📘 Signals & Systems – Module 1: Basic Signals
Signals are mathematical representations of physical quantities that vary with time. Understanding signal classification is the foundation of Signals & Systems.
🔹 1. Continuous Time Signal
A signal defined for every value of time.
Example: x(t) = sin(t), e-t, u(t)
Graph exists for all real values of t.🔹 2. Discrete Time Signal
Defined only at discrete instants of time.
Example: x[n] = (0.5)n, δ[n]
Only integer values of n.🔹 3. Basic Standard Signals
Unit Step Signal
u(t) = 1 for t ≥ 0 u(t) = 0 for t < 0
Unit Impulse Signal
∫ δ(t) dt = 1
Ramp Signal
r(t) = t u(t)
🔹 4. Even and Odd Signals
Even Signal
x(t) = x(-t)
Example: cos(t)Odd Signal
x(t) = -x(-t)
Example: sin(t)🔹 5. Energy and Power Signals
Energy Signal
E = ∫ |x(t)|² dt (Finite)
Power = 0Power Signal
P = lim (T→∞) (1/2T) ∫ |x(t)|² dt (Finite)
Energy = Infinite🔹 6. Periodic and Aperiodic Signals
Periodic signal:
x(t) = x(t + T)
Example: sin(t) Aperiodic: No repetition.🔹 7. Worked Example 1
Check if x(t) = e-tu(t) is energy or power signal.
Compute:
E = ∫₀^∞ e-2t dt = 1/2
Finite → Energy signal.🔹 8. Worked Example 2
Check if x(t) = sin(t) is energy or power signal.
Energy = Infinite Power = 1/2 Therefore → Power signal.🎯 GATE Important Points
- Energy vs Power frequently asked
- Even/Odd decomposition important
- Impulse properties used in convolution
- Unit step and delta fundamental
Strong Basics = Easy Convolution & Fourier
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