Digital Signal Processing Questions and Answers Part-14

1. What are the main characteristics of Anti aliasing filter?
a) Ensures that bandwidth of signal to be sampled is limited to frequency range
b) To limit the additive noise spectrum and other interference, which corrupts the signal
c) All of the mentioned
d) None of the mentioned

Answer: c
Explanation: The anti aliasing filter is an analog filter which has a twofold purpose. First, it ensures that the bandwidth of the signal to be sampled is limited to the desired frequency range. Using an anti aliasing filter is to limit the additive noise spectrum and other interference, which often corrupts the desired signal. Usually, additive noise is wide band and exceeds the bandwidth of the desired signal.

2. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.
a) True
b) False

Answer: a
Explanation: Analog signal processing operations cannot be done very precisely either, since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.

3. The term ‘bandwidth’ represents the quantitative measure of a signal.
a) True
b) False

Answer: a
Explanation: In addition to the relatively broad frequency domain classification of signals, it is often desirable to express quantitatively the range of frequencies over which the power or energy density spectrum is concentrated. This quantitative measure is called the ‘bandwidth’ of a signal.

4. If F1 and F2 are the lower and upper cutoff frequencies of a band pass signal, then what is the condition to be satisfied to call such a band pass signal as narrow band signal?
a) (F1-F2)>\(\frac{F_1+F_2}{2}\)(factor of 3 or less)
b) (F1-F2)⋙\(\frac{F_1+F_2}{2}\)(factor of 10 or more)
c) (F1-F2)<\(\frac{F_1+F_2}{2}\)(factor of 3 or less)
d) (F1-F2)⋘\(\frac{F_1+F_2}{2}\)(factor of 10 or more)

Answer: d
Explanation: If the difference in the cutoff frequencies is much less than the mean frequency, the such a band pass signal is known as narrow band signal.

5. What is the frequency range(in Hz) of Electroencephalogram(EEG)?
a) 10-40
b) 1000-2000
c) 0-100
d) None of the mentioned

Answer: c
Explanation: Electroencephalogram(EEG) signal has a frequency range of 0-100 Hz.

6. Which of the following electromagnetic signals has a frequency range of 30kHz-3MHz?
a) Radio broadcast
b) Shortwave radio signal
c) RADAR
d) Infrared signal

Answer: a
Explanation: Radio broadcast signal is an electromagnetic signal which has a frequency range of 30kHz-3MHz.

7. If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X(ω)=XR(ω)+jXI(ω), then what is the value of XR(ω)?
a) \(\sum_{n=0}^∞\)xR (n)cosωn-xI (n)sinωn
b) \(\sum_{n=0}^∞\)xR (n)cosωn+xI (n)sinωn
c) \(\sum_{n=-∞}^∞\)xR (n)cosωn+xI (n)sinωn
d) \(\sum_{n=-∞}^∞\)xR (n)cosωn-xI (n)sinωn

Answer: c
Explanation: We know that X(ω)=\(\sum_{n=-∞}^∞\) x(n)e-jωn
By substituting e-jω = cosω – jsinω in the above equation and separating the real and imaginary parts we get
XR(ω)=\(\sum_{n=-∞}^∞\)xR (n)cosωn+xI (n)sinωn

8. If x(n)=xR(n)+jxI(n) is a complex sequence whose Fourier transform is given as X(ω)=XR(ω)+jXI(ω), then what is the value of xI(n)?
a) \(\frac{1}{2π} \int_0^{2π}\)[XR(ω) sinωn+ XI(ω) cosωn] dω
b) \(\int_0^{2π}\)[XR(ω) sinωn+ XI(ω) cosωn] dω
c) \(\frac{1}{2π} \int_0^{2π}\)[XR(ω) sinωn – XI(ω) cosωn] dω
d) None of the mentioned

Answer: a
Explanation: We know that the inverse transform or the synthesis equation of a signal x(n) is given as
x(n)=\(\frac{1}{2π} \int_0^{2π}\) X(ω)ejωn
By substituting e = cosω + jsinω in the above equation and separating the real and imaginary parts we get
xI(n)=\(\frac{1}{2π} \int_0^{2π}\)[XR(ω) sinωn+ XI(ω) cosωn] dω

9. If x(n) is a real sequence, then what is the value of XI(ω)?
a) \(\sum_{n=-∞}^∞ x(n)sin⁡(ωn)\)
b) –\(\sum_{n=-∞}^∞ x(n)sin⁡(ωn)\)
c) \(\sum_{n=-∞}^∞ x(n)cos⁡(ωn)\)
d) –\(\sum_{n=-∞}^∞ x(n)cos⁡(ωn)\)

Answer: b
Explanation: If the signal x(n) is real, then xI(n)=0
We know that,
XI(ω)=\(\sum_{n=-∞}^∞ x_R (n)sinωn-x_I (n)cosωn\)
Now substitute xI(n)=0 in the above equation=>xR(n)=x(n)
=> XI(ω)=-\(\sum_{n=-∞}^∞ x(n)sin⁡(ωn)\).

10. Which of the following relations are true if x(n) is real?
a) X(ω)=X(-ω)
b) X(ω)=-X(-ω)
c) X*(ω)=X(ω)
d) X*(ω)=X(-ω)

Answer: d
Explanation: We know that, if x(n) is a real sequence
XR(ω)=\(\sum_{n=-∞}^∞\) x(n)cosωn=>XR(-ω)= XR(ω)
XI(ω)=-\(\sum_{n=-∞}^∞\) x(n)sin⁡(ωn)=>XI(-ω)=-XI(ω)
If we combine the above two equations, we get
X*(ω)=X(-ω)