The covariance function of a band limited white noise is :

The correct answer is A Dirac delta function.

Key Points

• A Dirac delta function is a mathematical function that peaks at a single point and is zero everywhere else.
• In the context of band-limited white noise, the covariance function describes how the signal values at different times are related to each other.
• A Dirac delta function indicates that the signal values are uncorrelated at different times, meaning that there is no predictable pattern or relationship between them.
• This is characteristic of white noise, which has a flat power spectral density, implying that it contains all frequency components with equal power.

Additional Information

• The Dirac delta function is often used in signal processing and systems theory to represent an idealized impulse.
• White noise is a random signal with a constant power spectral density, used in various fields such as electronics, acoustics, and finance.
• The concept of white noise is important in the study of stochastic processes and time series analysis.
• Band-limited white noise refers to white noise that has been filtered to include only a specific range of frequencies, making it more practical for real-world applications.