Technical Note · Signal Processing Fundamentals

Choosing a Window in Panther and Lynx

Every window Panther and Lynx offer, in the vibration control applications and in the Analyzer: what each one does to a spectrum, which applications set it for you and which let you choose, how the two scalings change what you read, and how to pick the right one for the measurement in front of you.

Key takeaways

Panther and Lynx run the same application software, so they offer the same windows: None, Hann, Hamming, Blackman, Blackman-Harris, Calibration (a flat top), Force/Impact and Correlation, each with Broadband (Power) or Narrowband (Amplitude) scaling.
The control applications choose for you: Hann with broadband scaling for every random control spectrum (Random, MIMO Random, Sine-on-Random, Random-on-Random) and no window on a shock pulse or on Random's pseudo-random system identification. You choose in the Analyzer, the Modal application and Road Simulation.
A new Analyzer test starts with the window set to None. Before measuring a continuous signal, select one: Hann for random and general work, Calibration for sine amplitudes, Blackman-Harris for small components next to large ones.
The scaling decides what reads correctly: Broadband for the PSD and RMS of random signals, Narrowband for the amplitude of discrete tones. The wrong choice is off by the window's noise bandwidth: 1.76 dB with Hann, 5.35 dB with Calibration.
Events that start and end inside the frame need no window: shock pulses, shock response spectra (the Analyzer turns windowing off for SRS) and, with Force/Impact, hammer impacts.
Force/Impact adds damping. Its exponential makes a ringing response die out within the frame, but adds D/(2πfT) of damping to every mode: 2.0% at 40 Hz with the default Decay of 5 and a 1-second frame.

The windows Panther and Lynx offer

Panther and Lynx run the same applications on the host computer, and every application builds its windows with the same code. The table lists them as they appear in the software. Our FFT Fundamentals note explains why windows are needed at all: the FFT assumes each frame repeats forever, and a signal that does not fit the frame exactly leaks into neighboring lines. This note is about choosing among the windows Panther and Lynx actually provide.

Table 1. The windows, as named in the software
Name	What it is	Use it for
None	Rectangular (uniform): every sample weighted equally	Transients that start and end inside the frame; signals that repeat exactly within the frame
Hann	Raised cosine, 0.5 − 0.5 cos; falls to zero at both ends	Random vibration and general analysis; the control applications' choice
Hamming	0.54 − 0.46 cos; stops short of zero at the ends	Closely spaced components of similar level, where the nearest side lobes matter more than distant leakage
Blackman	Three-term cosine sum (0.42, 0.50, 0.08)	More leakage suppression than Hann at a modest cost in peak width
Blackman-Harris	Four-term minimum-side-lobe cosine sum (0.35875, 0.48829, 0.14128, 0.01168); side lobes 92 dB down	Small components next to large ones; measurements that use the full dynamic range
Calibration	Four-term flat top (0.2395, 0.4581, 0.2585, 0.0439); amplitude-accurate to 0.01 dB anywhere between lines	The amplitude of tones: sensor calibration, sine levels, harmonics
Force/Impact	An exponential decay on every channel, plus a force window on the force (reference) channel; set by Decay and Width	Impact hammer testing
Correlation	The first half of the frame weighted √2, the second half set to zero	Auto- and cross-correlation functions

Names to watch. Calibration is a flat top window; the event log and some lists call it Flat Top. Blackman and Blackman-Harris are two different windows, 58 dB and 92 dB side lobes. In Road Simulation, whose list reads None, Hann, Blackman, Flat Top, the entry labeled Blackman is the four-term Blackman-Harris. Hann is the window older documents, including our FFT Fundamentals note, call Hanning. None means rectangular.

Which applications choose for you

Where a measurement drives a control loop, the application sets the window and its scaling, so the loop always compares like with like. Where a measurement is the result you report, you choose.

Table 2. The window in each application
Application	Window	Can you change it?	Scaling
Random (single-axis and MIMO)	Hann	No (overlap is selectable)	Broadband
Sine-on-Random, Random-on-Random	Hann on the random. Tones are measured by a time-domain fit with its own built-in weighting	No	Broadband
Sine	The tone is measured with tracking filters (see Tracking Filters). Where an order or tone is taken from an FFT, Blackman-Harris	No	Amplitude
Shock	None on the pulse	No	–
System identification: Random	None. The drive is pseudo-random noise, which repeats exactly every frame	No	–
System identification: Sine, Shock, Sine-on-Random, Random-on-Random, Road Simulation	Hann	No	Broadband
Road Simulation	None (default), Hann, Blackman (= Blackman-Harris), Flat Top	Yes	Broadband (default) or Narrowband
Analyzer and Modal	All eight in Table 1; None by default	Yes, with Decay and Width for Force/Impact	Broadband (default) or Narrowband

Random control compares a measured PSD with a reference PSD, line by line, and Hann with broadband scaling is the right pairing for that: low enough leakage to follow a notched or steep profile, a narrow enough peak to resolve resonances, and power-correct levels. A shock pulse is different: it sits inside the frame, and tapering it would weight the pulse by where it happened to land, so Shock analyzes it unwindowed. Random's system identification shows the other case for None: its pseudo-random drive repeats exactly every frame, so every component falls on a line and nothing leaks.

