Signal Processing Blockset™

Minimum - Find minimum values in input or sequence of inputs

Library

Statistics

dspstat3

Description

The Minimum block identifies the value and/or position of the smallest element in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input. The Minimum block can also track the minimum values in a sequence of inputs over a period of time. The Mode parameter specifies the block's mode of operation, and can be set to Value, Index, Value and Index, or Running.

The Minimum block supports real and complex floating-point, fixed-point, and Boolean inputs. Real fixed-point inputs can be either signed or unsigned, while complex fixed-point inputs must be signed. The data type of the minimum values output by the block match the data type of the input. The index values output by the block are double when the input is double, and uint32 otherwise.

The frame status of the block output is the same as that of the input, except when the Find the minimum value of parameter is set to Entire input. The output is always sample-based when Entire input is selected.

For the Value, Index, and Value and Index modes, the Minimum block produces identical results as the MATLAB^® min function when it is called as [y I] = min(u,[],D), where u and y are the input and output, respectively, D is the dimension, and I is the index.

Value Mode

When the Mode parameter is set to Value, the block computes the minimum value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input at each sample time, and outputs the array y. Each element in y is the minimum value in the corresponding column, row, vector, or entire input. The output y depends on the setting of the Find the minimum value over parameter. For example, consider a 3-dimensional input signal of size M-by-N-by-P:

• Each row — The output at each sample time consists of an M-by-1-by-P array, where each element contains the minimum value of each vector over the second dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is an M-by-1 column vector. In this mode, the frame status of the output is the same as that of the input.

• Each column — The output at each sample time consists of a 1-by-N-by-P array, where each element contains the minimum value of each vector over the first dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is a 1-by-N row vector. In this mode, the frame status of the output is the same as that of the input.

  For convenience, length-M 1-D vector inputs are treated as M-by-1 column vectors when the block is in this mode. Sample-based length-M row vector inputs are also treated as M-by-1 column vectors when the Treat sample-based row input as a column check box is selected.

• Entire input — The output at each sample time is a scalar that contains the minimum value in the M-by-N-by-P input matrix. In this mode, the block output is always sample based.

• Specified dimension — The output at each sample time depends on Dimension. If Dimension is set to 1, the output is the same as when you select Each column. If Dimension is set to 2, the output is the same as when you select Each row. If Dimension is set to 3, the output at each sample time is an M-by-N matrix containing the minimum value of each vector over the third dimension of the input. In this mode, the frame status of the output is the same as that of the input.

For complex inputs, the block selects the value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input that has the minimum magnitude squared as shown below. For complex value , the magnitude squared is .

Index Mode

When Mode is set to Index, the block computes the minimum value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input, and outputs the index array I. Each element in I is an integer indexing the minimum value in the corresponding column, row, vector, or entire input. The output I depends on the setting of the Find the minimum value over parameter. For example, consider a 3-dimensional input signal of size M-by-N-by-P:

• Each row — The output at each sample time consists of an M-by-1-by-P array, where each element contains the index of the minimum value of each vector over the second dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is an M-by-1 column vector. In this mode, the frame status of the output is the same as that of the input.

• Each column — The output at each sample time consists of a 1-by-N-by-P array, where each element contains the index of the minimum value of each vector over the first dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is an Mx1 column vector. In this mode, the frame status of the output is the same as that of the input.

  For convenience, length-M 1-D vector inputs are treated as M-by-1 column vectors when the block is in this mode. Sample-based length-M row vector inputs are also treated as M-by-1 column vectors when the Treat sample-based row input as a column check box is selected.

  For an input that is an M-by-N matrix, the output at each sample time is an M-by-1 column vector.

• Entire input — The output at each sample time is a 1-by-3 vector that contains the location of the minimum value in the M-by-N-by-P input matrix. In this mode, the block output is always sample based. For an input that is an M-by-N matrix, the output will be a 1-by-2 vector.

• Specified dimension — The output at each sample time depends on Dimension. If Dimension is set to 1, the output is the same as when you select Each column. If Dimension is set to 2, the output is the same as when you select Each row. If Dimension is set to 3, the output at each sample time is an M-by-N matrix containing the indices of the minimum values of each vector over the third dimension of the input. In this mode, the frame status of the output is the same as that of the input.

When a minimum value occurs more than once, the computed index corresponds to the first occurrence. For example, when the input is the column vector [-1 2 3 2 -1]', the computed one-based index of the minimum value is 1 rather than 5 when Each column is selected.

Value and Index Mode

When Mode is set to Value and Index, the block outputs both the minima and the indices.

Running Mode

When Mode is set to Running, the block tracks the minimum value of each channel in a time sequence of M-by-N inputs. For sample-based inputs, the output is a sample-based M-by-N array with each element y_ij containing the minimum value observed in element u_ij for all inputs since the last reset. For frame-based inputs, the output is a frame-based M-by-N array with each element y_ij containing the minimum value observed in the jth column of all inputs since the last reset, up to and including element u_ij of the current input.

N-D signals cannot be frame based. When the block is set to Running mode, each element of the N-D signal is considered as a separate channel. There are channels, where d_i is the size of the ith dimension.

Resetting the Running Minimum

The block resets the running minimum whenever a reset event is detected at the optional Rst port. The reset sample time must be a positive integer multiple of the input sample time.

