Window Function (DSP Blockset)

Compute a specified window, and apply it to an input signal.

Library

Signal Operations, in General DSP; DSP Sources

Description

The Window Function block has three modes of operation, which are selected by the Operation parameter. In each mode of operation, the block computes samples of the window specified by the Window type parameter. The length of the sampled window, N_w, is determined by the size of the input, or specified by the Window length parameter if there is no input.


Operation	Description
Apply window to input	Multiplies the sampled window, `w`, element-wise with the input vector, `u`: y = w .* u The output is the result of this multiplication.
Generate window	Outputs the sampled window, `w`. There is no input.
Generate and apply window	Outputs the product of the window and the input, w.*u, in output 1, and outputs the sampled window, `w`, in output 2.

The Sampling parameter determines whether the window samples are computed in a periodic or a symmetric manner. For example, if Sampling is set to Symmetric, a Hamming window of Window length N_w is computed as

w = hamming(Nw)      % symmetric (aperiodic) window

If Sampling is set to Periodic, the same window is computed as

w = hamming(Nw+1)    % periodic (asymmetric) window
w = w(1:Nw)

The periodic window option only applies to the generalized-cosine windows (Blackman, Hamming, and Hanning).

The available window types are shown below. The Beta and Stopband ripple parameters specify the characteristics of the Chebyshev and Kaiser windows, and are only available when the respective window designs are selected.


Window Type	Description
Bartlett	Applies a Bartlett window to the real input vector: w = bartlett(Nw)
Blackman	Applies a Blackman window to the real input vector: w = blackman(Nw)
Boxcar	Applies a Boxcar window to the real input vector: w = boxcar(Nw)
Chebyshev	Applies a Chebyshev window to the real input vector: w = chebwin(Nw,R)
Hamming	Applies a Hamming window to the real input vector: w = hamming(Nw)
Hanning	Applies a Hanning window to the real input vector: w = hanning(Nw)
Kaiser	Applies a Kaiser window to the real input vector: w = kaiser(Nw,beta)
Triang	Applies a triangular window to the real input vector: w = triang(Nw)

Frame-Based Operation

In the cases when the window is being applied to an input (Generate and apply window or Apply window to input selected from the Operation menu), the block assumes that the input is an M-by-N frame matrix. Each of the N frames in the matrix contains M sequential time samples from an independent signal. The Number of channels parameter specifies the number of independent channels (columns, N) in the matrix. The block computes a window to match the input frame size (N_w=M), and applies the window to each channel independently. The output is the same size as the input. Frame-based operation provides substantial increases in throughput rates, at the expense of greater model latency.

Dialog Box

The parameters displayed in the dialog box vary for different operation/window type combinations. Not all of the parameters listed below are active in the dialog box at any one time.

Operation: The block's operation: generate a window, apply a window to an input, or both.
Window type: The type of window to apply.
Window length: The length of the window to apply, N_w.
Stopband ripple: The level (dB) of stopband ripple, R_s, for the Chebyshev window.
Beta: The Kaiser window parameter. Increasing Beta widens the mainlobe and decreases the amplitude of the window sidelobes in the window's frequency magnitude response.
Sampling: The window sampling, symmetric or periodic.
Number of channels: For frame-based operation, the number of channels (columns) in the input matrix, N.