DSP Blockset

Chirp

Generate a swept-frequency cosine.

Library

DSP Sources

Description

The Chirp block generates a unity-amplitude swept-frequency cosine (chirp) signal. The instantaneous output frequency is initialized to the Initial frequency parameter value, f(0), and then varies continuously for the duration of the Sweep period. The curve of the transition between these two frequencies is specified by the Frequency sweep parameter, and can be Swept cosine, Linear, Quadratic, or Logarithmic.

When Sweep mode is set to Unidirectional, the cosine frequency is immediately reset to f(0) after the Sweep period is traversed. Thus, the block repeats the unidirectional frequency sweep at the interval specified by the Sweep period, Tsw. When the Sweep mode is set to Bidirectional, the frequency sweep reverses direction half way through the period, and returns to f(0) along a symmetrical trajectory. The block repeats the bidirectional frequency sweep at the interval specified by the Sweep period as well.

The method that the block uses to transition between the specified instantaneous frequencies is set by the Frequency sweep parameter, and can be Swept cosine, Linear, Quadratic, or Logarithmic. You must choose the Target time, t_g, and Target frequency, f(t_g), to appropriately set the value for the constant term in the formulas below. Note that the instantaneous frequency at the end of a frequency sweep is defined to be the value of the frequency sweep function at the sweep period, or f(Tsw).

• Swept cosine is similar to Linear, described below, but does not compensate for high frequencies introduced by short signal durations. As a result, the actual frequency content of the chirp signal may be far greater than the frequency range specified by f(t₀) and f(Tsw). The Linear, Quadratic, and Logarithmic frequency sweeps compensate for such signal transients; most of the frequencies generated by these methods lie within the range between f(0) and f(t_g).
• Linear uses an instantaneous frequency sweep f(t) of

where

• Quadratic uses an instantaneous frequency sweep f(t) of

where is the same as in the linear case.

• Logarithmic uses an instantaneous frequency sweep f(t) of

where

For the logarithmic sweep, the Frequency at target time parameter value must be greater than the Initial frequency parameter value. That is, f(t_g) > f(0).

Dialog Box

Frequency sweep

The type of function that defines the instantaneous frequency trajectory. Tunable.

Sweep mode

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

Initial frequency (Hz)

The initial frequency, f(0), of the output cosine. Tunable.

Target frequency (Hz)

The frequency, f(t_g), that, along with the target time, t_g, defines the value of the constant in the frequency sweep function. Tunable.

Target time (sec)

The target time t_g corresponding to the terminal frequency f(t_g). Tunable.

Sweep period (sec)

The interval Tsw between successive repetitions of the frequency sweep. 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.

See Also

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

See Creating Signals Using Signal Generator Blocks for related information.

Check Signal Attributes

Cholesky Factorization