--- title: "Where a small peak in a spectrum can come from" description: "Cutting a signal creates spectral sidelobes. Follow windows, observation time and noise density to interpret a small peak beside a strong one." canonical_url: "https://sandboxphysics.com/stories/instruments/spectrum-analyzer/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/instruments/spectrum-analyzer/" last_modified: "2026-10-28" --- [How physics instruments measure](https://sandboxphysics.com/stories/instruments/) Inside the instrument # Where a small peak in a spectrum can come from A small spectral peak may be another tone, or a sidelobe left by cutting a strong tone into a finite recording. The cut spreads a concentrated spectral line across nearby frequencies. Gradually reducing the ends of the recording suppresses distant leakage, but broadens the main peak. Sandbox Physics · 2026-10-28 ## Cut a piece and join its ends Picture a continuous sine wave, rising and falling like a vibrating string. Record just one second of it. An FFT expresses that finite piece as a sum of repeating oscillations. Each oscillation joins smoothly to itself at the record boundary, so the calculation treats the recorded piece as if it repeated. A cut after a whole number of cycles can join neatly. A cut at an awkward point may join a rising voltage to a very different value. Repeating that piece creates a jump. Describing the jump requires additional frequencies, and small peaks appear beside the strong one. This spread into other frequencies is called spectral leakage. Sources: [1] ## Gentler ends reduce distant sidelobes Multiply each recorded sample by a weight. Keep more of the middle and less of each end. The shape of these weights is a window function. A Hann window resembles a smooth hill, gradually reducing the voltage near the join. A rectangular window gives every sample the same weight and retains the abrupt cut. Hann reduces distant sidelobes substantially. A weak tone hidden beneath leakage from a strong one may then emerge. Tektronix’s FFT application note illustrates the trade with window-response diagrams: the Hann response concentrates more energy near the main peak, whose central peak becomes wider than with a rectangular window. If the weak tone is very close, that wider lobe can cover both signals. Window choice therefore depends on the problem: widely unequal tones some distance apart, or two similarly sized tones very close together. Comparing windows on the same samples helps reveal which features move with the processing. Sources: [1] [4] ## A longer observation records a finer distinction Extend the observation from one second to two and the instrument receives more real motion of the voltage. Two slightly different tones have longer to slip out of step, making their difference easier to record. The unpadded frequency interval also shrinks from one hertz to half a hertz. Appending zeros adds no observed motion. It evaluates the same recording on a denser frequency grid, a process called zero padding. The broad peak keeps its width. Adding more plotted points cannot give an unresolved pair new physical resolution. The original frequency interval is not a universal threshold for separating any pair of peaks either. The window and the relative signal sizes matter. Keeping the actual observation time and window with a result is more useful than reporting the number of plotted points alone. $$ \Delta f_{\mathrm{record}}=\frac{1}{T} $$ The left side is the frequency interval before zero padding. The observation time on the right is in seconds, giving an interval in hertz. This describes the frequency grid; the window also determines the main-peak width. Sources: [1] [2] ## Noise height depends on the bandwidth behind a point White noise spreads voltage fluctuations over a broad frequency range. Observe for longer and each original spectral point collects noise from a narrower band. Its noise floor falls when displayed as power per frequency point. To compare different observation times, express mean-square voltage per hertz: power spectral density. For the same white noise, its average density stays approximately constant. The window sets how much surrounding noise contributes to a point. Equivalent noise bandwidth compares its response with an ideal rectangular frequency band that passes the same white-noise power. A Hann window applied to one second of data has a noise bandwidth of about 1.5 hertz. FFT and swept superheterodyne analyzers can use different definitions of their reported resolution bandwidth, so the definition belongs with the number. A real measurement first needs a voltage scale and a clock. Separate known voltage levels check scale and offset; an independent time reference checks sample rate. Integrating the calibrated density across a selected band then gives its mean-square voltage. Leakage from a strong tone, a weak signal and noise all contribute when they lie inside that band. Sources: [2] [3] ## [Put another window on the same recording](https://sandboxphysics.com/labs/spectrum-analyzer/) Compare Hann with a rectangular window, then lengthen the real time gate and watch a weak neighbour and an unresolved pair. The FFT instrument stores ADC codes and independent voltage/clock calibration, then calculates amplitude, density and band integrals using saved window weights. ## Sources and further reading 1. [Tektronix · FFT Applications for TDS Oscilloscopes · 55W-8815-2, 05/05](https://download.tek.com/document/55W_8815_2.pdf) Pages 15–23, sections 1.16–1.24, explain record length, leakage, wider window main lobes, scalloping and coherent-gain correction. This 2005 application note supplies the physical examples, not the specification of the teaching instrument. 2. [National Instruments · LabVIEW Analysis Concepts · March 2004, 370192C-01](https://download.ni.com/support/manuals/370192c.pdf) Printed pages 4-22–4-29 distinguish single/two-sided spectra, line amplitude and noise density; pages 5-23–5-24 explain window scaling and equivalent noise bandwidth. 3. [Keysight 89600 VSA Help · About Resolution Bandwidth · 2026 Update 2.0](https://helpfiles.keysight.com/csg/89600B/Webhelp/Subsystems/gui/content/rbw_about_rbw.htm) Distinguishes the FFT analyzer’s equivalent-noise-bandwidth convention from a swept analyzer’s three-decibel IF filter width. Consulted 28 October 2026. 4. [Keysight 89600 VSA Help · Window Shapefactor and Equivalent Noise Bandwidth · 2026 Update 2.0](https://helpfiles.keysight.com/csg/89600B/Webhelp/Subsystems/gui/content/windows_shapefactor_and_equiv_noisebw.htm) The window summary gives Hann noise bandwidth as 1.5 divided by observation time and describes the trade between main-peak width and sidelobes. 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