Singularity functions consist of:

• A. Sine, cosine, and exponential.
• B. Step, ramp, and delta functions.
• C. Heaviside function only.
• D. Only delta functions.

Answer: (B)

Singularity functions are the basic time-domain signals that model abrupt changes and piecewise behavior. They include the unit impulse, the unit step, and the unit ramp. The delta (impulse) captures an instantaneous, all-at-once input with area one, representing a sudden burst at a single moment. The step function introduces a sudden change from one level to another at t = 0, creating a discontinuity. The ramp starts at zero and grows linearly for t > 0, providing a smoothly increasing input whose derivative is the step function. These relationships—derivative of the step is the impulse, and the derivative of the ramp is the step—show how these functions are linked and why they’re treated as a fundamental set.

Sine, cosine, and exponential functions are smooth and do not embody the kind of instantaneous or piecewise behavior that singularity functions are intended to model. A set containing only the step would miss the impulse and the ramp, while a set with only the delta would miss the step and ramp.