What a window does to a tone

A window trades three things against each other: how far leakage spreads (the side lobes), how wide a single tone appears (the main lobe), and how much a tone's reading drops when it falls between two lines (the scalloping error). Figures 1 to 3 show the six tapering choices, computed from the definitions in the software.

Figure 1. The six tapering choices as weights across one frame. None weights every sample equally. Hann, Blackman and Blackman-Harris taper to zero at the ends, progressively harder; Hamming stops at 0.08; Calibration (the flat top) dips slightly below zero near each end, which is what makes its frequency response flat.

Figure 2. What each window turns a single tone into. None has the narrowest peak but side lobes only 13 dB down. Hann's first side lobe is 31 dB down and falls quickly; Hamming starts lower (−43 dB) but falls slowly. Blackman-Harris holds every side lobe below −92 dB, and Calibration below −70 dB, both with a peak about four lines wide.

Figure 3. How low a tone reads depending on where it falls between two lines, with narrowband scaling. Unwindowed, a tone halfway between lines reads 3.92 dB low; Hann 1.42 dB, Blackman-Harris 0.82 dB. Calibration reads within 0.01 dB wherever the tone falls, which is why it is the window for amplitudes.

Table 3. Window characteristics, computed from the definitions in the software
Window	Highest side lobe	Side-lobe fall-off	Peak width (−3 dB)	Noise bandwidth (ENBW)	Worst tone error	Coherent gain
None	−13.3 dB	6 dB/octave	0.89 lines	1.00 lines	−3.92 dB	1.00
Hann	−31.5 dB	18 dB/octave	1.45 lines	1.50 lines	−1.42 dB	0.50
Hamming	−42.7 dB	6 dB/octave	1.30 lines	1.36 lines	−1.75 dB	0.54
Blackman	−58.1 dB	18 dB/octave	1.65 lines	1.73 lines	−1.10 dB	0.42
Blackman-Harris	−92.0 dB	6 dB/octave	1.91 lines	2.00 lines	−0.82 dB	0.36
Calibration (flat top)	−70.2 dB	6 dB/octave	3.39 lines	3.43 lines	+0.01 dB	0.24

Flat top windows differ. Panther's Calibration window is a four-term flat top with 70 dB side lobes and a noise bandwidth of 3.43 lines. The five-term flat top in our FFT Fundamentals note reaches 93 dB, at the cost of a wider peak. Both read a tone's amplitude to about 0.01 dB.

Broadband or Narrowband: the scaling

Tapering lowers the signal the FFT sees, so every window is scaled to put the level back. There are two ways to do that, and they cannot both be right at once.

Broadband (Power) scales the window so its mean square is 1. The power of a random signal, and so its PSD and RMS, read correctly. A tone reads low, by the window's noise bandwidth.
Narrowband (Amplitude) scales the window so its average is 1. A tone on a line reads its true amplitude. The PSD of a random signal reads high, by the same amount.

Figure 4. One Hann-windowed measurement of a 1 g peak sine in 0.001 g²/Hz of noise, read both ways (400 averages, 2.5 Hz lines). (a) Narrowband scaling reads the sine at its true 0.707 g rms; broadband scaling reads 0.577 g rms, 1.76 dB low. (b) Broadband scaling reads the noise at its true 0.001 g²/Hz; narrowband scaling reads 0.0015 g²/Hz, 1.76 dB high.

Table 4. Scale factors in the software, and the error of using the wrong one
Window	Broadband factor	Narrowband factor	A tone, with Broadband scaling	Random PSD, with Narrowband scaling
None	1	1	correct	correct
Hann	1.633	2.000	−1.76 dB	+1.76 dB
Hamming	1.586	1.852	−1.35 dB	+1.35 dB
Blackman	1.812	2.381	−2.37 dB	+2.37 dB
Blackman-Harris	1.969	2.788	−3.02 dB	+3.02 dB
Calibration	2.255	4.175	−5.35 dB	+5.35 dB

Choose the scaling for the number you will report. If a measurement holds both tones and random, decide which one matters, or measure it twice.
Band RMS values are corrected for you. Process lines that sum spectral lines into an RMS value apply the broadband correction whichever scaling is selected, so a band's RMS reads correctly either way. The spectrum display shows what the selected scaling preserves.
Ratios don't care. A transmissibility or FRF divides two channels windowed the same way, so the scaling cancels.

