Downsample

Resample input at lower rate by deleting samples

• Library:

• DSP System Toolbox / Signal Operations

  DSP System Toolbox HDL Support / Signal Operations

• 

Description

The Downsample block decreases the sampling rate of the input by deleting samples. When the block performs frame-based processing, it resamples the data in each column of the P_i-by-Q input matrix independently. When the block performs sample-based processing, it treats each element of the input as a separate channel and resamples each channel of the input array across time. The resample rate is K times lower than the input sample rate, where K is the value of the Downsample factor parameter. The Downsample block resamples the input by discarding K–1 consecutive samples following each sample that is output.

This block supports triggered subsystems when you set the Rate options parameter to Enforce single-rate processing.

Ports

Input

Port_1 — Data input

column vector | matrix | N-D array

Data input whose sampling rate you want to decrease by using the block, specified as a column vector or a matrix.

When you set the Input processing parameter to Elements as channels (sample based), the input can be an N-D array.

The block supports variable-size input signals when you set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing. That is, the frame length (number of rows) and the number of channels (columns) can change during simulation. When the block accepts variable-size input signals, they can be of arbitrary frame length. That is, the input frame length does not have to be a multiple of the downsampling factor. When you specify fixed-size signals, the frame length can be arbitrary under certain conditions. For more details, see Frame-Based Processing and Sample-Based Processing.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Complex Number Support: Yes

Output

Port_1 — Downsampled output

column vector | matrix

Downsampled output with a sampling rate that is 1/K times the input sampling rate, returned as a column vector or a matrix.

When you set Rate options to:

• Enforce single-rate processing –– The block maintains the input sample rate and downsamples the signal by decreasing the output frame size by a factor of K.

  The output has an upper bound size of ceil(P/K)-by-Q for an input of size P-by-Q.

• Allow multirate processing –– The block downsamples the signal such that the output sample rate is K times slower than the input sample rate.

  The output frame size is the same as the input frame size.

For more details, see Frame-Based Processing and Sample-Based Processing.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Complex Number Support: Yes

Parameters

Downsample factor, K — Downsampling factor

2 (default) | positive integer

The integer factor, K, by which to decrease the input sample rate.

Sample offset (0 to K-1) — Sample offset

0 (default) | integer

The Sample offset parameter delays the output samples by an integer number of sample periods, D, where 0 ≤ D ≤ (K–1), so that any of the K possible output phases can be selected. For example, when you downsample the sequence 1, 2, 3, ... by a factor of 4, you can select from four phases.

Input Sequence	Sample Offset, D	Output Sequence (K = 4)
1,2,3,...	0	1,5,9,13,17,21,25,29,...
1,2,3,...	1	0,2,6,10,14,18,22,26,...
1,2,3,...	2	0,3,7,11,15,19,23,27,...
1,2,3,...	3	0,4,8,12,16,20,24,28,...

The initial zero in each of the latter three output sequences in the table is a result of the default zero Initial conditions parameter setting for this example. See Latency for more information on the Initial conditions parameter.

Input processing — Method to process input

Columns as channels (frame based) (default) | Elements as channels (sample based)

Specify the method for input processing:

• Columns as channels (frame based) –– When you set the Input processing parameter to Columns as channels (frame based), the block treats each of the Q input columns as an individual channel containing P_i sequential time samples. The block downsamples each channel independently by discarding K–1 rows of the input matrix following each row that it outputs.

  For more information, see What Is Frame-Based Processing?.

• Elements as channels (sample based) –– When you set the Input processing parameter to Elements as channels (sample based), the input can be an Q-D array. The Downsample block treats each element of the input as a separate channel, and resamples each channel of the input over time. The block downsamples the input array by discarding K–1 samples following each sample that it passes through to the output. The input and output sizes of the Downsample block are identical.

  For more information, see What Is Sample-Based Processing?.

Rate options — Enforce single-rate or allow multirate processing

Enforce single-rate processing (default) | Allow multirate processing

Specify the method by which the block adjusts the rate at the output to accommodate the reduced number of samples. You can select one of the following options. The behavior of these options depends on whether the Input processing parameter is set to Elements as channels (sample based) (sample-based processing mode) or Columns as channels (frame based) (frame-based processing mode).

• Elements as channels (sample based)

  • Enforce single-rate processing

    The block forces the output sample rate to match the input sample rate (T_so = T_si) by repeating every Kth input sample K times at the output. In this mode, the behavior of the block is similar to the operation of a Sample and Hold block with a repeating trigger event of period KT_si.

