Minimum

Library:
DSP System Toolbox / Statistics
DSP System Toolbox HDL Support / Statistics

Ports

Input

`In` — Data input
vector | matrix | N-D array

The block accepts real-valued or complex-valued multichannel and multidimensional inputs. The input can be floating-point, fixed-point, or Boolean. Real fixed-point inputs can be either signed or unsigned. Complex fixed-point inputs must be signed.

This port is unnamed until you set the Mode parameter to Running and the Reset port parameter to any option other than None.

`Rst` — Reset port
scalar

Specify the reset event that causes the block to reset the running minimum. The sample time of the Rst input must be a positive integer multiple of the input sample time.

Dependencies

To enable this port, set the Mode parameter to Running and the Reset port parameter to any option other than None.

Output

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`Val` — Minimum values along the specified dimension
scalar | vector | matrix | N-D array

The data type of the minimum value matches the data type of the input.

When the Mode parameter is set to either Value and Index or Value, the following applies:

The size of the dimension for which the block computes the minimum value is 1. The sizes of all other dimensions match those of the input array. For example, when the input is an M-by-N-by-P array, with the dimension set to 1, the block outputs a 1-by-N-by-P array. When the dimension is set to 3, the block outputs a two-dimensional M-by-N matrix.
When the input is an M-by-N matrix, with the dimension set to 1, the block outputs a 1-by-N matrix.

If you specify the block to compute the minimum value over the entire input, the block outputs a scalar.

When the Mode parameter is set Running, the block tracks the minimum value of each channel in a time sequence of M-by-N inputs. In this mode, you must also specify the Input processing parameter as one of the following:

Elements as channels (sample based) — The block treats each element of the input as a separate channel. For a three-dimensional input signal of size M-by-N-by-P, the block outputs an M-by-N-by-P array. Each y_ijk element of the output contains the minimum value observed in element u_ijk for all inputs since the last reset.
When a reset event occurs, the running minimum y_ijk in the current frame is reset to the element u_ijk.
Columns as channels (frame based) — The block treats each column of the input as a separate channel. This option does not support an N-dimensional input signal, where N > 2. For a two-dimensional input signal of size M-by-N, the block outputs an M-by-N matrix. Each element y_ij of the output contains 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.
When a reset event occurs, the running minimum for each channel becomes the minimum value of all the samples in the current input frame, up to and including the current input sample.

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.

Dependencies

To enable this port, set the Mode parameter to either Value and Index or Value.

`Idx` — Index of the minimum values along the specified dimension
scalar | vector | matrix | N-D array

When the input is double, the index values are also double. Otherwise, the index values are uint32.

Dependencies

To enable this port, set the Mode parameter to either Value and Index or Index.

Data Types: double | uint32

Parameters

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Main Tab

`Mode` — Mode in which the block operates
`Value and Index` (default) | `Value` | `Index` | `Running`

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. Consider a three dimensional input signal of size M-by-N-by-P. Set Find the minimum value over to:
- Each row — The output y 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.
- Each column — The output y 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 block treats length-M unoriented vector inputs as M-by-1 column vectors.
- Entire input — The output y at each sample time is a scalar that contains the minimum value in the M-by-N-by-P input matrix.
- Specified dimension — The output y 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.
Complex Inputs
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 in the following figure. For complex value $u = a + b i$ , the magnitude squared is $a^{2} + b^{2}$ .
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. Consider a three dimensional input signal of size M-by-N-by-P:
- Each row — The output I 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.
- Each column — The output I 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 a 1-by-N row vector.
  In this mode, the block treats length-M unoriented vector inputs as M-by-1 column vectors.
- Entire input — The output I 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. For an input that is an M-by-N matrix, the output is a 1-by-2 vector.
- Specified dimension — The output I 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.
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 [3 2 1 2 3]', the computed one-based index of the minimum value is 1, rather than 5 when Each column is selected.
Value and Index — The block outputs 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 the corresponding index array I.
Running — The block tracks the minimum value of each channel in a time sequence of M-by-N inputs. 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. In this mode, you must also specify the Input processing parameter as one of the following:
- Elements as channels (sample based) — The block treats each element of the input as a separate channel. For a three-dimensional input signal of size M-by-N-by-P, the block outputs an M-by-N-by-P array. Each y_ijk element of the output contains the minimum value observed in element u_ijk for all inputs since the last reset.
  When a reset event occurs, the running minimum y_ijk in the current frame is reset to the element u_ijk.
- Columns as channels (frame based) — The block treats each column of the input as a separate channel. This option does not support an N-dimensional input signal, where N > 2. For a two-dimensional input signal of size M-by-N, the block outputs an M-by-N matrix. Each element y_ij of the output contains 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.
  When a reset event occurs, the running minimum for each channel becomes the minimum value of all the samples in the current input frame, up to and including the current input sample.
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.
Running Mode for Variable-Size Inputs
When the input is a variable-size signal, and you set the Mode to Running, then:
- If you set the Input processing parameter to Elements as channels (sample based), the state is reset.
- If you set the Input processing parameter to Columns as channels (frame based), then:
  - When the input size difference is in the number of channels (columns), the state is reset.
  - When the input size difference is in the length of channels (rows), there is no reset and the running operation is carried out as usual.

