Sine Wave (DSP Blockset)

Generate samples of one or more sine waves over time.

Library

DSP Sources

Description

The Sine Wave block generates one or more sinusoidal signals with independent amplitude, frequency, and phase characteristics.

The Amplitude, Frequency, and Phase parameters specify the characteristics (A,

, and

) of the generated sine waves. Each parameter value can be a scalar or a length-N vector, where N is the number of sine waves to output. A particular sine wave in the output is defined by the corresponding elements of the A,

, and

vectors. For example, A₅,

₅, and

₅ define the characteristics of the fifth sinusoid in the output, y₅. If a scalar value is specified for one of these parameters, the value is applied to each output sinusoid.

The figure below shows the block dialog configured to generate 3 sinusoidal signals:

1.: A = 1, = 2, = 0

2.: A = 2, = , = 0

3.: A = 3, = /2, = /2

The Sample mode parameter specifies the block's sampling property, Continuous or Discrete:

Continuous

In continuous mode, each sinusoid in the output, y_i, is computed as a continuous function

and the block's output is continuous. In this mode, the block's operation is the same as that of the Simulink Sine Wave block when that block's Sample time is set to 0. It offers high accuracy, but requires trigonometric function evaluations at each simulation step, which is computationally expensive. Additionally, because this method tracks absolute simulation time, a discontinuity will eventually occur when the time value reaches its maximum limit.

Discrete

In discrete mode, the block's discrete-time output can be generated by directly evaluating the trigonometric function, or by a differential method. The two options are explained below.

Discrete Computational Methods

When Discrete is selected from the Sample mode parameter, the Computation method parameter provides two options for generating the discrete sinusoid, Trigonometric functions and Differential method.

Trigonometric functions

Each sinusoid in the output, y_i, is computed by sampling the continuous function

with a period of T_s, where T_s is specified by the Sample time parameter. This mode of operation is a more efficient (but otherwise identical) implementation of a Simulink Sine Wave block with Sample time set to 0 followed by a Zero-Order Hold block with Sample time set to T_s. It shares the same benefits and liabilities as the Continuous sample mode, described above.

Differential method

The differential method uses an incremental (differential) algorithm rather than one based on absolute time. The algorithm computes the output samples based on the values computed at the previous sample time and precomputed update terms, making use of the following identities.

The update equations for each sinusoid in the output, y_i, can therefore be written in matrix form as

where T_s is specified by the Sample time parameter. Since T_s is constant, the right-hand matrix is a constant and can be computed once at the start of the simulation. The value of A_isin[_i(t+T_s)+_i] is then computed from the values of sin(_it+_i) and cos(_it+_i) by a simple matrix multiplication at each time step.

This mode of operation is the same as that of the Simulink Sine Wave block with Sample time set to a positive number (discrete). It offers reduced computational effort, but is subject to drift over time due to the cumulative quantization errors. Because the method is not contingent on an absolute time, there is no danger of discontinuity during extended operations (when an absolute time variable might overflow). This is therefore the recommended method to use when running long simulations and real-time systems.

Frame-Based Operation

In both discrete modes (differential or transcendental), the block can optionally buffer the output samples into frames.

In these modes the block computes and buffers the number of samples (for each individual sine) specified by the Samples per frame parameter value, M, and outputs this frame of samples with a frame period of M*T_s (where T_s is specified by the Sample time parameter). When the Samples per frame value is 1 (default), the block successively outputs the individual samples with a sample period of T_s.

For the general case of N independent sinusoidal outputs, the output is an M-by-N matrix with each column representing a distinct signal channel.

Dialog Box

Amplitude: A vector containing the individual amplitudes of the sine waves in the output (one amplitude for each sine), or a scalar to be applied to all. The vector length must be the same as that specified for the Frequency and Phase parameters. The amplitude values can be altered while a simulation is running, but the vector length must remain the same.
Frequency: A vector containing the frequencies of the sine waves in the output (one frequency for each sine, in rads/sec), or a scalar to be applied to all. The vector length must be the same as that specified for the Amplitude and Phase parameters. The frequency values can be altered while a simulation is running, but the vector length must remain the same. (The Frequency parameter is not tunable in Simulink's external mode when using the differential method.)
Phase: A vector containing the phase offsets of the sine waves in the output (one phase offset for each sine, in radians), or a scalar to be applied to all. The vector length must be the same as that specified for the Amplitude and Frequency parameters. The phase values can be altered while a simulation is running, but the vector length must remain the same. (The Frequency parameter is not tunable in Simulink's external mode when using the differential method.)
Sample mode: The block's sampling behavior, Continuous or Discrete.
Computation method: The method by which discrete-time sinusoids are generated.
Sample time: The period with which the sine wave is sampled, T_s. The block's output frame period is M*T_s, where M is specified by the Samples per frame parameter.
Samples per frame: The number of consecutive samples from each sinusoid to buffer into the output frame, M.
State when reenabled: The behavior of the block when a disabled subsystem that contains it is reenabled. The block can either reset itself to its starting state (Restart at time zero), or resume generating the sinusoid based on the current simulation time (Catch up to simulation time).