You will be able to
- Explain finite-record leakage and window trade-offs.
- Separate zero-padding grid density from resolving power.
A record boundary is part of the model
The DFT basis assumes the finite record repeats. A tone with a non-integer number of cycles can have a jump at that periodic boundary, spreading its coefficients across bins. Multiplying by a tapered window softens boundaries and reduces distant sidelobes, but widens the main lobe.
A finer grid is not a longer observation
Zero-padding before an FFT samples the same windowed record’s spectrum more densely. It does not create extra measured time or guarantee separation of nearby tones. Window amplitude correction depends on purpose: this lab divides by coherent gain for tone amplitude, while noise-power density needs a different calibration.
Worked example
At 64 samples/s with 64 samples, a 5 Hz tone is bin-centred; 5.5 Hz is not. A longer measured record narrows frequency features, whereas padding the same record only supplies more grid points.
A common trap
A window does not universally improve resolution: lower sidelobes usually come with a wider main lobe.
Predict, then experiment
Will Hann tapering make the 5.5 Hz tone appear in exactly one bin? Before touching the controls, say or write your prediction.
Try it yourself
A tone between bins
Where does a finite record put its spectral amplitude?
64 samples at 64 Hz. Solid is rectangular-window spectrum; dashed is selected window spectrum. 0=rectangular, 1=symmetric Hann. One-sided tone amplitude is corrected by window coherent gain; this is not a noise-density calibration.
Your experiment
Compare rectangular and Hann windows for 5 and 5.5 Hz. Inspect both main-lobe width and distant bins; the displayed amplitude has coherent-gain compensation.
Change one parameter at a time. Compare what you observed with your prediction and record an explanation in your notes.
Check your understanding
Try from memory first. Hints and feedback are part of learning, not a penalty. These checks are for self-study, not a graded qualification.
Reference answers (after your attempt)
- densifies the frequency grid — Correct: it interpolates spectral grid samples.
- 4Hz — 1,000/250=4 Hz. This is grid spacing, not a universal two-tone resolution guarantee.
Apply it: Choose a window with a reason
Use paper, your notes, or a local notebook/editor. Code examples are Python 3 starting points to run yourself; this page does not execute code or automatically assess the practical task.
- Consider a small tone beside a much larger nearby tone.
- Explain why sidelobes and main-lobe width both matter.
- State what changing record duration does.
Reference solution & review criteria
Low sidelobes reduce masking by the large tone, but a wider main lobe may merge close tones. A longer actual observation can narrow features; padding alone cannot supply that benefit.
Your notebook
Notes and progress stay in this browser. They are not sent to the server; ordinary web-server request logs still operate. Export a backup from the course page.
Completion requires both correct checks and your practical-task acknowledgement.
Go deeper
Sources support further study; the worked examples and questions here are original. Browser experiments are small, disclosed models—not evidence of production-model quality or hardware performance.