Window Function

Compute and apply window to input signal

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Libraries:
DSP System Toolbox / Signal Operations

Description

The Window Function block has three modes of operation that enable you to apply a window, or compute a window, or compute and apply a window to an input signal. You can select the mode via the Operation parameter. In each mode, the block first creates a window vector w by sampling the window specified in the Window type parameter.

Examples

Generate and Apply Hamming Window

Generates and applies a Hamming window using Window Function block.

• Open Model

Ports

Input

In — Input signal

vector | matrix | N-D array

Input signal, specified as a vector, matrix, or an N-D array.

If the input is fixed point, it must be a signed integer or a signed fixed point value with a power-of-two slope and zero bias.

This port is enabled only when you set Operation to either Apply window to input or Generate and apply window.

This port is unnamed when you set Operation to Apply window to input.

Data Types: single | double | int8 | int16 | int32 | fixed point

Output

Out — Output

vector | matrix | N-D array

Output signal, returned as a vector, matrix, or an N-D array.

The Out port is enabled only when Operation is set to:

• Apply window to input –– The block computes an M-by-1 window vector w and applies it to the M-by-N input, where M is the number of rows in the input signal.

• Generate and apply window –– The block generates an M-by-1 window vector w and applies it to the input.

The output signal has the same dimensions as the input signal. For more details, see Operation.

Data Types: single | double | int8 | int16 | int32 | fixed point

Win — Window output

vector

Window output, returned as a vector. When Operation is set to Apply window to input or Generate and apply window, the window vector is of the same length as the number of rows in the input signal. When Operation is set to Generate window, the length of window vector is determined by the Window length parameter.

Data Types: single | double | int8 | int16 | int32 | fixed point

Parameters

Main

Operation — Modes of operation

Apply window to input (default) | Generate window | Generate and apply window

The Window Function block has three modes of operation that you can select through the Operation parameter. In each mode, the block first creates a window vector w by sampling the window specified in the Window type parameter at M discrete points. The operation modes are:

• Apply window to input

  In this mode, the block computes an M-by-1 window vector w and applies it to the input. The output y always has the same dimension as the input.

  When the input is an M-by-N matrix u, the window is multiplied element-wise with each of the N channels in the input matrix u. This is equivalent to the following MATLAB^® code:

  y = repmat(w,1,N) .* u								% Equivalent MATLAB code
  

  The window is always applied to the first dimension:

  $$y(i,j,\mathrm{...},k)=w(i)*u(i,j,\mathrm{...},k)i=1,\mathrm{...},M,j=1,\mathrm{...},N,\mathrm{...},k=1,\mathrm{...},P$$

  A length-M unoriented vector input is treated as an M-by-1 vector.

• Generate window

  In this mode, the block generates an unoriented window vector w with length M specified by the Window length parameter. The In port is disabled for this mode.

• Generate and apply window

  In this mode, the block generates an M-by-1 window vector w and applies it to the input. The block produces two outputs:

  • At the Out port, the block produces the result of the multiplication y, which has the same dimension as the input.

  • At the Win port, the block produces the M-by-1 window vector w.

  When the input is an M-by-N matrix u, the window is multiplied element-wise with each of the N channels in the input matrix u. This is equivalent to the following MATLAB code:

  y = repmat(w,1,N) .* u								% Equivalent MATLAB code
  

  The window is always applied to the first dimension:

  $$y(i,j,\mathrm{...},k)=w(i)*u(i,j,\mathrm{...},k)i=1,\mathrm{...},M,j=1,\mathrm{...},N,\mathrm{...},k=1,\mathrm{...},P$$

  A length-M 1-D vector input is treated as an M-by-1 vector.

Window type — Type of window

Hamming (default) | Bartlett | Blackman | ...

This table lists the available window types.

Window Type	Description
Bartlett	Computes a Bartlett window. w = bartlett(M)
Blackman	Computes a Blackman window. w = blackman(M)
Boxcar	Computes a rectangular window. w = rectwin(M)
Chebyshev	Computes a Chebyshev window with stopband ripple R. w = chebwin(M,R)
Hamming	Computes a Hamming window. w = hamming(M)
Hann	Computes a Hann window (also known as a Hanning window). w = hann(M)
Hanning	Obsolete. This window type is included only for compatibility with older models. Use the Hann Window type instead of Hanning whenever possible.
Kaiser	Computes a Kaiser window with the Kaiser parameter beta. w = kaiser(M,beta)
Taylor	Computes a Taylor window. w = taylorwin(M)
Triang	Computes a triangular window. w = triang(M)
User Defined	Computes the user-defined window function specified by the entry in the Window function name parameter, usrwin. w = usrwin(M) % Window takes no extra parameters w = usrwin(M,x1,...,xn) % Window takes extra parameters {x1 ... xn}

Sampling — Type of sampling

Symmetric (default) | Periodic

Specify the window sampling for generalized-cosine windows.

