DSP Blockset

Chirp

Generate a swept-frequency cosine (chirp) signal.

Library

DSP Sources

Description

The Chirp block outputs a swept-frequency cosine (chirp) signal with unity amplitude and continuous phase. To specify the desired output chirp signal, you must define its instantaneous frequency function, also known as the output frequency sweep. The frequency sweep can be linear, quadratic, or logarithmic, and repeats once every Sweep time by default. See other sections of this reference page for more details about the block.

Sections of This Reference Page

• Variables Used in This Reference Page
• Setting the Output Frame Status
• Shaping the Frequency Sweep by Setting Frequency Sweep and Sweep Mode
• Unidirectional and Bidirectional Sweep Modes
• Setting Instantaneous Frequency Sweep Values
• Block Computation Methods
• Cautions Regarding the Swept Cosine Sweep
• Examples
• Dialog Box
• Supported Data Types
• See Also

Variables Used in This Reference Page

f0	Initial frequency parameter (Hz)
fi(tg)	Target frequency parameter (Hz)
tg	Target time parameter (seconds)
Tsw	Sweep time parameter (seconds)
	Initial phase parameter (radians)
	Phase of the chirp signal (radians)
fi(t)	User-specified output instantaneous frequency function (Hz); user-specified sweep
fi(actual)(t)	Actual output instantaneous frequency function (Hz); actual output sweep
ychirp(t)	Output chirp function

Setting the Output Frame Status

Use Samples per frame parameter to set the block's output frame status, as summarized in the table. The Sample time parameter sets the sample time of both sample- and frame-based outputs.

Setting of Samples Per Frame Parameter	Output Frame Status
1	Sample-based
n (any integer greater than 1)	Frame-based, frame size n

Shaping the Frequency Sweep by Setting Frequency Sweep and Sweep Mode

The basic shape of the output instantaneous frequency sweep, f_i(t), is set by the Frequency sweep and Sweep mode parameters, described in the following table.

Parameters for Setting Sweep Shape	Possible Settings	Parameter Description
Frequency sweep	Linear Quadratic Logarithmic Swept cosine	Determines whether the sweep frequencies vary linearly, quadratically, or logarithmically. (Linear and swept cosine sweeps both vary linearly.)
Sweep mode	Unidirectional Bidirectional	Determines whether the sweep is unidirectional or bidirectional. For details, see Unidirectional and Bidirectional Sweep Modes.

The following diagram illustrates the possible shapes of the frequency sweep that you can obtain by setting the Frequency sweep and Sweep mode parameters.

For information on how to set the frequency values in your sweep, see Setting Instantaneous Frequency Sweep Values.

Unidirectional and Bidirectional Sweep Modes

The Sweep mode parameter determines whether your sweep is unidirectional or bidirectional, which affects the shape of your output frequency sweep (see Shaping the Frequency Sweep by Setting Frequency Sweep and Sweep Mode). The following table describes the characteristics of unidirectional and bidirectional sweeps.

Sweep mode Parameter Settings	Sweep Characteristics
Unidirectional	Lasts for one Sweep time, Tsw Repeats once every Tsw
Bidirectional	Lasts for twice the Sweep time, 2*Tsw Repeats once every 2*Tsw First half is identical to its unidirectional counterpart. Second half is a mirror image of the first half.

The following diagram illustrates a linear sweep in both sweep modes. For information on setting the frequency values in your sweep, see Setting Instantaneous Frequency Sweep Values.

Setting Instantaneous Frequency Sweep Values

Set the following parameters to tune the frequency values of your output frequency sweep:

• Initial frequency (Hertz), f₀
• Target frequency (Hertz), f_i(t_g)
• Target time (seconds), t_g

The following table summarizes the sweep values at specific times for all Frequency sweep settings. For information on the formulas used to compute sweep values at other times, see Block Computation Methods.

