This set of Signals & Systems Assessment Questions and Answers focuses on “Periodic Signals – 2”.
1. Is the sum of discrete time periodic signals periodic?
a) No, they are not
b) Yes they are
c) Depends on the signal
d) Not periodic if their ratio is not rational
Explanation: The sum of discrete time periodic signals always periodic because the period ratios N/N are always rational.
For the continuous time, it depends on the ratio.
2. How can we generate a periodic signal from a periodic signal itself?
a) By extending a signal with duration T
b) Cannot be extended
c) By extending the periodic signal’s amplitude
d) By extending the sugar with duration 2π
Explanation: A periodic signal x(t) can be generated by a periodic extension of any segment of x of duration T( the period).
As a result, we can generate x(t) from any segment x(t) having a duration of one period by replacing this segment and reproduction thereof end to end ad infinitum on either side.
3. Is a non periodic signal same as aperiodic signal?
a) No, it is not same as an aperiodic signal
b) Yes it is the other name of aperiodic signal
c) It is a branch of aperiodic signal
d) Aperiodic signal is a branch of non periodic signal
Explanation: A signal which does not satisfy the condition:
x(t) = x(t+T) is called an aperiodic signal.
Non periodic is another name of an aperiodic signal. Hence it is exactly the same.
4. What is the period of the signal: 2cost/6?
Explanation: Comparing the above signal with the standard form Acos2πFt, where A is the amplitude and F is the frequency,
We get, 2πF=⅙
So, F= 1/12π
Hence, t= 12π.
5. When a continuous signal is a mixture of two continuous periodic signals, what is its periodicity?
a) LCM of the periods of the two signals, provide their ratio is unity
b) LCM of the periods of the two signals, provide their ratio is rational
c) HCF of the periods of the two signals, provide their ratio is rational
d) LCM of the periods of the two signals provide their ratio is real
Explanation: When a continuous signal is a mixture of two continuous periodic signals if their time periods are T1 and T2, and their ratio is rational number, then, the periodicity of the continuous time signal will be the LCM of T1 and T2.
6. Is the signal eαt periodic?
a) Not periodic
b) Yes periodic
c) Depends on the value of
d) Semi- periodic
Explanation: Using the definition of x(t),
x(t) = eαt
ejwt = ejwt+jwαT
For any value of α, if alpha is positive, it has a remaining term ejwαT
Hence it is not periodic.
7. What is a fundamental angular frequency?
a) The inverse of the fundamental time period
b) The inverse of fundamental frequency
c) Fundamental frequency in radians
d) Fundamental frequency in degree
Explanation: The inverse of the fundamental time period is called fundamental frequency. If it is F, then 2πF is called the fundamental angular frequency ie it is a fundamental frequency in radians.
8. What is the period of cos3t + sin14t?
Explanation: We know, T1= 2 π/3 and T2= 2 π/14
So, LCM gives the time period as π.
9. What is the periodicity of a discrete time signal?
Explanation: Using exponential function, we can show that
Which when rearranged gets us 2πm/w.
10. What is the condition of a periodicity of exponential signal eαt?
d) Depends on equation
Explanation: From, x(t+T)= eαt+T = eαt eαt. For any value of α, eαt ≠1 so x(t+T) ≠x(t). So only if α=1, the signal will be periodic.
Sanfoundry Global Education & Learning Series – Signals & Systems.
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