Window Function Comparison
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About This MicroSim
The previous MicroSim showed the problem: a frame that does not hold whole cycles has a step at its boundary, and that step leaks across the spectrum.
A window function fixes the boundary instead of the frequency. Multiply your samples by a shape that tapers to zero at both ends, and the periodic extension joins at zero no matter what the signal was doing.
Nothing is free. Tapering the ends throws away real data near the frame edges, and the cost shows up as a wider main lobe.
The Trade, In Numbers
Click through the four windows in order and watch both numbers move together:
| Window | Main lobe width | Highest side lobe |
|---|---|---|
| Rectangular | 2.0 bins | -13.3 dB |
| Hann | 4.0 bins | -31.5 dB |
| Hamming | 4.0 bins | -41.7 dB |
| Blackman | 6.1 bins | -58.1 dB |
Every step down the table buys about 18-27 dB of side lobe suppression and pays for it in main lobe width. These are not quoted from a table — the sim computes them from the actual zero-padded transform of each window.
Which One Should You Use?
It depends on what would ruin your measurement:
- Two tones close together → you need a narrow main lobe. Rectangular resolves best, at the cost of horrible leakage.
- One loud tone masking a quiet one → you need low side lobes. Blackman keeps the loud tone's skirts from burying the quiet one 50 dB down.
- General-purpose → Hann. It is the usual default because 31 dB of suppression for a 2× main lobe penalty is a good deal, and it is cheap to compute.
Notice that Hamming and Hann have the same main lobe width but Hamming's side lobes are 10 dB lower. Hamming's coefficients are tuned to cancel the first side lobe specifically — but look at its far side lobes, which fall off more slowly than Hann's. There is no free lunch, only differently shaped bills.
How to Use
- Start with Rectangular. Note the narrow main lobe and the side lobes only 13 dB down — barely suppressed at all.
- Switch to Hann. The main lobe doubles; the side lobes drop by 18 dB.
- Switch to Hamming. Same main lobe as Hann, side lobes 10 dB lower still. Compare their far side lobes at ±5 bins.
- Switch to Blackman. The widest main lobe and the deepest side lobes.
- Look at the time-domain shapes. The more aggressively a window tapers, the more it suppresses side lobes — and the less of your frame it actually uses.
Lesson Plan
Grade Level
Undergraduate (college junior/senior)
Duration
12-15 minutes
Prerequisites
- Spectral leakage and the periodic assumption
- Decibels
Learning Objective
Students will be able to compare the time-domain shape and frequency-domain response of four windows, and distinguish the specific tradeoff each makes.
Activities
- Fill the table (5 min): Students record both metrics for all four windows from the readout.
- Hann versus Hamming (5 min): Students identify what is the same and what differs, including the far side lobe behavior.
- Choose for a purpose (5 min): Given two scenarios — resolving two close tones, and finding a quiet tone beside a loud one — students choose a window and justify it with numbers from the table.
Assessment
Ask: "You need to detect a component 45 dB below a nearby loud tone. Which windows can possibly work, and which is the cheapest of those?"
Related Resources
References
- Window function — definitions and comparison tables for these and many other windows.
- Harris, "On the Use of Windows for Harmonic Analysis" — the definitive comparison paper.
- Spectral leakage — the problem windows exist to manage.