FFT Average

FFT Averaging combines multiple spectral blocks to reduce the random variability (variance) of spectral estimates. Since a single FFT of a random signal has a normalized random error of 100%, averaging is essential for obtaining reliable, repeatable spectral measurements.

Theory

For a stationary random signal, the normalized random error ε of the averaged power spectrum decreases with the number of independent averages n_d:

ε = 1 / √n_d

With 100 averages, the random error is 10%. With 400 averages, it is 5%. This fundamental relationship governs the trade-off between measurement duration and spectral reliability.

Averaging Modes

Linear (Stable) Average

Each spectrum contributes equally to the final result. After n blocks, the averaged spectrum is:

S_avg(f) = (1/n) ∑_k=1ⁿ S_k(f)

Linear averaging is the standard mode for stationary signals. It produces the minimum-variance estimate and is required for valid coherence and transfer function computations. The measurement stops after the specified number of averages is reached.

Exponential (Running) Average

Recent spectra are weighted more heavily than older ones, providing a continuously updated estimate that tracks slow spectral changes:

S_avg^(k)(f) = α · S_k(f) + (1 − α) · S_avg^(k−1)(f)

The weighting factor α = 1/n_eff controls the effective memory length. Exponential averaging runs continuously and never stops, making it suitable for real-time monitoring of slowly varying sources.

Peak Hold

Retains the maximum value at each frequency bin. See FFT Peak Hold for details.

Overlap Processing

To increase the averaging rate without extending the measurement time, successive FFT blocks can be overlapped. The overlap percentage determines how many new samples are introduced in each block:

Overlap	New Samples per Block	Effective Averaging Rate	Recommended Window
0%	N	1×	Rectangular (no window)
50%	N/2	~1.9× (Hanning)	Hanning
66.7%	N/3	~2.6× (Hanning)	Hanning
75%	N/4	~3.4× (Hanning)	Flat Top, Kaiser

Overlapped blocks are not statistically independent. The effective number of independent averages n_d is always less than the total number of blocks processed. The improvement factor depends on the window function. For a Hanning window at 50% overlap, approximately 1.89 independent averages are obtained per 2 blocks.

Parameters

Parameter	Options	Description
Averaging Mode	Linear, Exponential, Peak Hold	Determines how successive spectra are combined.
Number of Averages	1 – unlimited	Target count for linear averaging; effective time constant for exponential.
Overlap	0% – 95%	Percentage of overlap between successive FFT blocks.
Spectrum Size	256 – 65536	FFT block size. Larger blocks give finer frequency resolution.
Window	Hanning, Hamming, Flat Top, etc.	Window function. Must be matched with an appropriate overlap.
Trigger	Free Run, Manual, External	How block acquisition is initiated.

Choosing the Number of Averages

The required number of averages depends on the desired confidence level and the signal characteristics:

Averages (n_d)	Random Error (ε)	Typical Application
10	32%	Quick survey, rough estimate
50	14%	General NVH testing
100	10%	Standard quality requirement
400	5%	Precision measurement, regulatory compliance
1000+	< 3%	Research, reference spectra

Practical Tips

For stationary signals, always use linear averaging with a defined number of averages. Exponential averaging introduces bias for non-stationary signals and prevents precise error quantification.
Match the overlap to your window function: 50% for Hanning, 66.7% for Hanning with maximum efficiency, 75% for Flat Top.
Monitor the averaged spectrum as it builds up. If the shape changes significantly with additional averages, the signal may not be stationary, and the averaging assumptions are violated.
For triggered measurements (e.g., impact testing), use zero overlap and synchronize each block to the trigger event to ensure each average captures an independent response.
When comparing spectra across test conditions, use the same number of averages to ensure equal statistical reliability.

Insufficient averaging is one of the most common sources of error in spectral analysis. A spectrum with only 5 averages has a random error of 45%, meaning individual spectral peaks may differ by up to 3–4 dB between repeated measurements of the same signal.