For an ideal white-noise process used in communications engineering, how does the power spectral density (PSD) vary with frequency?
Correct Answer: It is constant with frequency (flat spectrum)
Introduction / Context:White noise is a fundamental model in receiver analysis, representing thermal noise and other wideband disturbances. Understanding its power spectral density (PSD) is essential for calculating noise power in a given bandwidth and predicting signal-to-noise ratios.
Given Data / Assumptions:
- White noise is an idealization with uniform PSD across frequency.
- Real systems are bandlimited by front-end filters and components.
- Thermal noise approximates white within limited bandwidths.
Concept / Approach:
By definition, white noise has a flat PSD: Sn(f) = N0/2 (single-sided conventions vary). Total noise power is PSD multiplied by the receiver bandwidth. While 1/f noise (flicker) and device corner frequencies exist, these are separate phenomena and not part of the ideal white-noise definition.
Step-by-Step Solution:
Recall the definition of white noise: constant spectral density.Relate to noise power: Pn = (PSD) * B.Select “constant with frequency”.Verification / Alternative check:
Receiver noise figure measurements assume a flat thermal-noise density kT over the measurement bandwidth, consistent with white-noise modeling.
Why Other Options Are Wrong:
- Increasing/decreasing with frequency: describes colored noise, not white.
- 1/f: flicker noise, significant at very low frequencies but not white.
- Bandlimited to IF only: limitation of the receiver front end, not of white noise itself.
Common Pitfalls:
Confusing white noise (flat PSD) with pink or flicker noise that has frequency-dependent spectra.
Final Answer:
It is constant with frequency (flat spectrum)