Signals and Systems
Signals
Practice questions from Signals.
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IncorrectConsider a continuous-time signal
where is the continuous-time unit step function. Let be the continuous time unit impulse function. The value of is
Hence, option (a) is correct.
A continuous time periodic signal x(t) is
If is the period of , then __________ (round off to the nearest integer).
This expression represents Power contained in the signal as per Parseval's Energy Theorem Since, the signal is in terms of a Fourier Series all the signals are orthogonal and hence their powers can be directly added.
The input and the output of a system are related as
The output of the system to two inputs are
Linearity:-
hence linear
Time-variance
For
Let
to
to
Now,
Consider the discrete-time systems and defined as follows:
Which one of the following statements is true?
and are BIBO stable.
and are not BIBO stable.
is BIBO stable but is not BIBO stable.
is not BIBO stable but is BIBO stable.
For impulse response of this system we have to consider the input as Impulse Signal.
Since the impulse response is not absolutely summable the system is Unstable.
Assume x[n] is bounded that is
For
The above signal is bounded for all values of n and hence for a bounded input we are getting bounded output so the system is BIBO Stable.
If the energy of a continuous-time signal is and the energy of the signal is , then is ________ (rounded off to 1 decimal place).
Energy of a signal is not affected by time shifting
Energy of a signal changes due to time scaling
After amplitude scaling the energy becomes
The period of the discrete-time signal described by the equation below is __________ (Round off to the nearest integer).
Period of
Period of
= rational ∴ overall signal is periodic
N = LCM (N1, N2) = LCM (16, 6) = 48