series coefficients are complex valued, so we can represent ck in the following way.
ck=|ck|[latex]e^\text{jθk}[/latex]
When we plot |ck| as a function of frequency, the spectrum thus obtained is known as Magnitude voltage spectrum.
8. Which of the following is used in the realization of a system?
a) Delay elements
b) Multipliers
c) Adders
d) All of the mentioned
Answer: Option (d)
Explanation:
From each set of equations, we can construct a block diagram consisting of an interconnection of delay elements, multipliers and adders.
9. Computational complexity refers to the number of:
a) Additions
b) Arithmetic operations
c) Multiplications
d) None of the mentioned
Answer: Option (d)
Explanation:
Computational complexity is one of the factor which is used in the implementation of the system. It refers to the numbers of Arithmetic operations (Additions, multiplications and divisions).
10. Which of the following refers the number of memory locations required to store the system parameters, past inputs, past outputs and any intermediate computed values?
a) Computational complexity
b) Finite world length effect
c) Memory requirements
d) None of the mentioned
Answer: Option (c)
Explanation:
Memory requirements refers the number of memory locations required to store the system parameters, past inputs, past outputs and any intermediate computed values.