For the generalized-cosine windows (Blackman, Hamming, Hann, and Hanning), the Sampling parameter determines whether the window samples are computed in a periodic or a symmetric manner. For example, when Sampling is set to Symmetric, a Hamming window of length M is computed as:

w = hamming(M)					% Symmetric (aperiodic) window

When Sampling is set to Periodic, the same window is computed as:

w = hamming(M+1)					% Periodic (asymmetric) window
w = w(1:M)

Tunable (Simulink) in simulation only.

Dependencies

This parameter is visible only when you select Blackman, Hamming, Hann, or Hanning for the Window type parameter.

Sample mode — Sample mode

Continuous (default) | Discrete

Specify the sample mode for the block, Continuous or Discrete, when it is in the Generate window mode. In the Apply window to input and Generate and apply window modes, the block inherits the sample mode from its driving block.

Dependencies

This parameter is visible only when you select Generate window for the Operation parameter.

Sample time — Sample time

1 (default) | real scalar

Specify the sample time for the block when Operation is set to Generate window and Sample mode is set to Discrete. When Operation is set to Apply window to input and Generate and apply window, the block inherits the sample time from its driving block.

Dependencies

This parameter is visible only when you set Sample mode to Discrete.

Window length — Length of window

64 (default) | positive integer

Specify the length of the window to apply.

Dependencies

This parameter is visible only when you select Generate window for the Operation parameter. Otherwise, the window vector length is computed to match the length of the first dimension of the input.

Stopband attenuation in dB — Stopband attenuation in dB

50 (default) | nonnegative scalar

Specify the level of stopband attenuation R_s in decibels.

Tunable (Simulink) in simulation only.

Dependencies

This parameter is visible only when you select Chebyshev for the Window type parameter.

Beta — Kaiser window β parameter

10 (default) | real scalar

Specify the Kaiser window β parameter. Increasing β widens the mainlobe and decreases the amplitude of the window sidelobes in the window's frequency magnitude response.

Tunable (Simulink) in simulation only.

Dependencies

This parameter is visible only when you select Kaiser for the Window type parameter.

Number of sidelobes — Number of sidelobes

4 (default) | positive integer

Specify the number of sidelobes as a scalar integer value greater than zero.

Dependencies

This parameter is visible only when you select Taylor for the Window type parameter.

Maximum sidelobe level relative to mainlobe (dB) — Maximum sidelobe level relative to mainlobe

-30 (default) | scalar less than or equal to zero

Specify in decibels the maximum sidelobe level relative to the mainlobe. This parameter must be a scalar less than or equal to zero. The default value of –30 produces sidelobes with peaks 30 dB down from the mainlobe peak.

Dependencies

This parameter is visible only when you select Taylor for the Window type parameter.

Window function name — Window function name

hamming (default) | character vector

Specify the name of the user-defined window function to be calculated by the block. The output window vector returned by the custom window function must be of data type double.

Dependencies

This parameter is visible only when you select User defined for the Window type parameter.

Specify additional arguments to the hamming function — Specify additional arguments to the window function

off (default) | on

Select to enable the Cell array of additional arguments parameter, when the user-defined window requires parameters other than the window length.

Dependencies

This parameter is visible only when you select User defined for the Window type parameter.

Cell array of additional arguments — Additional arguments

{'symmetric'} (default) | cell array

Specify the extra parameters required by the user-defined window function, besides the window length.

Dependencies

This parameter is only available when you select the Specify additional arguments to the hamming function parameter. The entry must be a cell array.

Data Types

When the Operation parameter on the Main tab is set to Generate window, the following parameters appear.

Window data type — Window data type

double (default) | single | Fixed-point | User-defined | Inherit via back propagation

Specify the window data type in one of the following ways:

• double

• single

• Fixed-point –– To specify the window data type and scaling in the Signed, Word length, Set fraction length in output to, and Fraction length parameters.

