Chirp - Wikiparency

# Chirp A **chirp** is a signal whose frequency changes with time, rising in an up-chirp or falling in a down-chirp, in contrast with a [[Sine_wave|sine wave]] or any other signal whose frequency stays fixed. The name comes from the sound a bird's own frequency-swept call makes, and the same shape turns up for the same practical reason wherever it is used: sweeping frequency, rather than holding it constant, lets a signal's duration and its bandwidth be chosen almost independently of each other. A three.js microsim elsewhere on the site renders the chirp waveform itself, sweeping its time-bandwidth product upward from one so the shape a wider sweep produces can be watched directly. Radar, [[Sonar]] and spread-spectrum radio all transmit a chirp for much the reason [[Pulse_compression|pulse compression]] describes: a long pulse that a fixed-frequency signal could not afford to shorten without losing energy can be swept in frequency instead, correlated against a reference on reception, and collapsed back down to a short pulse's resolution. What follows defines the shape precisely, distinguishes the linear sweep radar prefers from the exponential and hyperbolic sweeps other applications favour, and follows the signal from how it is generated to the several senses the word has since picked up beyond its original one. ## Definitions A chirp's defining property is that its instantaneous frequency, the rate of change of its phase divided by 2π, is itself a function of time rather than a constant. Written as `s(t) = A(t)·cos(φ(t))`, an ordinary sine wave has `φ(t) = 2π·f·t`, a phase that advances at the fixed rate f; a chirp instead has a phase whose rate of advance, `f_inst(t) = (1/2π)·dφ/dt`, changes smoothly over the pulse, rising through an up-chirp and falling through a down-chirp. The concept generalizes beyond audible pitch: any measurable quantity whose local rate of oscillation changes systematically over time is a chirp in this sense, whether the oscillation is a sound-pressure wave, a radio voltage, or a light wave's electric field. A chirp's signature is easiest to see on a [[Spectrogram|spectrogram]], where a plot of frequency against time turns the sweep into a single, unmistakably diagonal or curved streak, in clear contrast with the flat horizontal line a constant-frequency tone draws on the same plot. ## Types How the instantaneous frequency changes with time separates the handful of chirp shapes in common use. ### Linear A linear chirp's instantaneous frequency rises or falls at a constant rate, `f(t) = f0 + k·t`, where the chirp rate `k = B/τ` spreads a total swept bandwidth B evenly across the pulse's duration τ. This is the shape radar and most sonar pulse compression use, since a constant sweep rate keeps the correlation peak described in pulse compression narrow and its sidelobes predictable, and it is common enough in audio analysis that a downward-sweeping example is a standard teaching illustration: one widely used recording sweeps linearly from about 500 hertz down to about 300 hertz over roughly 1.4 seconds.[^downey-chirp] ### Exponential An exponential chirp's instantaneous frequency instead multiplies by a constant factor per unit time rather than adding a constant increment, so it covers each octave, each doubling of frequency, in the same amount of time regardless of how high or low that octave sits. Because human pitch perception is itself closer to logarithmic than linear, exponential sweeps are a standard test signal for measuring how a room or a loudspeaker responds across the audible range: a fixed sweep duration then devotes as much time to the lowest octave as to the highest, rather than rushing through the bass the way a linear sweep would.[^log-sweep] ### Hyperbolic A hyperbolic chirp's instantaneous frequency varies as the reciprocal of time instead, a shape less common in engineered systems but well documented in nature: several echolocating bat species emit calls that sweep hyperbolically, and the shape has a genuine advantage for a moving emitter or a moving target, since a hyperbolic sweep's matched-filter response is far less sensitive to the [[Doppler_effect|Doppler]] shift a fast-moving bat or target imposes than a linear sweep's is, so the compressed echo keeps its shape and timing where a linear chirp's would smear and shift.[^bat-chirp] ## Generation Analog chirp generators sweep a [[Voltage|voltage]]-controlled oscillator with a ramp, or pass a sharp impulse through a dispersive delay line, commonly built from a surface-acoustic-wave device, whose different frequency components travel at different speeds and so emerge spread out in time as a chirp; the same device run in reverse recompresses a matching chirp back toward an impulse. Digital generation instead computes the swept phase directly, accumulating a frequency value that itself increases or decreases sample by sample and feeding the running phase to a lookup table before handing the result to a [[Digital-to-analog_converter|digital-to-analog converter]], a technique flexible enough to produce a linear, exponential or hyperbolic sweep on the same hardware simply by changing how the frequency word is stepped. Whichever method produces it, the chirp's rate of frequency change is the one parameter every later stage, from an antenna's bandwidth to a matched filter's reference, must already know, whether that reference lives in a length of surface-acoustic-wave delay line or in a table of stored numbers. ## Relation to an impulse signal A chirp can be understood as a stretched-out [[Dirac_delta_function|impulse]]: passing a genuine impulse, in principle infinitely short and infinitely wide in frequency, through a dispersive medium or filter that delays each frequency component by a different amount spreads that single instant out into a long signal whose frequency visibly changes with time, which is a chirp by another route than sweeping an oscillator directly. Running the resulting chirp back through the inverse of that same dispersive delay, or equivalently correlating it against a reference copy of itself, undoes the spreading and collapses the signal back toward the impulse it began as. This is not merely an analogy: it is the same operation [[Pulse_compression|pulse compression]] performs on a radar or sonar echo, described there as cross-correlation