DSP Blockset

Cumulative Sum

Compute the cumulative sum of channel, column, or row elements

Library

Math Functions / Math Operations

Description

The Cumulative Sum block computes the cumulative sum of the elements in each channel, column, or row of the M-by-N input matrix.

The inputs can be sample-based or frame-based vectors and matrices. The output always has the same size, dimension, rate, frame status, data type, and complexity as the input.

Sections of This Reference Page

• Input and Output Characteristics
• Summing Along Channels
• Resetting the Cumulative Sum Along Channels
• Summing Along Columns
• Summing Along Rows
• Dialog Box
• Supported Data Types
• See Also

Input and Output Characteristics

Valid Input to Sum.   The block computes the cumulative sum of both sample- and frame-based vector and matrix inputs. Inputs can be real or complex. When summing along channels or columns, 1-D unoriented vectors are treated as column vectors. When summing along rows, 1-D vectors are treated as row vectors.

Valid Reset Signal.   The optional reset port, Rst, accepts scalar values, which can be any built-in Simulink data type including Boolean. The rate of the reset signal must be a positive integer multiple of the rate of the data signal input.

Output Characteristics.   The output always has the same size, dimension, rate, frame status, data type, and complexity as the data signal input.

Summing Along Channels

When the Sum input along parameter is set to Channels (running sum), the block computes the cumulative sum of the elements in each input channel. The running sum of the current input takes into account the running sum of all previous inputs. See the following sections for more information:

• Summing Along Channels of Frame-Based Inputs
• Summing Along Channels of Sample-Based Inputs
• Resetting the Cumulative Sum Along Channels

Summing Along Channels of Frame-Based Inputs.   For frame-based inputs, the block treats each input column as an independent channel. As the following figure and equation illustrate, the output has the following characteristics:

• The first row of the first output is the same as the first row of the first input.
• The first row of each subsequent output is the sum of the first row of the current input (time t), and the last row of the previous output (time t - T_f, where T_f is the frame period).
• The output has the same size, dimension, frame status, data type, and complexity as the input.

Given an M-by-N frame-based input, u, the output, y, is a frame-based M-by-N matrix whose first row has elements

Summing Along Channels of Sample-Based Inputs.   For sample-based inputs, the block treats each element of the input matrix as an independent channel. As the following figure and equation illustrate, the output has the following characteristics:

• The first output is the same as the first input.
• Each subsequent output is the sum of the current input (time t) and the previous output (time t - T_s, where T_s is the sample period).
• The output has the same size, dimension, frame status, data type, and complexity as the input.

Given an M-by-N sample-based input, u, the output, y, is a sample-based M-by-N matrix with the elements

Resetting the Cumulative Sum Along Channels.   When you set the Sum input along parameter to Channels (running sum), you can set the block to reset the running sum whenever it detects a reset event at the optional Rst port. The rate of the reset signal must be a positive integer multiple of the rate of the data signal input. The input to the Rst port can be of the Boolean data type.

When the block is reset for sample-based inputs, the block initializes the current output to the values of the current input. For frame-based inputs, the block initializes the first row of the current output to the values in the first row of the current input.

The Reset port parameter specifies the reset event, which can be one of the following:

• 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, sample-based reset signals have a one-sample latency, and frame-based reset signals have one frame of latency. Thus, there is a one-sample or one-frame delay between the time the block detects a reset event, and when it applies the reset. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and the topic on the Simulation Parameters dialog box in the Simulink documentation.

Summing Along Columns

When the Sum input along parameter is set to Columns, the block computes the cumulative sum of each column of the input, where the current cumulative sum is independent of the cumulative sums of previous inputs.

• y = cumsum(u)            % Equivalent MATLAB code
  

The output has the same size, dimension, frame status, data type, and complexity as the input. The mth output row is the sum of the first m input rows.

Given an M-by-N input, u, the output, y, is an M-by-N matrix whose jth column has elements

The block treats length-M 1-D vector inputs as M-by-1 column vectors when summing along columns.

Summing Along Rows

When the Sum input along parameter is set to Rows, the block computes the cumulative sum of the row elements, where the current cumulative sum is independent of the cumulative sums of previous inputs.

• y = cumsum(u,2)          % Equivalent MATLAB code
  

The output has the same size, dimension, frame status, and data type as the input. The nth output column is the sum of the first n input columns.

Given an M-by-N input, u, the output, y, is an M-by-N matrix whose ith row has elements

The block treats length-N 1-D vector inputs as 1-by-N row vectors when summing along rows.

Dialog Box

Sum input along

The dimension along which to compute the cumulative summations. The options allow you to sum along Channels (running sum), Columns, and Rows. For more information, see the following sections:

• Summing Along Channels
• Summing Along Columns
• Summing Along Rows

Reset port

Determines the reset event that causes the block to reset the sum along channels. 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 Sum input along parameter to Channels (running sum). For more information, see Resetting the Cumulative Sum Along Channels.

Supported Data Types

Input and Output Ports	Supported Data Types
Data input port, In	Double-precision floating point Single-precision floating point
Reset input port, Rst	All built-in Simulink data types: Double-precision floating point Single-precision floating point Boolean 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers
Output port	Always has same data type as data input

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

Cumulative Product	DSP Blockset
Difference	DSP Blockset
Matrix Sum	DSP Blockset
cumsum	MATLAB

Cumulative Product

dB Conversion