Table 7-1: Instantaneous Frequency Sweep Values

Frequency Sweep	Sweep Value at t = 0	Sweep Value at t = tg	Time When Sweep Value is Target Frequency, fi(tg)
Linear	f0	fi(tg)	tg
Quadratic	f0	fi(tg)	tg
Logarithmic	f0 + 1	fi(tg)	tg
Swept cosine	f0	2fi(tg) - f0	tg/2

Block Computation Methods

The Chirp block uses one of two formulas to compute the block output, depending on the Frequency Sweep parameter setting. For details, see the following sections:

• Equations for Output Computation
• Output Computation Method for Linear, Quadratic, and Logarithmic Frequency Sweeps
• Output Computation Method for Swept Cosine Frequency Sweep

Equations for Output Computation.   The following table shows the equations used by the block to compute the user-specified output frequency sweep, f_i(t), the block output, y_chirp(t), and the actual output frequency sweep, f_i(actual)(t). The only time the user-specified sweep is not the actual output sweep is when the Frequency sweep parameter is set to Swept cosine.

Note    The following equations apply only to unidirectional sweeps in which fi(0) < fi(tg). To derive equations for other cases, you may find it helpful to examine the following table and the diagram in Shaping the Frequency Sweep by Setting Frequency Sweep and Sweep Mode.

Table 7-2 contains the following variables:

• f_i(t) -- the user-specified frequency sweep
• f_i(actual)(t) -- the actual output frequency sweep, usually equal to f_i(t)
• y_chirp(t) -- the Chirp block output
•  -- the phase of the chirp signal, where  , and   is the derivative of the phase

•  -- the Initial phase parameter value, where 

Table 7-2: Equations Used by the Chirp Block for Unidirectional Positive Sweeps

Frequency Sweep	Block Output Chirp Signal	User-Specified Frequency Sweep, fi(t)		Actual Frequency Sweep, fi(actual)(t)
Linear
Quadratic	Same as Linear
Logarithmic	Same as Linear	Note fi(0) = f0 + 1	Where fi(tg) > f0
Swept cosine		Same as Linear	Same as Linear

Output Computation Method for Linear, Quadratic, and Logarithmic Frequency Sweeps.   The derivative of the phase of a chirp function gives the instantaneous frequency of the chirp function. The Chirp block uses this principle to calculate the chirp output when the Frequency Sweep parameter is set to Linear, Quadratic, or Logarithmic.

	Linear, quadratic, or logarithmic chirp signal with phase
	Phase derivative is instantaneous frequency (7-1)

For instance, if you want a chirp signal with a linear instantaneous frequency sweep, you should set the Frequency Sweep parameter to Linear, and tune the linear sweep values by setting other parameters appropriately. The block will output a chirp signal, the phase derivative of which is the specified linear sweep. This ensures that the instantaneous frequency of the output is the linear sweep you desired. For equations describing the linear, quadratic, and logarithmic sweeps, see Equations for Output Computation.

Output Computation Method for Swept Cosine Frequency Sweep.   To generate the swept cosine chirp signal, the block sets the swept cosine chirp output as follows.

Swept cosine chirp output (Equation 7-1 does not hold.)

Note that Equation 7-1 does not hold for the swept cosine chirp, so the user-defined frequency sweep, f_i(t), is not the actual output frequency sweep, f_i(actual)(t), of the swept cosine chirp. Thus, the swept cosine output may not behave as you expect. To learn more about swept cosine chirp behavior, see Cautions Regarding the Swept Cosine Sweep and Equations for Output Computation.

Cautions Regarding the Swept Cosine Sweep

If you want a linearly swept chirp signal, we recommend you use a linear frequency sweep. Though a swept cosine frequency sweep also yields a linearly swept chirp signal, the output may have unexpected frequency content. For details, see the following two sections.