  • Allow multirate processing

    The sample period of the output is K times longer than the input sample period (T_so = KT_si).

  For more details, see Sample-Based Processing

• Columns as channels (frame based)

  • Enforce single rate processing

    The block generates the output at the slower (downsampled) rate using a proportionally smaller frame size than the input. The output has an upper bound size of ceil(P/K), where P is the input frame length and K is the downsample factor specified in the Downsample factor, K parameter. The input and output frame rates are equal. For more details, see Frame-Based Processing.

    The ex_downsample_ref2 model shows a single-channel input with a frame size of 64 being downsampled by a factor of 4 to a frame size of 16. The input and output frame rates are identical.

    

  • Allow multirate processing

    The block generates the output at the slower (downsampled) rate by using a proportionally longer frame period at the output port than at the input port. For downsampling by a factor of K, the output frame period is K times longer than the input frame period (T_fo = KT_fi), but the input and output frame sizes are equal. For more details, see Frame-Based Processing.

    The ex_downsample_ref1 model shows a single-channel input with a frame period of 1 second being downsampled by a factor of 4 to a frame period of 4 seconds. The input and output frame sizes are identical.

    

Allow arbitrary frame length for fixed-size input signals — Allow arbitrary frame length for fixed-size input signals

on (default) | off

Specify whether fixed-size input signals (whose size does not change during simulation) can have an arbitrary frame length, where the frame length does not have to be a multiple of the downsampling factor. The block uses this parameter setting only for fixed-size input signals and ignores this parameter if the input has a variable-size.

When the input signal is a variable-size signal, the signal can have arbitrary frame length, that is, the frame length does not have to be a multiple of the decimation factor.

For fixed-size input signals, if you:

• Select the Allow arbitrary frame length for fixed-size input signals parameter, the frame length of the signal does not have to be a multiple of the downsampling factor. If the input is not a multiple of the downsampling factor, then the output is generally a variable-size signal. Therefore, to support arbitrary input size, the block must also support variable-size operations, which you can enable by selecting the Allow arbitrary frame length for fixed-size input signals parameter.

• Clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be a multiple of the downsampling factor.

Dependency

To enable this parameter, set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing.

Initial conditions — Initial value

0 (default) | real scalar | array

The initial block value for cases of nonzero latency. You can specify a scalar or an array of the same size as the input.

Dependencies

This parameter does not appear when Input processing is set to Columns as channels (frame based) and Rate options is set to Enforce single-rate processing.

Model Examples

Acoustic Noise Cancellation (LMS)

Use the Least Mean Square (LMS) algorithm to subtract noise from an input signal. The LMS adaptive filter uses the reference signal on the Input port and the desired signal on the Desired port to automatically match the filter response. As it converges to the correct filter model, the filtered noise is subtracted and the error signal should contain only the original signal.

Open Model

Downsample a Signal

Downsampling operation on a signal with one-frame latency.

Open Model

Block Characteristics

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

More About

Frame-Based Processing

When you set the Input processing parameter to Columns as channels (frame based) and use an input signal of size P-by-Q, the block treats each of the Q input columns as an individual channel containing P sequential time samples. The block downsamples each channel independently by discarding K–1 rows of the input matrix following each row that it outputs.

In this mode, the block can perform either single-rate or multirate processing. You can use the Rate options parameter to specify how the block adjusts the rate at the output to accommodate the reduced number of samples.

• When you set the Rate options parameter to Enforce single-rate processing, the block generates the output at the slower (downsampled) rate using a proportionally smaller frame size than the input.

  The output has an upper bound size of ceil(P/K), where P is the input frame length and K is the downsample factor specified in the Downsample factor, K parameter.

  In this mode, if you input a fixed-size signal (signal dimensions do not change during simulation) and select the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length can be arbitrary and does not have to be a multiple of the downsampling factor. If you clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be a multiple of the downsampling factor.

  In this mode, if you input a variable-size signal (signal dimensions change during simulation), the Allow arbitrary frame length for fixed-size input signals appears on the block dialog box but does not have any impact on the input frame size requirements. You can input a variable-size signal of any frame size even if you do not select the Allow arbitrary frame length for fixed-size input signals parameter.

  This table summarizes the support for arbitrary input frame length when you set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing.

  Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
  Fixed-size input signal	Yes	When you select Allow arbitrary frame length for fixed-size input signals	P-by-Q	Upper bound size of ceil(P/K)-by-Q
  Variable-size input signal	Yes	Always	P-by-Q	Upper bound size of ceil(P/K)-by-Q

• When you set the Rate options parameter to Allow multirate processing, the input and output of the Downsample block are of the same size, but the sample rate of the output is K times slower than that of the input. In this mode, the block treats a P-by-Q matrix input as Q independent channels.

  In this mode, the block accepts only fixed-size signals and these signals can have an arbitrary frame length.

  This table summarizes the support for arbitrary input frame length when you set Input processing to Columns as channels (frame based) and Rate options to Allow multirate processing.

  Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
  Fixed-size input signal	Yes	Always	P-by-Q	P-by-Q
  Variable-size input signal	No	Not applicable	Not applicable	Not applicable

Sample-Based Processing

When you set the Input processing parameter to Elements as channels (sample based), the block treats a P-by-Q matrix input as P*Q independent channels, and resamples each channel over time. The output sample period (T_so) is K times longer than the input sample period (T_so = K*T_si), and the input and output sizes are identical.

In this mode, the block accepts only fixed-size signals and these signals can have an arbitrary frame length.

This table summarizes the support for arbitrary input frame length when you set Input processing to Elements as channels (sample based).

Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
Fixed-size input signal	Yes	Always	P-by-Q	P-by-Q
Variable-size input signal	No	Not applicable	Not applicable	Not applicable

Latency

Latency is the delay, measured in samples or frames, between the input and the output of the block.

The Downsample block has zero-tasking latency in the following cases:

• The Downsample factor parameter, K, is 1.

• The Input processing parameter is set to Columns as channels (frame based), and the Rate options parameter is set to Enforce single-rate processing.

• The Input processing parameter is set to Columns as channels (frame based), the Rate options parameter is set to Allow multirate processing, the Sample offset parameter, D, is set to 0, and the input frame size is equal to 1.

• The Input processing parameter is set to Elements as channels (sample based), and the Sample offset parameter, D, is 0.

Zero-tasking latency means that the block propagates input sample D+1 (received at t = 0) as the first output sample, followed by input sample D+1+K, input sample D+1+2K, and so on. When there is zero-tasking latency, the block ignores the value of the Initial conditions parameter.

In all other cases, the latency is nonzero:

• When the Input processing parameter is set to Elements as channels (sample based), the latency is one sample.

• When the Input processing parameter is set to Columns as channels (frame based) and the input frame size is greater than one, the latency is one frame.

In all cases of one-sample latency, the initial condition for each channel appears as the first output sample. Input sample D+1 appears as the second output sample for each channel, followed by input sample D+1+K, input sample D+1+2K, and so on. The Initial conditions parameter can be an array of the same size as the input or a scalar to be applied to all signal channels.

In all cases of one-frame latency, the P_i rows of the initial condition matrix appear in sequence as the first P_i output rows. Input sample D+1 (row D+1 of the input matrix) appears in the output as sample P_i+1, followed by input sample D+1+K, input sample D+1+2K, and so on. The Initial conditions value can be an P_i-by-Q matrix containing one value for each channel or a scalar to be repeated across all elements of the P_i-by-Q matrix.

Note

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).

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

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.

Best Practices

It is good practice to follow the Downsample block with a unit delay. Doing so prevents the code generator from inserting an extra bypass register in the HDL code.

See also Multirate Model Requirements for HDL Code Generation (HDL Coder).

HDL Architecture

This block has one default HDL architecture.

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).

Complex Data Support

This block supports code generation for complex signals.

Restrictions

• Input processing set to Columns as channels (frame based) is not supported.

• For Input processing set to Elements as channels (sample based), select Allow multirate processing. With this setting, if Sample offset is set to 0, Initial conditions has no effect on generated code.

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

Version History

Introduced before R2006a

R2022b: Support for arbitrary input frame length and variable input frame sizes

Starting in R2022b, this block supports input signals with arbitrary frame lengths when the:

• Input signal is a fixed-size signal (signal dimensions do not change during simulation) and the block allows for multirate processing

• Input signal is a fixed-size signal, block enforces single-rate processing, and you select the Allow arbitrary frame length for fixed-size input signals parameter (if enabled)

• Input signal is a variable-size signal (signal dimensions change during simulation)

When this block supports an arbitrary frame length input signal, the input frame length does not have to be a multiple of the downsampling factor.

For more details, see Frame-Based Processing and Sample-Based Processing.