FOURIER SERIES FOR PERIODIC SIGNAL

What is the trigonometric function that represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angled triangle?

• cosine

• tangent

• secant

• sine

Which trigonometric function represents the ratio of the length of the side adjacent to the angle to the length of the hypotenuse in a right-angled triangle?

• sine

• tangent

• cosine

• secant

What is a periodic signal?

• A signal that only occurs once

• A signal that repeats its pattern over time

• A signal that changes its pattern over time

• A signal that has no specific pattern

Give an example of a periodic signal in real life.

• Traffic light

• Seasonal changes

• Solar eclipse

• Heartbeat

What are Fourier series coefficients?

• Coefficients used to represent a signal as a sum of tangent and cotangent functions

• Coefficients used to represent a periodic signal as a sum of sine and cosine functions

• Coefficients used to represent a non-periodic signal

• Coefficients used to represent a signal as a sum of exponential functions

How are Fourier series coefficients calculated for a periodic signal?

• Using the formula: cn = (1/T) * ∫[T] f(t) * e^(-jnω0t) dt

• By taking the derivative of the signal

• By adding the signal to a random periodic function

• By multiplying the signal with a random constant

What is harmonic analysis in the context of Fourier series?

• Adding a random noise to a periodic signal

• Multiplying a periodic signal by a constant value

• Decomposing a periodic signal into a sum of sinusoidal functions with different frequencies and amplitudes

• Dividing a periodic signal by a constant value

Explain the concept of harmonics in the context of periodic signals.

• Harmonics are integer multiples of the fundamental frequency in a periodic signal.

• Harmonics are always lower in frequency than the fundamental frequency in a periodic signal.

• Harmonics have no relationship to the fundamental frequency in a periodic signal.

• Harmonics are non-integer multiples of the fundamental frequency in a periodic signal.

Why are sine and cosine functions considered orthogonal in the context of Fourier series?

• They have the same phase shift

• Their inner product over one period is zero.

• They have the same amplitude

• They have the same frequency

How does the orthogonality of sine and cosine functions help in analyzing periodic signals?

• By amplifying the signal

• By decomposing the signal into its constituent frequency components using Fourier series.

• By reducing the signal to its lowest frequency

• By increasing the signal's amplitude