17 Questions
What is a signal in the context of this text?
A physical quantity or variable
How is a signal typically denoted in terms of time representation?
Both Continuous-Time (CT) and Discrete-Time (DT)
What characterizes a continuous-time signal?
It is a continuous variable
How can discrete-time signals be obtained?
By sampling continuous-time signals
What defines an analog signal?
It can take on any value in a continuous interval
How is a digital signal characterized?
It represents discrete values only
What is the proper order to apply time shifting and time scaling to a signal x(t) of the form x(at + b)?
Time shifting first, then time scaling
If x(t) is multiplied by A, what operation is being performed on the signal?
Amplitude scaling
What does y(t) = x(at – b) represent in terms of signal operations?
Time-shifted signal
Which operation results in y(t) = x1(t) + x2(t)?
Addition of signals
What happens if time scaling is applied to x(t) to get y(t)?
y(t) is a scaled version of x(t)
Which type of signals have values that are completely specified?
Deterministic signals
What property defines even signals?
$x(-t) = x(t)$
What characteristic defines an odd signal?
$x(t) = -x(-t)$
When is a continuous-time signal periodic?
$x(t + T) = x(t)$ for a positive non zero $T$
Which type of signal can be expressed as the sum of an even signal and an odd signal?
Any signal
What defines a CT complex exponential signal?
$e^{(at)}$ where 'C' and 'a' are complex numbers
Study Notes
Signals and Their Characteristics
- A signal is a function representing a physical quantity or variable and typically contains information about the behavior of a phenomenon.
Continuous-Time (CT) and Discrete-Time (DT) Signals
- A signal is continuous-time if it is a continuous variable.
- A signal is discrete-time if it is defined at discrete times.
- A continuous-time signal can take on any value in a continuous interval, making it an analog signal.
- A discrete-time signal can take on only a finite number of distinct values, making it a digital signal.
Real and Complex Signals
- Signals can be real or complex.
- A general complex signal x(t) is a function of the form x(t) = s(t) + jv(t), where s(t) and v(t) are real signals.
Deterministic and Random Signals
- Deterministic signals are those signals whose values are completely specified.
- Random signals take on random values at any given time.
Even and Odd Signals
- Even signals: x(-t) = x(t) or x[-n] = x[n].
- Odd signals: x(-t) = -x(t) or x[-n] = -x[n].
- Any signal can be expressed as the sum of an even signal and an odd signal.
Periodic and Non-Periodic Signals
- A CT signal x(t) is said to be periodic with period ‘T’ if x(t + T) = x(t) for all t.
- A DT signal x[n] is periodic with period N if x[n + N] = x[n].
- Any DT or CT signal which is not periodic is non-periodic or aperiodic.
Basic Continuous-Time Signals
- The CT complex exponential signal is of the form x(t) = Ce^(at).
- If C and a are real, then x(t) is a real exponential of the form x(t) = C*e^(at).
- If a > 0, then the signal is linearly compressed.
Time-Shifting and Time-Scaling Operations
- The time-shifting operation is performed first on x(t) resulting in an intermediate signal.
- Then, time scaling (or reversal) is performed on the intermediate signal resulting in the desired output.
Explore the concept of signals in the context of physical quantities or variables. Learn about continuous-time and discrete-time signals, how they are represented, and their characteristics such as voltage across a capacitor or current flowing in a resistor.
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