Integer Delay (DSP Blockset)

Delay an input by an integer number of sample periods.

Library

Description

The Integer Delay block delays a discrete-time input by the number of sample intervals specified in the Delay parameter. Noninteger delay values are rounded to the nearest integer, and negative delays are clipped at 0.

Sample-Based Operation

When the input is a sample-based M-by-N matrix, the block treats each of the M*N matrix elements as an independent channel. The Delay parameter, v, can be an M-by-N matrix of positive integers that specifies the number of sample intervals to delay each channel of the input, or a scalar integer by which to equally delay all channels.

For example, if the input is M-by-1 and v is the matrix [v(1) v(2) ... v(M)]', the first channel is delayed by v(1) sample intervals, the second channel is delayed by v(2) sample intervals, and so on. Note that when a channel is delayed for sample-time units, the output sample at time is the input sample at time . If is negative, then the output is the corresponding value specified by the Initial conditions parameter.

A 1-D vector of length M is treated as an M-by-1 matrix, and the output is 1-D.

The Initial conditions parameter specifies the output of the block during the initial delay in each channel. The initial delay for a particular channel is the time elapsed from the start of the simulation until the first input in that channel is propagated to the output. Both fixed and time-varying initial conditions can be specified in a variety of ways to suit the dimensions of the input.

Fixed Initial Conditions. A fixed initial condition in sample-based mode can be specified as one of the following:

Scalar value to be repeated at each sample time of the initial delay (for every channel). For a 2-by-2 input with the parameter settings below,

the block generates the following sequence of matrices at the start of the simulation,

where

is the i,jth element of the kth matrix in the input sequence.

Array of size M-by-N-by-d. In this case, you can set different fixed initial conditions for each element of a sample-based input. This setting is explained further in the Array bullet in Time-Varying Initial Conditions below.

Initial conditions cannot be specified by full matrices.

Time-Varying Initial Conditions. A time-varying initial condition in sample-based mode can be specified in one of the following ways:

Vector of length d, where d is the maximum value specified for any channel in the Delay parameter. The vector can be a L-by-d, 1-by-d, or 1-by-1-by-d. The d elements of the vector are output in sequence, one at each sample time of the initial delay.

For a scalar input and the parameters shown below,

the block outputs the sequence -1, -1, -1, 0, 1,... at the start of the simulation.

Array of dimension M-by-N-by-d, where d is the value specified for the Delay parameter (the maximum value if the Delay is a vector) and M and N are the number of rows and columns, respectively, in the input matrix. The d pages of the array are output in sequence, one at each sample time of the initial delay. For a 2-by-3 input, and the parameters below,

the block outputs the matrix sequence

at the start of the simulation. Note that setting Initial conditions to an array with the same matrix for each entry implements constant initial conditions; a different constant initial condition for each input matrix element (channel).

Initial conditions cannot be specified by full matrices.

Frame-Based Operation

When the input is a frame-based M-by-N matrix, the block treats each of the N columns as an independent channel, and delays each channel as specified by the Delay parameter.

For frame-based inputs, the Delay parameter can be a scalar integer by which to equally delay all channels. It can also be a 1-by-N row vector, each element of which serves as the delay for the corresponding channel of the N-channel input. Likewise, it can also be an M-by-1 column vector, each element of which serves as the delay for one of the corresponding M samples for each channel. The Delay parameter can be an M-by-N matrix of positive integers as well; in this case, each element of each channel is delayed by the corresponding element in the delay matrix. For instance, if the fifth element of the third column of the delay matrix was 3, then the fifth element of the third channel of the input matrix is always delayed by three sample-time units.

When a channel is delayed for sample-time units, the output sample at time is the input sample at time . If is negative, then the output is the corresponding value specified in the Initial conditions parameter.

The Initial conditions parameter specifies the output during the initial delay. Both fixed and time-varying initial conditions can be specified. The initial delay for a particular channel is the time elapsed from the start of the simulation until the first input in that channel is propagated to the output.

Fixed Initial Conditions. The settings shown below specify fixed initial conditions. The value entered in the Initial conditions parameter is repeated at the output for each sample time of the initial delay. A fixed initial condition in frame-based mode can be one of the following:

Scalar value to be repeated for all channels of the output at each sample time of the initial delay. For a general M-by-N input with the parameter settings below,

the first five samples in each of the N channels are zero. Note that if the frame size is larger than the delay, all of these zeros are all included in the first output from the block.

Array of size 1-by-N-by-D. In this case, you can also 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 time-varying initial conditions, the values specified in the Initial conditions parameter are output in sequence during the initial delay. A time-varying initial condition in frame-based mode can be specified in the following ways:

Vector of length D, where each of the N channels have the same initial conditions sequence specified in the vector. D is defined as follows:

When an element of the delay entry is less than the frame size,

D = d + 1

where d is the maximum delay.

When the all elements of the delay entry are greater than the input frame size,

D = d + input frame size - 1

Only the first d entries of the initial condition vector will be used; the rest of the values are ignored, but you must include them nonetheless. For a two-channel ramp input [1:100; 1:100]' with a frame size of 4 and the parameter settings below,

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

Note that since one of the delays, 2, is less than the frame size of the input, 4, the length of the Initial conditions vector is the sum of the maximum delay and 1 (5+1), which is 6. The first five entries of the initial conditions vector are used by the channel with the maximum delay, and the rest of the entries are ignored. Since the first channel is delayed for less than the maximum delay (2 sample time units), it only makes use of two of the initial condition entries.

Array of size 1-by-N-by-D, where D is defined in the Vector bullet above in Time-Varying Initial Conditions. In this case, the kth entry of each 1-by-N entry in the array corresponds to an initial condition for the kth channel of the input matrix. Thus, a 1-by-N-by-D initial conditions input allows you to specify different initial conditions for each channel. For instance, for a two-channel ramp input [1:100; 1:100]' with a frame size of 4 and the parameter settings below,

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

Note that the channels have distinct time varying initial conditions; the initial conditions for channel 1 correspond to the first entry of each length-2 row vector in the initial conditions array, and the initial conditions for channel 2 correspond to the second entry of each row vector in the initial conditions array. Only the first five entries in the initial conditions array are used; the rest are ignored.

The 1-by-N-by-D array entry can also specify different fixed initial conditions for every channel; in this case, every 1-by-N entry in the array would be identical, so that the initial conditions for each column are fixed over time.

Initial conditions cannot be specified by full matrices.

Examples

The dspafxr demo illustrates an audio reverberation system built around the Integer Delay block.

Dialog Box

Delay: The number of sample periods to delay the input signal.
Initial conditions: The value of the block's output during the initial delay.

See Also

Unit Delay
Simulink

Variable Fractional Delay
DSP Blockset

Variable Integer Delay
DSP Blockset

Unit Delay	Simulink
Variable Fractional Delay	DSP Blockset
Variable Integer Delay	DSP Blockset

Inherit Complexity Kalman Adaptive Filter