rather than as reversing a dispersive delay, and a chirp is, in that sense, an impulse deliberately spread out in time so that it can be sent with the energy a bare impulse could never carry. ## Uses and occurrences The chirp shape appears wherever a signal's duration and its bandwidth need to be set separately rather than tied together, and the word has since spread to a few uses that share little beyond the name. A continuously repeating linear chirp, rather than a single pulsed burst, is also the transmitted waveform of [[Frequency_modulation|frequency-modulated]] [[Continuous-wave_radar|continuous-wave radar]], which reads range from the beat frequency between the chirp going out and its echo coming back rather than from a pulse's round-trip delay. ### Chirp modulation Chirp spread spectrum modulation encodes each transmitted symbol as a chirp with a particular starting frequency or time shift, chosen from a small set the receiver can tell apart by correlating the received signal against every possible reference chirp in turn. Because the chirp spreads a symbol's energy across a wide bandwidth for the whole symbol period, the technique inherits pulse compression's resistance to narrowband interference and, in low-power wide-area networks built around it, lets a receiver recover a signal well below the noise floor at the cost of a lower data rate for a given bandwidth.[^css-name] ### Chirplet transform A chirplet transform extends the idea behind a wavelet transform, which analyses a signal against scaled and shifted copies of one fixed wave shape, by also letting the analysing shape itself be a short chirp rather than a plain oscillation. Adding sweep rate as a fourth parameter alongside a wavelet's scale, position and frequency lets a chirplet decomposition describe a signal whose own frequency is sweeping, such as a bird call, an echo from an accelerating target, or a chirp radar's own return, far more compactly than a basis of fixed, unswept shapes would need.[^chirplet-origin] ### Key chirp Away from signal theory entirely, "chirp" is also the everyday word for the short, high-pitched confirmation tone many electronic locks and alarms emit, most familiarly the sound a vehicle's remote key fob triggers on locking or unlocking. This everyday chirp is a fixed, brief tone rather than a genuine frequency sweep, so the word here describes a sound's character rather than the swept-frequency signal defined earlier in this article.[^key-chirp-name] ## Microsims A three.js companion elsewhere on the site renders the chirp waveform itself, sweeping its time-bandwidth product upward from one so the shape a wider sweep produces can be watched directly, in more depth than this article's own text attempts. This article carries no p5.js sketch of its own, so the reader who wants to see a chirp acting inside a system, rather than as a waveform on its own, is better served by two neighbouring articles' sketches. The Radar sketch transmits a plain, unswept pulse rather than a chirp, and widening that pulse reproduces exactly the resolution loss a chirp's independent bandwidth is built to avoid. The Doppler effect sketch shows a different, unrelated way a received frequency can change with time: not because a transmitter swept it on purpose, as a chirp does, but because the source and the observer are moving relative to each other. *Try:* in the [[Radar]] sketch, widen the transmitted pulse and watch the zoomed inset's close targets merge into one hump, the same loss of resolution a chirp escapes by sweeping bandwidth apart from duration rather than by shortening the pulse. *Try:* in the [[Doppler_effect]] sketch, change the source's speed rather than its frequency, and notice the resulting shift is fixed by geometry alone for as long as the speed holds steady, unlike a chirp's frequency, which a transmitter sweeps deliberately whether or not anything is moving at all. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Chirp) : [Wikitube](https://en.wikitube.io/wiki/Chirp) Skeleton mirrored at revision 1309378581. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Pulse_compression]] - [[Continuous-wave_radar]] - [[Radar]] - [[Sonar]] - [[Doppler_effect]] - [[Matched_filter]] - [[Spectrogram]] ## References The core relations here, the instantaneous-frequency definition and the linear chirp's `f(t) = f0 + k·t`, are standard signal-theory material and are not separately footnoted, per the Wikitube style guide's §6.1. Page numbers below are PDF pages of the open editions linked in Further reading. [^downey-chirp]: Downey, A. *Think DSP: Digital Signal Processing in Python*. 2012, p. 68 (PDF page). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python . CC BY-NC. [^log-sweep]: Citation needed: the standard reference for exponential (logarithmic) sine-sweep measurement of room and loudspeaker impulse responses would confirm the method's origin and usual attribution. [^bat-chirp]: Citation needed: a bioacoustics study naming the echolocating bat species that use hyperbolic frequency-modulated calls, and quantifying the Doppler-tolerance advantage claimed here, would support this claim precisely. [^css-name]: Citation needed: the technical standard or founding patent for a named chirp-spread-spectrum wireless technology would confirm the specific claims made here about its data rate and interference resistance. [^chirplet-origin]: Citation needed: the original paper defining the chirplet transform would confirm its inventors and date. [^key-chirp-name]: Citation needed: a source documenting the origin and scope of "chirp" as a name for a keyless-entry or alarm confirmation tone would support this claim precisely. **Further reading** — the open textbooks this article draws on, since the pair carries no separate Further reading heading of its own: - Allen Downey. *Think DSP: Digital Signal Processing in Python* (2012). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python - Steven Ellingson. *Radio Systems Engineering, Revised First Edition* (2023). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory* (2026). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory ## External links This article carries no live sketch of its own. The three.js companion introduced above, and the neighbouring sketches named in Microsims, hold the site's interactive material for this topic.