Spectrum Density Calculator

Power Spectral Density Formula:

\[ PSD = \lim_{T \to \infty} \frac{1}{T} E[|X(f)|^2] \]

Power Spectral Density (PSD):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Power Spectral Density?

Power Spectral Density (PSD) describes how the power of a signal or time series is distributed with frequency. It represents the power present in the signal as a function of frequency, per unit frequency.

2. How Does the Calculator Work?

The calculator uses the PSD formula:

\[ PSD = \lim_{T \to \infty} \frac{1}{T} E[|X(f)|^2] \]

Where:

\( T \) — Time interval (seconds)
\( X(f) \) — Amplitude at frequency f
\( E[·] \) — Expected value operator

Explanation: The equation calculates the power distribution across different frequencies in a signal, providing insight into the signal's frequency characteristics.

3. Importance of PSD Calculation

Details: PSD is crucial for signal processing, communications engineering, vibration analysis, and many other fields where frequency domain analysis is required.

4. Using the Calculator

Tips: Enter time interval in seconds, frequency in Hz, and amplitude value. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What units does PSD have?
A: PSD has units of power per unit frequency (e.g., watts/Hz, volts²/Hz, etc.)

Q2: How is PSD different from power spectrum?
A: PSD is the limit of the power spectrum as the time interval approaches infinity, providing a density function.

Q3: What are typical applications of PSD?
A: Signal analysis, noise characterization, vibration analysis, communications systems design, and spectral estimation.

Q4: How does windowing affect PSD calculation?
A: Windowing reduces spectral leakage but may introduce some bias in the estimation. Different window functions have different trade-offs.

Q5: Can PSD be calculated for non-stationary signals?
A: For non-stationary signals, time-frequency analysis methods like spectrograms or wavelet transforms are more appropriate.