# Documentation

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# chirp

Swept-frequency cosine

## Syntax

`y = chirp(t,f0,t1,f1)y = chirp(t,f0,t1,f1,'method')y = chirp(t,f0,t1,f1,'method',phi)y = chirp(t,f0,t1,f1,'quadratic',phi,'shape')`

## Description

`y = chirp(t,f0,t1,f1)` generates samples of a linear swept-frequency cosine signal at the time instances defined in array `t`, where `f0` is the instantaneous frequency at time 0, and `f1` is the instantaneous frequency at time `t1`. `f0` and `f1` are both in hertz. If unspecified, `f0` is e-6 for logarithmic chirp and 0 for all other methods, `t1` is `1`, and `f1` is `100`.

`y = chirp(t,f0,t1,f1,'method')` specifies alternative sweep method options, where `method` can be:

• `linear`, which specifies an instantaneous frequency sweep fi(t)given by

`${f}_{i}\left(t\right)={f}_{0}+\beta t$`

where

`$\beta =\left({f}_{1}-{f}_{0}\right)/{t}_{1}$`

and the default value for f0 is 0. β ensures that the desired frequency breakpoint f1 at time t1 is maintained.

• `quadratic`, which specifies an instantaneous frequency sweep fi(t) given by

`${f}_{i}\left(t\right)={f}_{0}+\beta {t}^{2}$`

where

`$\beta =\left({f}_{1}-{f}_{0}\right)/{t}_{1}{}^{2}$`

and the default value for f0 is 0. If f0 > f1 (downsweep), the default shape is convex. If ff1 (upsweep), the default shape is concave.

• `logarithmic` specifies an instantaneous frequency sweep fi(t) given by

`${f}_{i}\left(t\right)={f}_{0}×{\beta }^{t}$`

where

`$\beta ={\left(\frac{{f}_{1}}{{f}_{0}}\right)}^{\frac{1}{{t}_{1}}}$`

and the default value for f0 is 1e-6. Both an upsweep (ff0) and a downsweep (f0 > f1) of frequency is possible.

Each of the above methods can be entered as `'li'`, `'q'`, and `'lo'`, respectively.

`y = chirp(t,f0,t1,f1,'method',phi)` allows an initial phase `phi` to be specified in degrees. If unspecified, `phi` is `0`. Default values are substituted for empty or omitted trailing input arguments.

`y = chirp(t,f0,t1,f1,'quadratic',phi,'shape')` specifies the `shape` of the quadratic swept-frequency signal's spectrogram. `shape` is either `concave` or `convex`, which describes the shape of the parabola in the positive frequency axis. If `shape` is omitted, the default is convex for downsweep (f0 > f1) and is concave for upsweep (ff1).

## Examples

collapse all

Generate a chirp with linear instantaneous frequency deviation. The chirp is sampled at 1 kHz for 2 seconds. The instantaneous frequency is 0 at t = 0 and crosses 250 Hz at t = 1 second.

```t = 0:1/1e3:2; y = chirp(t,0,1,250); ```

Compute and plot the spectrogram of the chirp. Specify 256 DFT points, a Hamming window of the same length, and 250 samples of overlap.

```spectrogram(y,256,250,256,1e3,'yaxis') ```

Generate a chirp with quadratic instantaneous frequency deviation. The chirp is sampled at 1 kHz for 2 seconds. The instantaneous frequency is 100 Hz at t = 0 and crosses 200 Hz at t = 1 second.

```t = 0:1/1e3:2; y = chirp(t,100,1,200,'quadratic'); ```

Compute and plot the spectrogram of the chirp. Specify 128 DFT points, a Hamming window of the same length, and 120 samples of overlap.

```spectrogram(y,128,120,128,1e3,'yaxis') ```

Generate a convex quadratic chirp sampled at 1 kHz for 2 seconds. The instantaneous frequency is 400 Hz at t = 0 and crosses 300 Hz at t = 1 second.

```t = 0:1/1e3:2; fo = 400; f1 = 300; y = chirp(t,fo,1,f1,'quadratic',[],'convex'); ```

Compute and plot the spectrogram of the chirp. Specify 256 DFT points, a Hamming window of the same length, and 200 samples of overlap.

```spectrogram(y,256,200,256,1e3,'yaxis') ```

Generate a concave quadratic chirp sampled at 1 kHz for 4 seconds. Specify the time vector so that the instantaneous frequency is symmetric about the halfway point of the sampling interval, with a minimum frequency of 100 Hz and a maximum frequency of 500 Hz.

```t = -2:1/1e3:2; fo = 100; f1 = 200; y = chirp(t,fo,1,f1,'quadratic',[],'concave'); ```

Compute and plot the spectrogram of the chirp. Specify 128 DFT points, a Hann window of the same length, and 120 samples of overlap. Note that the `spectrogram` function measures time starting at t = 0;

```spectrogram(y,hann(128),120,128,1e3,'yaxis') ```

Generate a logarithmic chirp sampled at 1 kHz for 10 seconds. The instantaneous frequency is 10 Hz initially and 400 Hz at the end.

```t = 0:1/1e3:10; fo = 10; f1 = 400; y = chirp(t,fo,10,f1,'logarithmic'); ```

Compute and plot the spectrogram of the chirp. Specify 256 DFT points, a Hamming window of the same length, and 200 samples of overlap.

```spectrogram(y,256,200,256,1e3,'yaxis') ```