**Even signal** is a signal which satisfies the relation ** f(t) = f(−t). **Even signal is symmetric about the

*y-axis*. Example: cost.

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f(t) = cost

f(−t) = cos(−t) = cost

Hence, f(t) = f(−t)

* Odd signal is a signal which satisfies the relation f(t) = −f(−t).* Odd signal is symmetric about the

*origin*. Example: sinωt.

f(t) = sint

f(−t) = sin(−t) = −sint

Hence, f(t) = −f(−t)

## Properties

The time derivative of even signal gives an odd signal and the time derivative of even signal gives an even signal.

3. The even part of a signal f(t) is given as

4. The odd part of a signal f(t) is given as

Therefore, f(t) = f_{e}(t) + f_{o}(t)

*5. f(t) + f(−t) → It always represents an even signal.*

**Proof:** Let x(t) = f(t) + f(−t)

x(−t) = f(−t) + f(t)

Therefore, x(t) = x(−t)

Hence x(t) is an even signal.

*6. f(t) − f(−t) → It always represents an odd signal.*

**Proof:** Let x(t) = f(t) − f(−t)

x(−t) = f(−t) − f(t)

x(−t) = −[−f(−t) + f(t)] = −x(−t)

Therefore, x(t) = −x(−t)

Hence x(t) is an odd signal.