When the block is reset for sample-based inputs, the running minimum for each channel is initialized to the value in the corresponding channel of the current input. For frame-based inputs, the running minimum for each channel is initialized to the earliest value in each channel of the current input.

You specify the reset event by the Reset port parameter:

• None — Disables the Rst port

• Rising edge — Triggers a reset operation when the Rst input does one of the following:

  • Rises from a negative value to a positive value or zero

  • Rises from zero to a positive value, where the rise is not a continuation of a rise from a negative value to zero (see the following figure)

    

• Falling edge — Triggers a reset operation when the Rst input does one of the following:

  • Falls from a positive value to a negative value or zero

  • Falls from zero to a negative value, where the fall is not a continuation of a fall from a positive value to zero (see the following figure)

    

• Either edge — Triggers a reset operation when the Rst input is a Rising edge or Falling edge (as described above)

• Non-zero sample — Triggers a reset operation at each sample time that the Rst input is not zero

Note   When running simulations in the Simulink® MultiTasking mode, reset signals have a one-sample latency. Therefore, when the block detects a reset event, there is a one-sample delay at the reset port rate before the block applies the reset. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Models with Multiple Sample Rates in the Real-Time Workshop® User's Guide.

Fixed-Point Data Types

The parameters on the Fixed-point pane of the block dialog are only used for complex fixed-point inputs. The sum of the squares of the real and imaginary parts of such an input are formed before a comparison is made, as described in Value Mode. The results of the squares of the real and imaginary parts are placed into the product output data type. The result of the sum of the squares is placed into the accumulator data type. These parameters are ignored for other types of inputs.

Examples

The Minimum block in the following model calculates the running minimum of a frame-based 3-by-2 (two-channel) matrix input. The running minimum is reset at t=2 by an impulse to the block's Rst port.

The Minimum block has the following settings:

• Mode = Running

• Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

• Signal = u

• Sample time = 1/3

• Samples per frame = 3

where

u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 2 6 2 5 0 4 17]' 

The Discrete Impulse block has the following settings:

• Delay (samples) = 2

• Sample time = 1

• Samples per frame = 1

The block's operation is shown in the figure below.

Dialog Box

The Main pane of the Minimum block dialog appears as follows.

Mode

Specify the block's mode of operation:

• Value — Output the minimum value of each input

• Index — Output the index of the minimum value

• Value and index — Output both the value and the index

• Running — Track the minimum value of the input sequence over time

For more information, see Description.

Index base

Specify whether the index of the minimum value is reported using one-based or zero-based numbering. This parameter is only visible when the Mode parameter is set to Index or Value and index.

Find the minimum value over

Specify whether to find the minimum value along rows, columns, entire input, or the dimension specified in the Dimension parameter. For more information, see Description.

Treat sample-based row input as a column

Select to treat sample-based length-M row vector inputs as M-by-1 column vectors. This parameter is only visible when the Find the minimum value of parameter is set to Each column.

Reset port

Specify the reset event detected at the RST input port when you select Running for the Mode parameter. The rate of the reset signal must be a positive integer multiple of the rate of the data signal input. This parameter is enabled only when you set the Mode parameter to Running. For information about the possible values of this parameter, see Resetting the Running Minimum.

Dimension

Specify the dimension (one-based value) of the input signal, over which the minimum is computed. The value of this parameter cannot exceed the number of dimensions in the input signal. This parameter is only visible when the Find the minimum value over parameter is set to Specified dimension.

The Fixed-point pane of the Minimum block dialog appears as follows.

Note   The parameters on the Fixed-point pane are only used for complex fixed-point inputs. The sum of the squares of the real and imaginary parts of such an input are formed before a comparison is made, as described in Value Mode. The results of the squares of the real and imaginary parts are placed into the product output data type. The result of the sum of the squares is placed into the accumulator data type. These parameters are ignored for other types of inputs.

Rounding mode

Select the rounding mode for fixed-point operations.

Overflow mode

Select the overflow mode for fixed-point operations.

Product output

Use this parameter to specify how you would like to designate the product output word and fraction lengths resulting from a complex-complex multiplication in the block. See Multiplication Data Types for more information:

• When you select Same as input, these characteristics match those of the input to the block.

• When you select Binary point scaling, you can enter the word length and the fraction length of the product output, in bits.

• When you select Slope and bias scaling, you can enter the word length, in bits, and the slope of the product output. This block requires power-of-two slope and a bias of zero.

Accumulator

Use this parameter to specify the accumulator word and fraction lengths resulting from a complex-complex multiplication in the block. See Multiplication Data Types for more information:

• When you select Same as product output, these characteristics match those of the product output.

• When you select Same as input, these characteristics match those of the input to the block.

• When you select Binary point scaling, you can enter the word length and the fraction length of the accumulator, in bits.

• When you select Slope and bias scaling, you can enter the word length, in bits, and the slope of the accumulator. This block requires power-of-two slope and a bias of zero.

Lock scaling against changes by the autoscaling tool

Select this parameter to prevent any fixed-point scaling you specify in this block mask from being overridden by the autoscaling feature of the Fixed-Point Tool. See the fxptdlg reference page for more information.

Supported Data Types

See Also

Median

Modified Covariance AR Estimator