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)

y = chirp(___,cplx)

Description

y = chirp(t,f0,t1,f1) generates samples of a linear swept-frequency cosine signal at the time instances defined in array t. The instantaneous frequency at time 0 is f0 and the instantaneous frequency at time t1 is f1.

y = chirp(t,f0,t1,f1,method) specifies an alternative sweep method option.

y = chirp(t,f0,t1,f1,method,phi) specifies the initial phase.

y = chirp(t,f0,t1,f1,'quadratic',phi,shape) specifies the shape of the spectrogram of a quadratic swept-frequency signal.

y = chirp(___,cplx) returns a real chirp if cplx is specified as 'real' and returns a complex chirp if cplx is specified as 'complex'.

Examples

Linear Chirp

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. Divide the signal into segments such that the time resolution is 0.1 second. Specify 99% of overlap between adjoining segments and a spectral leakage of 0.85.

pspectrum(y,1e3,'spectrogram','TimeResolution',0.1, ...
    'OverlapPercent',99,'Leakage',0.85)

Quadratic Chirp

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. Divide the signal into segments such that the time resolution is 0.1 second. Specify 99% of overlap between adjoining segments and a spectral leakage of 0.85.

pspectrum(y,1e3,'spectrogram','TimeResolution',0.1, ...
    'OverlapPercent',99,'Leakage',0.85)

Convex Quadratic Chirp

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. Divide the signal into segments such that the time resolution is 0.1 second. Specify 99% of overlap between adjoining segments and a spectral leakage of 0.85.

pspectrum(y,1e3,'spectrogram','TimeResolution',0.1, ...
    'OverlapPercent',99,'Leakage',0.85)

Symmetric Concave Quadratic Chirp

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. Divide the signal into segments such that the time resolution is 0.1 second. Specify 99% of overlap between adjoining segments and a spectral leakage of 0.85.

pspectrum(y,t,'spectrogram','TimeResolution',0.1, ...
    'OverlapPercent',99,'Leakage',0.85)

Logarithmic Chirp

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. Divide the signal into segments such that the time resolution is 0.2 second. Specify 99% of overlap between adjoining segments and a spectral leakage of 0.85.

pspectrum(y,t,'spectrogram','TimeResolution',0.2, ...
    'OverlapPercent',99,'Leakage',0.85)

Use a logarithmic scale for the frequency axis. The spectrogram becomes a line, with high uncertainty at low frequencies.

ax = gca;
ax.YScale = 'log';

Complex Chirp

Generate a complex linear chirp sampled at 1 kHz for 10 seconds. The instantaneous frequency is –200 Hz initially and 300 Hz at the end. The initial phase is zero.

t = 0:1/1e3:10;
fo = -200;
f1 = 300;

y = chirp(t,fo,t(end),f1,'linear',0,'complex');

Compute and plot the spectrogram of the chirp. Divide the signal into segments such that the time resolution is 0.2 second. Specify 99% of overlap between adjoining segments and a spectral leakage of 0.85.

pspectrum(y,t,'spectrogram','TimeResolution',0.2, ...
    'OverlapPercent',99,'Leakage',0.85)

Verify that a complex chirp has real and imaginary parts that are equal but with ${90}^{\circ }$ phase difference.

x = chirp(t,fo,t(end),f1,'linear',0) + 1j*chirp(t,fo,t(end),f1,'linear',-90);

pspectrum(x,t,'spectrogram','TimeResolution',0.2, ...
    'OverlapPercent',99,'Leakage',0.85)

Input Arguments

t — Time array

vector

Time array, specified as a vector.

Data Types: single | double

f0 — Instantaneous frequency at time 0

0 (default) | real scalar in Hz

Initial instantaneous frequency at time 0, specified as a real scalar expressed in Hz.

Data Types: single | double

t1 — Reference time

1 (default) | positive scalar in seconds

Reference time, specified as a positive scalar expressed in seconds.

Data Types: single | double

f1 — Instantaneous frequency at time t1

100 (default) | real scalar in Hz

Instantaneous frequency at time t1, specified as a real scalar expressed in Hz.

Data Types: single | double

method — Sweep method

'linear' (default) | 'quadratic' | 'logarithmic'

Sweep method, specified as 'linear', 'quadratic', or 'logarithmic'.

• 'linear' — Specifies an instantaneous frequency sweep f_i(t) given by

  $$f_i(t)=f_0+\beta t,$$

  where

  $$\beta =(f_1-f_0)/t_1$$

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

• 'quadratic' — Specifies an instantaneous frequency sweep f_i(t) given by

  $$f_i(t)=f_0+\beta t^2,$$

  where

  $$\beta =(f_1-f_0)/t_1{}^2$$

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

• 'logarithmic' — Specifies an instantaneous frequency sweep f_i(t) given by

  $$f_i(t)=f_0\times {\beta }^t,$$

  where

  $$\beta ={\left(\frac{f_1}{f_0}\right)}^{\frac{1}{t_1}}$$

  and the default value for f₀ is 10^–6.

phi — Initial phase

0 (default) | positive scalar in degrees

Initial phase, specified as a positive scalar expressed in degrees.

Data Types: single | double

shape — Spectrogram shape of quadratic chirp

'convex' | 'concave'

Spectrogram shape of quadratic chirp, specified as 'convex' or 'concave'. shape describes the shape of the parabola with respect to the positive frequency axis. If not specified, shape is 'convex' for the downsweep case with f₀ > f₁, and 'concave' for the upsweep case with f₀ < f₁.

cplx — Output complexity

'real' (default) | 'complex'

Output complexity, specified as 'real' or 'complex'.

Output Arguments

y — Swept-frequency cosine signal

vector

Swept-frequency cosine signal, returned as a vector.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.