`Index base` — Base of the minimum value index
`One` (default) | `Zero`

Specify whether the index of the minimum value is reported using one-based or zero-based numbering.

Dependencies

To enable this parameter, set Mode to either Index or Value and Index.

`Find the minimum value over` — Dimension over which the block computes the minimum value
`Each column` (default) | `Each row` | `Entire input` | `Specified dimension`

Each column — The block outputs the minimum value over each column.
Each row — The block outputs the minimum value over each row.
Entire input — The block outputs the minimum value over the entire input.
Specified dimension — The block outputs the minimum value over the dimension specified in the Dimension parameter.

Dependencies

To enable this parameter, set Mode to Value and Index, Value, or Index.

`Dimension` — Custom dimension
`1` (default) | scalar

Specify the dimension (one-based value) of the input signal over which the block computes the minimum. The value of this parameter must be greater than 0 and less than the number of dimensions in the input signal.

Dependencies

To enable this parameter, set Find the minimum value over to Specified dimension.

`Input processing` — Method to process the input in running mode
`Columns as channels (frame based)` (default) | `Elements as channels (sample based)`

Columns as channels (frame based) — The block treats each column of the input as a separate channel. This option does not support an N-dimensional input signal, where N > 2. For a two-dimensional input signal of size M-by-N, the block outputs an M-by-N matrix. Each element y_ij of the output contains 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.
When a reset event occurs, the running minimum for each channel becomes the minimum value of all the samples in the current input frame, up to and including the current input sample.
Elements as channels (sample based) — The block treats each element of the input as a separate channel. For a three-dimensional input signal of size M-by-N-by-P, the block outputs an M-by-N-by-P array. Each y_ijk element of the output contains the minimum value observed in element u_ijk for all inputs since the last reset.
When a reset event occurs, the running minimum y_ijk in the current frame is reset to the element u_ijk.

Dependencies

To enable this parameter, set Mode to Running.

`Reset port` — Reset event
`None` (default) | `Rising edge` | `Falling edge` | `Either edge` | `Non-zero sample`

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 which is a multiple of the input sample time.

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.
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.

Either edge — Triggers a reset operation when the Rst input is a Rising edge or Falling edge.
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 Time-Based Scheduling and Code Generation (Simulink Coder).

Dependencies

To enable this parameter, set Mode to Running.

Data Types Tab

Note

To use these parameters, the data input must be complex fixed-point.

`Rounding mode` — Method of rounding operation
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Specify the rounding mode for fixed-point operations as one of the following:

Floor
Ceiling
Convergent
Nearest
Round
Simplest
Zero

For more details, see rounding mode.

`Saturate on integer overflow` — Method of overflow action
off (default) | on

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see overflow mode for fixed-point operations.

`Product output` — Product output data type
`Inherit: Same as input` (default) | `fixdt([],16,0)`

Product output specifies the data type of the output of a product operation in the Minimum block. For more information on the product output data type, see Multiplication Data Types.

Inherit: Same as input — The block specifies the product output data type to be the same as the input data type.
fixdt([],16,0) — The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Product output data type by using the Data Type Assistant. To use the assistant, click the Show data type assistant button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

`Accumulator` — Accumulator data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `fixdt([],16,0)`

Accumulator specifies the data type of the output of an accumulation operation in the Minimum block.

Inherit: Same as product output — The block specifies the accumulator data type to be the same as the product output data type.
Inherit: Same as input — The block specifies the accumulator data type to be the same as the input data type.
fixdt([],16,0) — The block specifies an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Accumulator data type by using the Data Type Assistant. To use the assistant, click the Show data type assistant button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

`Lock data type settings against changes by the fixed-point tools` — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block dialog.

Model Examples

Compute the Minimum

Simulink model example to compute the minimum using the Minimum block.

Compute the Running Minimum

Simulink model example to compute the running minimum using the Minimum block.

Block Characteristics

Data Types	`double` \| `fixed point` \| `integer` \| `single`
Direct Feedthrough	`no`
Multidimensional Signals	`no`
Variable-Size Signals	`yes`
Zero-Crossing Detection	`no`

Algorithms

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Minimum

When you set Mode to one of Value, Index, or Value and Index, and specify a dimension, the block produces results identical to the MATLAB^® min function, when it is called as [y,I] = min(u,[],D).

u is the data input.
D is the dimension.
y is the minimum value.
I is the index of the minimum value.

