Signals and Systems

Exam 2 Terms

Cross-coorelation

Correlating one signal with another at various time delays
Examines when two signals are most alike

Gibbs artifact

The oscillations in the frequency representation that occur when a continuous finite sinusoidal series is used to represent a discontinuity

Fourier transform

Mathematical process that represents any periodic signal with a sum of harmonic sinusoids represented in a time to frequency domain

Frequency spectrum

Range of frequencies contained by a signal

Auto-correlation

Cross-correlating a signal with itself at various time delays and examines how a signal changes over time

Fourier synthesis equation

Original function as a linear equation of simple harmonic motions.
Goes from frequency to time domain.

Fourier analysis equation

Creates a family of harmonically related functions
Frequency decomposition and creates sine waves (time to frequency)

When do you use fourier transform? What is the process?

The fourier transform is in the frequency domain. It takes one signal and it turns it into sine and cosine waves.

When do you use correlation? What is the process?

Correlation is in the time domain. It compares 2 signals to see how they are similar.

How are both techniques similar?

Both of them multiply and take the mean.
Am and Bm coefficients in the Fourier use correlation within their frequencies