Minimum values of input or sequence of inputs
DSP System Toolbox / Statistics
The Minimum block identifies the value and position of the smallest element in each row or column of the input, or along vectors of a specified dimension of the input. It can also compute the minimum value 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 one of the following:
Value
— The block outputs the minimum
values in the specified dimension.
Index
— The block outputs the index
array of the minimum values in the specified dimension.
Value and Index
— The block outputs the
minimum values and the corresponding index array in the specified
dimension.
Running
— The block tracks the minimum
values in a sequence of inputs over a period of time.
You can specify the dimension using the Find the minimum value over parameter.
The Running mode in the Minimum block will be removed in a future release. To compute the running minimum in Simulink^{®}, use the Moving Minimum block instead.
In
— Data inputThe block accepts realvalued or complexvalued multichannel and multidimensional inputs. The input can be floatingpoint, fixedpoint, or Boolean. Real fixedpoint inputs can be either signed or unsigned. Complex fixedpoint 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
.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
 fixed point
Complex Number Support: Yes
Rst
— Reset portSpecify 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.
To enable this port, set the Mode parameter
to Running
and the Reset
port parameter to any option other than
None
.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
Val
— Minimum values along the specified dimensionThe 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
MbyNbyP
array, with the dimension set to 1
, the
block outputs a
1byNbyP array.
When the dimension is set to 3
, the block
outputs a twodimensional
MbyN
matrix.
When the input is an
MbyN matrix,
with the dimension set to 1
, the block
outputs a 1byN 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
MbyN 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
threedimensional input signal of size
MbyNbyP,
the block outputs an
MbyNbyP
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 Ndimensional input signal, where N > 2.
For a twodimensional input signal of size
MbyN, the block
outputs an MbyN
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.
To enable this port, set the Mode parameter
to either Value and Index
or
Value
.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
 fixed point
Complex Number Support: Yes
Idx
— Index of the minimum values along the specified dimensionWhen the input is double
, the index values are also
double
. Otherwise, the index values are
uint32
.
To enable this port, set the Mode parameter
to either Value and Index
or
Index
.
Data Types: double
 uint32
Mode
— Mode in which the block operatesValue 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
MbyNbyP.
Set Find the minimum value over to:
Each row
—
The output y at each sample
time consists of an
Mby1byP
array, where each element contains the minimum
value of each vector over the second dimension of
the input. For an input that is an
MbyN
matrix, the output at each sample time is an
Mby1 column vector.
Each column
— The output y at each
sample time consists of a
1byNbyP
array, where each element contains the minimum
value of each vector over the first dimension of
the input. For an input that is an
MbyN
matrix, the output at each sample time is a
1byN row vector.
In this mode, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
Entire input
— The output y at each
sample time is a scalar that contains the minimum
value in the
MbyNbyP
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
MbyN
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 $$u=a+bi$$, 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
MbyNbyP:
Each row
—
The output I at each sample
time consists of an
Mby1byP
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
MbyN
matrix, the output at each sample time is an
Mby1 column vector.
Each column
— The output I at each
sample time consists of a
1byNbyP
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
MbyN
matrix, the output at each sample time is a
1byN row vector.
In this mode, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
Entire input
— The output I at each
sample time is a 1by3 vector that contains the
location of the minimum value in the
MbyNbyP
input matrix. For an input that is an
MbyN
matrix, the output is a 1by2 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
MbyN
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 onebased 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 MbyN 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 threedimensional input signal of size
MbyNbyP,
the block outputs an
MbyNbyP
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 Ndimensional
input signal, where N > 2. For a
twodimensional input signal of size
MbyN, the
block outputs an
MbyN
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 VariableSize Inputs
When the input is a variablesize 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 indexOne
(default)  Zero
Specify whether the index of the minimum value is reported using onebased or zerobased numbering.
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 valueEach 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.
To enable this parameter, set Mode to
Value and Index
,
Value
, or
Index
.
Dimension
— Custom dimension1
(default)  scalarSpecify the dimension (onebased 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.
To enable this parameter, set Find the minimum value
over to Specified
dimension
.
Input processing
— Method to process the input in running modeColumns 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 Ndimensional input
signal, where N > 2. For a twodimensional input signal of
size MbyN, the block
outputs an MbyN 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 threedimensional input signal of size
MbyNbyP,
the block outputs an
MbyNbyP
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}.
To enable this parameter, set Mode to
Running
.
Reset port
— Reset eventNone
(default)  Rising edge
 Falling edge
 Either edge
 Nonzero 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
.
Nonzero sample
— Triggers a
reset operation at each sample time that the
Rst input is not zero.
When running simulations in the Simulink
MultiTasking
mode, reset signals
have a onesample latency. Therefore, when the block detects
a reset event, there is a onesample 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
TimeBased Scheduling and Code Generation (Simulink Coder).
To enable this parameter, set Mode to
Running
.
To use these parameters, the data input must be complex fixedpoint.
Rounding mode
— Method of rounding operationFloor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Specify the rounding mode for fixedpoint 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 actionWhen you select this parameter, the block saturates the result of its
fixedpoint operation. When you clear this parameter, the block wraps
the result of its fixedpoint operation. For details on
saturate
and wrap
, see overflow
mode for fixedpoint operations.
Product output
— Product output data typeInherit: 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, binarypoint, scaled, fixedpoint 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 typeInherit: 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, binarypoint, scaled, fixedpoint 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 fixedpoint tools
— Prevent fixedpoint tools from overriding data typesoff
(default)  on
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block dialog box.
Data Types 

Multidimensional Signals 

VariableSize Signals 

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(:))
.
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 twochannel 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 twochannel 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}.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
This block has multicycle 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). 
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

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

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

InstantiateStages  Generate a VHDL^{®} 
SerialPartition  Specify partitions for Cascadeserial implementations as a vector of the lengths of each partition. The default setting uses the minimum number of stages. See also SerialPartition (HDL Coder). 
The parameters on the Data Types Tab of the block are used only for complex fixedpoint 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.
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