DSP Blockset

Variable Integer Delay

Delay the input by a time-varying integer number of sample periods.

Library

Signal Operations

Description

The Variable Integer Delay block delays the discrete-time input at the In port by the integer number of sample intervals specified by the input to the Delay port. The Delay port input rate must be an integer multiple of the In port input rate. The delay for a sample-based input sequence is a scalar value to uniformly delay every channel. The delay for a frame-based input sequence can be a scalar value to uniformly delay every sample in every channel, a vector containing one delay value for each sample in the input frame, or a vector containing one delay value for each channel in the input frame.

The delay values should be in the range of 0 to D, where D is the Maximum delay. Delay values greater than D or less than 0 are clipped to those respective values and noninteger delays are rounded to the nearest integer value.

The Variable Integer Delay block differs from the Integer Delay block in the following ways.

Variable Integer Delay	Integer Delay
Delay is provided as an input to the Delay port.	Delay is specified as a parameter setting in the dialog box.
Delay can vary with time; for example, for a frame-based input, the nth element's delay in the first input frame can differ from the nth element's delay in the second input frame.	Delay cannot vary with time; for example, for a frame-based input, the nth element's delay is the same for every input frame.

Sample-Based Operation

When the input is an M-by-N sample-based matrix, the block treats each of the M*N matrix elements as an independent channel, and applies the delay at the Delay port to each channel.

The Variable Integer Delay block stores the D+1 most recent samples received at the In port for each channel. At each sample time the block outputs the stored sample(s) indexed by the input to the Delay port.

For example, if the input to the In port, u, is a scalar signal, the block stores a vector, U, of the D+1 most recent signal samples. If the current input sample is U(1), the previous input sample is U(2), and so on, then the block's output is

• y = U(v+1);          % Equivalent MATLAB code
  

where v is the input to the Delay port. Note that a delay value of 0 (v=0) causes the block to pass through the sample at the In port in the same simulation step that it is received. The block's memory is initialized to the Initial conditions value at the start of the simulation (see below).

The figure below shows the block output for a scalar ramp sequence at the In port, a Maximum delay of 5, an Initial conditions of 0, and a variety of different delays at the Delay port.

Note that the current input at each time-step is immediately stored in memory as U(1). This allows the current input to be available at the output for a delay of 0 (v=0).

The Initial conditions parameter specifies the values in the block's memory at the start of the simulation. Unlike the Integer Delay block, the Variable Integer Delay block does not have a fixed initial delay period during which the initial conditions appear at the output. Instead, the initial conditions are propagated to the output only when they are indexed in memory by the value at the Delay port. Both fixed and time-varying initial conditions can be specified in a variety of ways to suit the dimensions of the input sequence.

Fixed Initial Conditions.   The settings shown below specify fixed initial conditions. For a fixed initial condition, the block initializes each of D samples in memory to the value entered in the Initial conditions parameter. A fixed initial condition in sample-based mode can be specified in one of the following ways:

• Scalar value with which to initialize every sample of every channel in memory. For a general M-by-N input and the parameter settings below,

  

• the block initializes 100 M-by-N matrices in memory with zeros.

• Array of size M-by-N-by-D. In this case, you can specify different fixed initial conditions for each channel. See the Array bullet in Time-Varying Initial Conditions below for details.

Initial conditions cannot be specified by full matrices.

Time-Varying Initial Conditions.   The following settings specify time-varying initial conditions. For a time-varying initial condition, the block initializes each of D samples in memory to one of the values entered in the Initial conditions parameter. This allows you to specify a unique output value for each sample in memory. A time-varying initial condition in sample-based mode can be specified in one of the following ways:

• Vector containing D elements with which to initialize memory samples U(2:D+1), where D is the Maximum delay. For a scalar input and the parameters shown below,

  

• the block initializes U(2:6) with values [-1, -1, -1, 0, 1].

