Power Spectral Density Calculator
Find the power spectral density of white noise or a discrete tone, in V squared per Hz, V per root Hz, and dB.
📊 What is Power Spectral Density?
Power spectral density (PSD) describes how a signal's power is distributed across frequency, measured in power per unit bandwidth (volts squared per Hz for a voltage signal). Rather than answering "how much power does this signal have," PSD answers "how much power does this signal have in each small slice of frequency," which is exactly the information needed to compare noise sources, design filters, and predict how much noise will land in any given measurement bandwidth.
Analog and mixed-signal IC designers spend enormous effort minimizing amplifier and ADC input-referred noise density, specified directly in nV per root-Hz on datasheets. RF engineers use PSD to characterize interference and thermal noise floors across a receiver's bandwidth. Audio engineers use PSD estimates (via the periodogram or Welch's method) to visualize a recording's spectral content and identify hum, hiss, or resonances that a simple time-domain waveform view would hide.
A common misconception is that PSD and total power are interchangeable. They are not: PSD is power density (per Hz), while total power is what you get after integrating PSD across a specific bandwidth. A noise source with a very low PSD can still carry substantial total power if measured over a wide enough bandwidth, and a tone concentrated in a single bin can show an enormous PSD spike despite carrying only modest total power.
This calculator handles the two most common textbook cases: flat white noise spread evenly across the Nyquist bandwidth, and a discrete tone whose power lands in a single FFT bin, computing PSD and its square root, amplitude spectral density (ASD), for each.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — ADC Input-Referred Noise Floor
White noise, Vn = 1 mV RMS, fs = 48,000 Hz
Example 2 — Single Tone in a 1,024-Point FFT
Tone, Vs = 1 V RMS, fs = 44,100 Hz, N = 1,024
Example 3 — Larger Tone in a Smaller FFT
Tone, Vs = 2 V RMS, fs = 8,000 Hz, N = 512
❓ Frequently Asked Questions
🔗 Related Calculators
What is power spectral density (PSD)?
Power spectral density describes how a signal's power is distributed across frequency, expressed as power per unit of bandwidth (V squared per Hz for a voltage signal). Integrating PSD over a frequency range gives the total signal power contained in that range.
How do you calculate PSD from noise RMS voltage?
For white noise with a flat spectrum, PSD = Vn^2 / (fs/2), where Vn is the total measured RMS noise voltage and fs/2 is the Nyquist bandwidth the noise power spreads across. A higher sampling rate spreads the same total noise power over more bandwidth, lowering the apparent PSD.
How do you calculate PSD for a single tone?
A discrete tone's power concentrates in one FFT bin of width delta-f = fs/N, so its PSD estimate is PSD = Vs^2 / delta-f, where Vs is the tone's RMS amplitude. This is the standard periodogram estimate for a pure sinusoid captured in an N-point FFT.
What is amplitude spectral density (ASD)?
Amplitude spectral density is the square root of PSD, expressed in V per root-Hz. It is the unit most commonly printed on op-amp and ADC noise datasheets (for example, a low-noise amplifier might be specified at 4 nV per root-Hz), since it scales linearly with voltage rather than with voltage squared.
Why does the PSD unit include Hz in the denominator?
PSD measures power density, not total power, because a signal's power is spread across a continuous range of frequencies rather than concentrated at one point. Dividing by bandwidth (Hz) normalizes the measurement so it can be compared and integrated regardless of how wide a frequency range was actually measured.
Why does a bigger FFT size increase a tone's apparent PSD?
A larger FFT narrows each frequency bin (delta-f = fs/N gets smaller as N grows), concentrating the same fixed tone power into a narrower bandwidth. Since PSD = power / delta-f, a smaller delta-f with the same numerator produces a larger PSD value, even though the tone's actual power has not changed at all.
What is the difference between PSD and total signal power?
Total signal power is a single number (the mean-square value of the signal). PSD is that same power broken down by frequency, power per Hz, so that summing (integrating) PSD across all frequencies recovers the total power. A flat, wideband noise source has low PSD per Hz but can still carry a lot of total power if it spans a wide bandwidth.
How do dB PSD units work?
PSD in dB is typically expressed as 10*log10(PSD / 1 V^2/Hz), often written 'dB re 1 V^2/Hz'. ASD in dB uses 20*log10(ASD / 1 V/rtHz) instead, since ASD is a voltage-like (amplitude) quantity rather than a power-like quantity, the same factor-of-2 distinction used for regular dB voltage vs dB power.
Can this calculator estimate PSD from raw measured samples?
No, this calculator computes the idealized closed-form PSD for two textbook cases (flat white noise and a pure single tone) from summary values (RMS voltage, sampling rate, FFT size) you already know, rather than running an actual periodogram or Welch's method on raw sample data.
Why is PSD important for ADC and sensor noise specifications?
PSD lets engineers compare noise performance independent of measurement bandwidth, since total measured noise depends on how wide a band you happen to measure over. Specifying a fixed nV/root-Hz or pA/root-Hz figure lets a designer predict the actual noise in any application bandwidth by multiplying by the square root of that bandwidth.