Seeing a small component next to a large one

Leakage from a strong component spreads across its neighbors and can bury anything weaker nearby: a mount resonance under a strong forcing tone, sidebands around a gear mesh, a spur next to a drive line. How deep a window lets you see depends on its side lobes, not on the front end, which in Panther and Lynx covers more than 110 dB.

Figure 5. A tone 70 dB below a large one, 4.5 lines away, both between lines. The large tone's leakage at the small tone's position is −23 dB with None and −48.5 dB with Hann, so the small tone is hidden. With Calibration the leakage is −70 dB, level with the small tone. With Blackman-Harris it is −92 dB and the small tone stands clear.

Two levers help: a window with lower side lobes, and finer resolution. More lines move the two components further apart in lines, which helps every window; a lower-side-lobe window then decides how deep you can see.

Overlap and windows

A tapering window discards most of the data near the frame edges. Overlap processing starts each new frame before the previous one ends, so those samples are weighted fully in the next frame. Two numbers describe how well that works for each window: the overlap correlation, how much two successive frames repeat the same information (the lower, the more each average adds), and whether the overlapped weights add up to a flat total, so every sample counts equally.

Table 5. Overlap, by window
Window	Overlap correlation at 50%	at 75%	Weights add up flat at	Suggested overlap
None	50%	75%	0% (no overlap)	None: overlapping adds little new information
Hann	16.7%	65.9%	50%	50%; 75% for faster updates
Hamming	23.4%	70.7%	50%	50%
Blackman	9.0%	56.7%	67%	67% to 75%
Blackman-Harris	3.8%	46.0%	75%	75%
Calibration	−3.8%	12.0%	75%	75%

For random data this matters directly: frames that overlap but are nearly independent count almost as fully as separate ones toward the averaging, which is what sets the statistical accuracy of a PSD (see Statistical Degrees of Freedom). With Hann at 50% overlap, twice as many frames are processed in the same time, each only 16.7% correlated with the last. Random control lets you set its overlap; the Analyzer offers None, 25%, 50%, 75% and a custom value, and starts at None.

Transients: None and Force/Impact

When an event starts and ends inside the frame, there is no edge to taper and no leakage to control, so the right window is None. That covers shock pulses, drops and impacts that have died out before the frame ends, and anything analyzed as a shock response spectrum: an SRS must see the pulse as it happened, so the Analyzer switches windowing off when SRS is selected and tells you so.

An impact hammer test is the exception, because a lightly damped structure keeps ringing long after the hit. If the response has not died out by the end of the frame, it leaks like any continuous signal. Force/Impact handles both channels of the measurement:

Every channel is multiplied by an exponential decay, exp(−D·t/T), where D is the Decay setting and T the frame duration. The weight at the end of the frame is e^−D: 0.7% with the default Decay of 5.
The force channel (the reference channel) is kept from the start of the frame to the trigger point plus the Width, a percentage of the frame (10% by default), and set to zero after it. That removes the noise the force channel picks up once the hit is over, which would otherwise add to every line of the force spectrum.
Double hits are checked: a second hit after the first, above a threshold (10% of the peak by default), can warn or reject the frame.

Figure 6. Force/Impact with the default settings on a simulated hammer test: a 1-second frame, the hit at 5% of the frame, a 40 Hz mode with 0.5% damping. (a) The force channel is kept up to the trigger plus 10% of the frame; the noise after it is removed. (b) Unwindowed, the response is still at 32% of its peak when the frame ends. After the exponential it ends at 0.2%, so it no longer leaks.

The exponential works by adding damping. A decay with time constant T/D adds a damping ratio of

Δζ = D / (2π · f · T)Damping added to a mode at frequency f by an exponential with Decay D over a frame of duration T. With D = 5 and T = 1 s: 8.0% at 10 Hz, 2.0% at 40 Hz, 0.8% at 100 Hz, 0.08% at 1 kHz.

In Figure 6 the 40 Hz mode's true damping is 0.5%; measured through this window it would appear as about 2.5%. Because every channel gets the same exponential, the added damping is the same on every mode and can be subtracted after the fit, but it also broadens peaks and can merge closely spaced modes. Two rules keep it small: use the smallest Decay that brings the response near zero, and lengthen the frame first (finer resolution means a longer T), because a longer frame lets the structure decay on its own.

Correlation

Correlation functions are computed through the FFT, and the FFT treats each frame as circular: a lag that runs off the end of the frame wraps around to the start, and the result mixes the two. The Correlation window prevents that by keeping only the first half of the frame and setting the second half to zero, weighted by √2 so the frame keeps its power. Lags up to half the frame are then free of wrap-around. Use it for correlation and time-delay measurements, not for spectra.