• User-defined –– To specify the window data type and scaling in the User-defined data type, Set fraction length in output to, and Fraction length parameters.

• Inherit via back propagation –– To set the window data type and scaling to match the following block.

Signed — Window output is signed

on (default) | off

Select to output a signed fixed-point signal. Otherwise, the signal is unsigned.

Dependencies

This parameter appears only when you set Window data type to Fixed-point.

Word length — Word length

16 (default) | positive integer in the range [2 128]

Specify the word length of the fixed-point window data type in bits.

Dependencies

This parameter is visible only when you set Window data type to Fixed-point.

User-defined data type (e.g. sfix(16), float('single)) — user-defined data type

sfix(16) (default) | built-in data type | fixed-point data type

Specify any built-in or fixed-point data type. You can specify fixed-point data types using the fixdt (Simulink) function.

Dependencies

This parameter is only visible when you set Window data type to User-defined.

Set fraction length in output to — Scaling of fixed-point window data type

Best precision (default) | User-defined

Specify the scaling of the fixed-point window data type by using either of these methods:

• Choose Best precision to have the window data type scaling automatically set such that the output signal has the best possible precision.

• Choose User-defined to specify the window data type scaling in the Fraction length parameter.

Dependencies

This parameter is visible only when you set Window data type to Fixed-point or User-defined, and when the specified window data type is a fixed-point data type.

Fraction length — User-defined fraction length

15 (default) | integer

Specify the fraction length of the fixed-point window data type in bits.

Dependencies

This parameter is visible only when you set Window data type to Fixed-point or User-defined, and when you set Set fraction length in output to to User-defined.

When the Operation parameter on the Main tab is set to either Apply window to input or Generate and apply window, the following parameters appear.

Rounding mode — Rounding mode

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Select the rounding mode for fixed-point operations.

The window vector w does not obey this parameter. It always rounds to Nearest.

Note

The Rounding mode and Overflow mode settings have no effect on numerical results when both of these conditions exist:

• Product output is Inherit via internal rule

• Output is Same as product output

With these data type settings, the block is effectively operating in a full-precision mode.

Overflow mode — Overflow mode

Wrap (default) | Saturate

Select the overflow mode for fixed-point operations.

The window vector w does not obey this parameter. It is always saturated.

Window — Window data type

Same word length as input (default) | Specify word length | Binary point scaling | Slope and bias scaling

Choose how you specify the word length and fraction length of the window vector w.

When you select:

• Same word length as input –– The word length of the window vector elements is the same as the word length of the input. The fraction length is automatically set to the best precision possible.

• Specify word length –– You can enter the word length of the window vector elements in bits. The fraction length is automatically set to the best precision possible.

• Binary point scaling –– You can enter the word length and the fraction length of the window vector elements in bits.

• Slope and bias scaling –– You can enter the word length, in bits, and the slope of the window vector elements. This block requires power-of-two slope and a bias of zero.

The window vector does not obey the Rounding mode and Overflow mode parameters. It is always saturated and rounded to Nearest.

Product output — Product output data type

Inherit via internal rule (default) | Same as input | Binary point scaling | Slope and bias scaling

Use this parameter to specify how you want to designate the product output word and fraction lengths.

When you select:

• Inherit via internal rule –– The product output word length and fraction length are calculated automatically. For information on how the product output word and fraction lengths are calculated when an internal rule is used, see Inherit via Internal Rule.

• Same as input –– These characteristics match those of the input to the block.

• Binary point scaling –– You can enter the word length and the fraction length of the product output in bits.

• 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.

Output — Output data type

Same as product output (default) | Same as input | Binary point scaling | Slope and bias scaling

Choose how you specify the word length and fraction length of the output of the block.

When you select:

• Same as product output –– These characteristics match those of the product output.

• Same as input –– These characteristics match those of the input to the block.

• Binary point scaling –– You can enter the word length and the fraction length of the output in bits.

• Slope and bias scaling –– You can enter the word length in bits and the slope of the output. This block requires power-of-two slope and a bias of zero.

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 in the block dialog box.

Block Characteristics

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

More About

Fixed-Point Data Types

The following diagram shows the data types used within the Window Function block for fixed-point signals for each of the three operating modes.

You can set the window, product output, and output data types in the block dialog box.

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.

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

Version History

Introduced before R2006a