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A signal is defined as any physical quantity that varies with:
→ Time
→ Space or
→ any other independent variable
Mathematically, a signal is a function of one or more independent variables.
Types of signals- Analog and Digital Signals
A signal processing system is defined as a device that performs an operation on a signal.
Types: → Analog Signal Processing System (e.g.- Voice Amplifier)
→ Digital Signal Processing System (e.g. - DSP chip)
The signals, which are defined at discrete times are known as discrete signals. Therefore, every independent
variable has a distinct value. Thus, they are
represented as sequences of numbers.
1. Unit Impulse Signal
2. Unit Step Signal
3. Unit Ramp Signal
4. Exponential Signal
Independent variable (Time)-
→ Time shifting
→ Time reversal (folding)
→ Time scaling
Dependent variable (Amplitude)-
→ Amplitude scaling
→ Signal addition and multiplication
Discrete time system is a device or algorithm that operates on a discrete time
signal
- Represented as y (n) = T [x (n)]
1. Static and Dynamic systems
2. Causal and Noncausal systems
3. Linear and Nonlinear systems
4. Time variant and Time invariant systems
5. Stable and unstable systems
6. FIR and IIR systems
i) A signal is said to be periodic ,if it exhibits periodicity.i.e., X(t +T)=x(t), for all values of t.
Periodic signal has the property that it is unchanged by a time shift of
T.A signal that does not satisfy the above periodicity property is called an
aperiodic signal.
ii) A discrete time signal is said to be even when, x[-n]=x[n]. The continuous time signal is said to be
even when, x(-t)= x(t) For example,Cos(n) is an even signal.
The discrete time signal is said to be odd when x[-n]= -x[n].
The continuous time signal is said to be odd when x(-t)= -x(t). Odd signals are also known as non
symmetrical signals.
Sine wave signal is an odd signal.
iii) An energy signal has zero average power, whereas a power signal has
infinite energy
A system is said to be causal, if the system's response should depend on present and past inputs only and not on the future inputs. That is, causal systems are physically realizable systems. Non causal systems response depends on the future input values. Hence, non causal systems are physically unrealizable systems.
Aliasing refers to an effect due to which different signals become indistinguishable. It also refers to
distortion in the reconstructed signal when it is reconstructed from the original continuous signal.
To avoid aliasing we can simply filter out the high frequency components of the signal by using an
antialiasing filter like optical antialiasing filter.
Convolution is the technique of adding two signals in the time domain. This is achieved by changing the domain of signals from time domain to frequency domain using Fast Fourier Transform (FFT).
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