Fourier Series and Transforms

What is the primary purpose of a Fourier Series?

• To approximate a function with a polynomial

• To represent a function as a sum of trigonometric terms

• To solve linear equations

• To analyze data trends

Which type of functions can be represented using Fourier Series?

• Continuous functions only

• Periodic functions only

• Non-periodic functions only

• All types of functions

Fourier Series is primarily used to analyze which type of signals?

• Random signals

• Periodic signals

• Discrete signals

• Quantum signals

The Fourier Series representation relies on which mathematical principle?

• Superposition

• Differentiation

• Integration

• Extrapolation

Which of the following is NOT an application of Fourier Series?

• Image processing

• Vibration analysis

• Encryption

• Heat conduction

In a Fourier Series, which components describe the overall behavior of a periodic signal?

• Higher harmonics

• Fundamental frequency

• Non-periodic components

• Noise

Which term describes the process of breaking a periodic function into its components?

• Synthesis

• Decomposition

• Multiplication

• Transformation

What characteristic of a periodic function ensures a unique Fourier Series?

• Continuity

• Periodicity

• Differentiability

• Linearity

In signal processing, Fourier Series helps identify:

• Noise patterns

• Frequency components

• Non-linearities

• Statistical distributions

What happens if a function is not periodic but is represented using Fourier Series?

• The representation fails

• The function is assumed to repeat

• The series converges to infinity

• The output is always zero