The minimum value along the entire input is identical to calling the min function as [y,I] = min(u(:)).

Running Minimum

When you set Mode to Running, and Input processing to Columns as channels (frame based), the block treats each column of the input as a separate channel. In this example, the block processes a two-channel signal with a frame size of three under these settings.

The block outputs the minimum value over each channel since the last reset. At t = 2, the reset event occurs. The minimum value in the second column changes to 6, and then 2, even though these values are greater than 1, which was the minimum value since the previous reset event.

When you set Mode to Running, and Input processing to Elements as channels (sample based), the block treats each element of the input as a separate channel. In this example, the block processes a two-channel signal with a frame size of three under these settings.

Each element y_ij of the output contains the minimum value observed in element u_ij for all inputs since the last reset. The reset event occurs at t = 2. When a reset event occurs, the running minimum, y_ij, in the current frame is reset to the element u_ij.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has multi-cycle implementations that introduce additional latency in the generated code. To see the added latency, view the generated model or validation model. See Generated Model and Validation Model (HDL Coder).

Architecture	Additional cycles of latency	Description
`default` `Tree`	0	Generates a tree structure of comparators.
`Cascade`	1, when block has a single vector input port.	This implementation is optimized for latency * area, with medium speed. See Cascade Architecture Best Practices (HDL Coder).

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is `0`. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see OutputPipeline (HDL Coder).
InstantiateStages	Generate a VHDL^® `entity` or Verilog^® `module` for each cascade stage. The default is `off`. See also InstantiateStages (HDL Coder).
SerialPartition	Specify partitions for Cascade-serial implementations as a vector of the lengths of each partition. The default setting uses the minimum number of stages. See also SerialPartition (HDL Coder).

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

The parameters on the Data Types Tab of the block are used only 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 under the 'Mode' parameter in Main Tab. 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.

Documentation

Minimum

Description

Ports

Input

In — Data input vector | matrix | N-D array

Rst — Reset port scalar

Dependencies

Output

Val — Minimum values along the specified dimension scalar | vector | matrix | N-D array

Dependencies

Idx — Index of the minimum values along the specified dimension scalar | vector | matrix | N-D array

Dependencies

Parameters

Main Tab

Mode — Mode in which the block operates Value and Index (default) | Value | Index | Running

Index base — Base of the minimum value index One (default) | Zero

Dependencies

Find the minimum value over — Dimension over which the block computes the minimum value Each column (default) | Each row | Entire input | Specified dimension

Dependencies

Dimension — Custom dimension 1 (default) | scalar

Dependencies

Input processing — Method to process the input in running mode Columns as channels (frame based) (default) | Elements as channels (sample based)

Dependencies

Reset port — Reset event None (default) | Rising edge | Falling edge | Either edge | Non-zero sample

Dependencies

Data Types Tab

Rounding mode — Method of rounding operation Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Saturate on integer overflow — Method of overflow action off (default) | on

Product output — Product output data type Inherit: Same as input (default) | fixdt([],16,0)

Accumulator — Accumulator data type Inherit: Same as product output (default) | Inherit: Same as input | fixdt([],16,0)

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types off (default) | on

Model Examples

Compute the Minimum

Compute the Running Minimum

Block Characteristics

Algorithms

Minimum

Running Minimum

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

HDL Code Generation Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Fixed-Point Conversion Design and simulate fixed-point systems using Fixed-Point Designer™.

See Also

Functions

Objects

Blocks

DSP System Toolbox Documentation

Support

`In` — Data input
vector | matrix | N-D array

`Rst` — Reset port
scalar

`Val` — Minimum values along the specified dimension
scalar | vector | matrix | N-D array

`Idx` — Index of the minimum values along the specified dimension
scalar | vector | matrix | N-D array

`Mode` — Mode in which the block operates
`Value and Index` (default) | `Value` | `Index` | `Running`

`Index base` — Base of the minimum value index
`One` (default) | `Zero`

`Find the minimum value over` — Dimension over which the block computes the minimum value
`Each column` (default) | `Each row` | `Entire input` | `Specified dimension`

`Dimension` — Custom dimension
`1` (default) | scalar

`Input processing` — Method to process the input in running mode
`Columns as channels (frame based)` (default) | `Elements as channels (sample based)`

`Reset port` — Reset event
`None` (default) | `Rising edge` | `Falling edge` | `Either edge` | `Non-zero sample`

`Rounding mode` — Method of rounding operation
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

`Saturate on integer overflow` — Method of overflow action
off (default) | on

`Product output` — Product output data type
`Inherit: Same as input` (default) | `fixdt([],16,0)`

`Accumulator` — Accumulator data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `fixdt([],16,0)`

`Lock data type settings against changes by the fixed-point tools` — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.