Swept Cosine Instantaneous Output Frequency at the Target Time is not the Target Frequency.   The swept cosine sweep value at the Target time is not necessarily the Target frequency. This is because the user-specified sweep is not the actual frequency sweep of the swept cosine output, as noted in Output Computation Method for Swept Cosine Frequency Sweep. See Table 7-1, Instantaneous Frequency Sweep Values, for the actual value of the swept cosine sweep at the Target time.

Swept Cosine Output Frequency Content May Greatly Exceed Frequencies in the Sweep.   In Swept cosine mode, you should not set the parameters so that 1/Tsw is very large compared to the values of the Initial frequency and Target frequency parameters. In such cases, the actual frequency content of the swept cosine sweep may be closer to 1/Tsw, far exceeding the Initial frequency and Target frequency parameter values.

Examples

The first few examples demonstrate how to use the Chirp block's main parameters, how to view the output in the time domain, and how to view the output spectrogram:

• Example 1: Setting a Final Frequency Value for Unidirectional Sweeps
• Example 2: Bidirectional Sweeps
• Example 3: When Sweep Time is Greater Than Target Time

Examples 4 and 5 illustrate Chirp block settings that may produce unexpected outputs:

• Example 4: Output Sweep with Negative Frequencies
• Example 5: Output Sweep with Frequencies Greater Than Half the Sampling Frequency

Example 1: Setting a Final Frequency Value for Unidirectional Sweeps.   Often times, you may want a unidirectional sweep for which you know the initial and final frequency values. You can specify the final frequency of a unidirectional sweep by setting Target time equal to Sweep time, in which case the Target frequency becomes the final frequency in the sweep. The following model demonstrates this method.

This technique may not work for swept cosine sweeps. For details, see Cautions Regarding the Swept Cosine Sweep.

Open the Example 1 model by clicking here in the MATLAB Help Browser. You can also rebuild the model yourself; see the following list for model parameter settings (leave unlisted parameters in their default states).

Since Target time is set to equal Sweep time (1 second), the Target frequency (25 Hertz) is the final frequency of the unidirectional sweep. 

Run your model to see the time domain output, and then type the following command to view the chirp output spectrogram.

specgram(dsp_examples_yout,[0:.01:40],400,hamming(128),110)

Chirp Block Parameters for Example 1
Frequency sweep	Linear
Sweep mode	Unidirectional
Initial frequency	0
Target frequency	25
Target time	1
Sweep time	1
Initial phase	0
Sample time	1/400
Samples per frame	400
Vector Scope Block Parameters for Example 1
Input domain	Time
Time display span	6
Signal To Workspace Block Parameters for Example 1
Variable name	dsp_examples_yout
Simulation Parameters Dialog Parameters for Example 1
Stop time	5

Example 2: Bidirectional Sweeps.   Change the Sweep mode parameter in the Example 1 model to Bidirectional, and leave all other parameters the same to view the following bidirectional chirp. Note that in the bidirectional sweep, the period of the sweep is twice the Sweep time (2 seconds), whereas it was one Sweep time (1 second) for the unidirectional sweep in Example 1.

Open the Example 2 model by clicking here in the MATLAB Help Browser.

Run your model to see the time domain output, and then type the following command to view the chirp output spectrogram.

• specgram(dsp_examples_yout,[0:.01:40],400,hamming(128),110)
  

Example 3: When Sweep Time is Greater Than Target Time.   Setting Sweep time to 1.5 and leaving the rest of the parameters as in the Example 1 model gives the following output. The sweep still reaches the Target frequency (25 Hertz) at the Target time (1 second), but since Sweep time is greater than Target time, the sweep continues on its linear path until one Sweep time (1.5 seconds) is traversed.

Unexpected behavior may arise when you set Sweep time greater than Target time; see Example 4: Output Sweep with Negative Frequencies for details.

Open the Example 3 model by clicking here in the MATLAB Help Browser.  

Run your model to see the time domain output, and then type the following command to view the chirp output spectrogram.