• Array of dimension M-by-N-by-D with which to initialize memory samples U(2:D+1), where D is the Maximum delay and M and N are the number of rows and columns, respectively, in the input matrix. For a 2-by-3 input and the parameters below,

  

• the block initializes memory locations U(2:5) with values

An array initial condition can only be used with matrix inputs.

Initial conditions cannot be specified by full matrices.

Frame-Based Operation

When the input is an M-by-N frame-based matrix, the block treats each of the N input columns as a frame containing M sequential time samples from an independent channel.

In frame-based mode, the input at the Delay port can be a scalar value to uniformly delay every sample in every channel. It can also be a length-M vector, v = [v(1) v(2) ... v(M)], containing one delay for each sample in the input frame(s). The set of delays contained in vector v is applied identically to every channel of a multichannel input. The Delay port entry can also be a length-N vector, containing one delay for each channel.

Vector v does not specify when the samples in the current input frame will appear in the output. Rather, v indicates which previous input samples (stored in memory) should be included in the current output frame. The first sample in the current output frame is the input sample v(1) intervals earlier in the sequence, the second sample in the current output frame is the input sample v(2) intervals earlier in the sequence, and so on.

The illustration below shows how this works for an input with a sample period of 1 and frame size of 4. The Maximum delay (Dmax) is 5, and the Initial conditions parameter is set to -1. The delay input changes from [1 3 0 5] to [2 0 0 2] after the second input frame. Note that the samples in each output frame are the values in memory indexed by the elements of v.

• y(1) = U(v(1)+1)
  y(2) = U(v(2)+1)
  y(3) = U(v(3)+1)
  y(4) = U(v(4)+1)
  
  
  

The Initial conditions parameter specifies the values in the block's memory at the start of the simulation. Both fixed and time-varying initial conditions can be specified.

Fixed Initial Conditions.   The settings shown below specify fixed initial conditions. For a fixed initial condition, the block initializes each of D samples in memory to the value entered in the Initial conditions parameter. A fixed initial condition in frame-based mode can be one of the following:

• Scalar value with which to initialize every sample of every channel in memory. For a general M-by-N input with the parameter settings below,

  

• the block initializes five samples in memory with zeros.

• Array of size 1-by-N-by-D. In this case, you can specify different fixed initial conditions for each channel. See the Array bullet in Time-Varying Initial Conditions below for details.

Initial conditions cannot be specified by full matrices.

Time-Varying Initial Conditions.   The following setting specifies a time-varying initial condition. For a time-varying initial condition, the block initializes each of D samples in memory to one of the values entered in the Initial conditions parameter. This allows you to specify a unique output value for each sample in memory. A time-varying initial condition in frame-based mode can be specified in the following way:

• Vector of dimensions 1-by-D. In this case, all channels have the same set of time-varying initial conditions specified by the entries of the vector. For the ramp input [100; 100]' with a frame size of 4, delay of 5, and the parameter settings below,

  

• the block outputs the following sequence of frames at the start of the simulation.

• Array of size 1-by-N-by-D. In this case, you can specify different time-varying initial conditions for each channel. For the ramp input [100; 100]' with a frame size of 4, delay of 5, and the parameter settings below,

  

• the block outputs the following sequence of frames at the start of the simulation.

• Note that by specifying a 1-by-N-by-D initial condition array such that each 1-by-N vector entry is identical, you can implement different fixed initial conditions for each channel.

Initial conditions cannot be specified by full matrices.

Dialog Box

Maximum delay

The maximum delay that the block can produce for any sample. Delay input values exceeding this maximum are clipped at the maximum.

Initial conditions

The values with which the block's memory is initialized.

Supported Data Types

• Double-precision floating point
• Single-precision floating point
• Fixed-point
• Custom data types
• Boolean
• 8-, 16-, and 32-bit signed integers
• 8-, 16-, and 32-bit unsigned integers

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

Integer Delay	DSP Blockset
Variable Fractional Delay	DSP Blockset

Also see Signal Operations for a list of all the blocks in the Signal Operations library.

Variable Fractional Delay

Variable Selector