• specgram(dsp_examples_yout,[0:.01:40],400,hamming(128),110)
  

Example 4: Output Sweep with Negative Frequencies.   Modify the Example 1 model by changing Sweep time to 1.5, Initial frequency to 25, and Target frequency to 0. The output chirp of this example may not behave as you expect because the sweep contains negative frequencies between 1 and 1.5 seconds. The sweep reaches the Target frequency of 0 Hertz at one second, then continues on its negative slope, taking on negative frequency values until it traverses one Sweep time (1.5 seconds).

The spectrogram may reflect negative sweep frequencies along the x-axis so they appear to be positive, as in the one below. If you unexpectedly get a chirp output with a spectrogram resembling the one following, your chirp's sweep may contain negative frequencies. See the next example for another possible unexpected chirp output.

Open the Example 4 model by clicking here in the MATLAB Help Browser.

Run your model to see the time domain output, and then type the following command to view the chirp output spectrogram.

• specgram(dsp_examples_yout,[0:.1:30],400,hamming(128),110); 
  

Example 5: Output Sweep with Frequencies Greater Than Half the Sampling Frequency.   Modify the Example 1 model by changing the Target frequency parameter to 275. The output chirp of this model may not behave as you expect because the sweep contains frequencies greater than half the sampling frequency (200 Hertz), which causes aliasing. If you unexpectedly get a chirp output with a spectrogram resembling the one following, your chirp's sweep may contain frequencies greater than half the sampling frequency. See the previous example for another possible unexpected chirp output.

Open the Example 5 model by clicking here in the MATLAB Help Browser.

Run your model to see the time domain output, and then type the following command to view the chirp output spectrogram.

• specgram(dsp_examples_yout,256,400,hamming(64),60)
  

Dialog Box

Frequency sweep

The type of output instantaneous frequency sweep, f_i(t): Linear, Logarithmic, Quadratic, or Swept cosine. Tunable.

Sweep mode

The directionality of the chirp signal: Unidirectional or Bidirectional. Tunable.

Initial frequency (Hz)

For Linear, Quadratic, and Swept cosine sweeps, the initial frequency, f₀, of the output chirp signal. For Logarithmic sweeps, Initial frequency is one less than the actual initial frequency of the sweep. Also, when the sweep is Logarithmic, you must set the Initial frequency to be less than the Target frequency. Tunable.

Target frequency (Hz)

For Linear, Quadratic, and Logarithmic sweeps, the instantaneous frequency, f_i(t_g), of the output at the Target time, t_g. For a Swept cosine sweep, Target frequency is the instantaneous frequency of the output at half the Target time, t_g/2. When Frequency sweep is Logarithmic, you must set the Target frequency to be greater than the Initial frequency. Tunable.

Target time (sec)

For Linear, Quadratic, and Logarithmic sweeps, the time, t_g, at which the Target frequency, f_i(t_g), is reached by the sweep. For a Swept cosine sweep, Target time is the time at which the sweep reaches 2f_i(t_g) - f₀. You must set Target time to be no greater than Sweep time,  . Tunable.

Sweep time (sec)

In Unidirectional Sweep mode, the Sweep time, Tsw, is the period of the output frequency sweep. In Bidirectional Sweep mode, the Sweep time is half the period of the output frequency sweep. You must set Sweep time to be no less than Target time,  . Tunable.

Initial phase (radians)

The phase,  , of the cosine output at t=0;  . Tunable.

Sample time

The sample period, T_s, of the output. The output frame period is M_o*T_s.

Samples per frame

The number of samples, M_o, to buffer into each output frame.

Output data type

The data type of the output, single-precision or double-precision.

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Signal From Workspace	DSP Blockset
Signal Generator	Simulink
Sine Wave	DSP Blockset
chirp	Signal Processing Toolbox
specgram	Signal Processing Toolbox

Also see the following topics:

• Creating Signals Using Signal Generator Blocks -- How to use this and other blocks to generate signals
• DSP Sources -- List of all blocks in the DSP Sources library

Check Signal Attributes

Cholesky Factorization