Window Function — Control Systems/Windows

Window Function

Control Systems / Windows

Multiplies an incoming frame by a fixed window and publishes both answers:

y[i] = w[i]·u[i], and w itself on a second output.

The window length N is the height of the input port – there is no length parameter, because a window is only ever as long as the frame it multiplies. Eighteen shapes are offered, each computed once when the configuration loads.

Ports

• Input – the frame u to window, of any size [N,m]. N sets the window length; when m > 1 every column is windowed by the same w.
• Output 1 – the windowed frame y, the SAME size [N,m] as the input.
• Output 2 – the window w itself, always an [N,1] column. Leave it unconnected if you only want the product; it costs nothing.

Parameters

• Window Type – which of the eighteen shapes to use. Each is the function of the same name in MATLAB's Signal Processing Toolbox, reproduced to better than 1×10⁻¹⁵:
  • Bartlett – the triangle that reaches zero at both ends.
  • Bartlett-Hann – a blend of the two, flatter than either.
  • Blackman – the three-term cosine sum; low sidelobes, wide main lobe.
  • Blackman-Harris – the four-term minimum sidelobe sum.
  • Bohman – the convolution of two half-cosines; endpoints exactly zero.
  • Chebyshev – equiripple sidelobes at the level you ask for, via Chebyshev Sidelobe Attenuation (dB).
  • Flat Top – the five-term sum used for amplitude accuracy; it goes negative near the ends, which is correct and surprises people.
  • Gaussian – width set by Gaussian Alpha.
  • Hamming – the default, and the same 0.54/0.46 pair Simulink uses.
  • Hann – the raised cosine.
  • Kaiser – the near-optimal family, shaped by Kaiser Beta.
  • Nuttall – a four-term sum with continuous derivatives.
  • Parzen – the piecewise-cubic (de la Vallée Poussin) window.
  • Rectangular – all ones; the block is then a wire on output 1.
  • Taylor – radar's window, shaped by Taylor Sidelobes and Taylor Sidelobe Level (dB). It is not normalised to a peak of 1 and routinely exceeds it.
  • Triangular – the triangle whose ends are not zero. That is its whole difference from Bartlett, and the pair is the most confusable here.
  • Tukey – a flat top with cosine skirts, set by Tukey Ratio.
  • DPSS – the first discrete prolate spheroidal sequence, set by DPSS Time-Bandwidth. It is unit energy, not unit peak, so its values are much smaller than the others', and it is the one type with a bound relating its parameter to the window length.
• Sampling – symmetric (the default) or periodic. Periodic divides by N instead of N−1, which is what a window destined for a DFT wants. It applies to the six cosine-sum windows only – Blackman, Blackman-Harris, Flat Top, Hamming, Hann and Nuttall – because those are the only ones MATLAB's own functions accept the flag for; on the other twelve it is ignored and the block says so rather than inventing a second shape.
• Kaiser Beta – the Kaiser shape parameter, a scalar of zero or more; larger is a wider main lobe and lower sidelobes. Defaults to 10, as Simulink's does. Read only by the Kaiser type.
• Chebyshev Sidelobe Attenuation (dB) – how far the equiripple sidelobes sit below the peak, a positive scalar. Defaults to 50. Read only by the Chebyshev type.
• Taylor Sidelobes – the number of nearly-constant-level sidelobes either side of the main lobe, a whole number of 1 or more. Defaults to 4. Read only by the Taylor type.
• Taylor Sidelobe Level (dB) – the maximum sidelobe level relative to the peak, a negative scalar. Defaults to −30. Read only by the Taylor type.
• Gaussian Alpha – the reciprocal of the standard deviation, in half-window widths; larger is narrower. Defaults to 2.5. Read only by the Gaussian type.
• Tukey Ratio – the fraction of the window taken up by the two cosine skirts, between 0 and 1. At 0 it is Rectangular and at 1 it is Hann. Defaults to 0.5. Read only by the Tukey type.
• DPSS Time-Bandwidth – the time-half-bandwidth product NW, a positive scalar that must be strictly less than half the window length – the same bound MATLAB's dpss enforces, and a value at or above it stops the run with a message naming both numbers. Defaults to 2.5, which is valid from a six-sample frame upwards; 4 would be the natural-looking choice and is invalid on every frame of eight or fewer. Read only by the DPSS type.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The N window values are baked into the core at export time as literals rather than exposed as tunable parameters: the window is structural, and one whose shape could be retuned on a built core would be a different block.

No emitted core evaluates a window. Not a cosine, not a Bessel function, not a Chebyshev polynomial, not the eigenproblem behind DPSS – all of that happens once when the configuration loads, and what reaches a target is N constants and one multiply per element. That is what keeps the three HDL targets genuine synthesizable Q16.16 rather than simulation-only real arithmetic, even for the types whose closed form is transcendental.

Simulink bridge

Import and export, mapped to dspsigops/Window Function – the DSP System Toolbox block, not a core Simulink one. winmode is always emitted as Generate and apply window, because that is the one setting whose port list matches this block's: measured on R2026a, its three values give 1 in / 1 out, 0 in / 1 out and 1 in / 2 out respectively, and only the last carries both of this block's outputs.

"Window Type" to wintype, "Sampling" to winsamp, "Kaiser Beta" to beta, "Chebyshev Sidelobe Attenuation (dB)" to Rs, "Taylor Sidelobes" to numSidelobes and "Taylor Sidelobe Level (dB)" to sidelobeLevel.

Nine of the eighteen types do not cross, and that is a property of the Simulink block rather than a gap here: its wintype list holds ten entries, of which nine match a type offered here (Rectangular crosses as Boxcar and Triangular as Triang; Hann is also accepted back under Simulink's alias Hanning). Bartlett-Hann, Blackman-Harris, Bohman, Flat Top, Gaussian, Nuttall, Parzen, Tukey and DPSS have no entry in that list, so exporting a model that uses one of them reports the value by name and leaves the Simulink block at its default rather than substituting a different window. Gaussian Alpha, Tukey Ratio and DPSS Time-Bandwidth do not cross either, for the same reason: there is no parameter on the other side for them to reach.

"Sampling Time (s)" does not cross. dspsigops/Window Function defines no SampleTime parameter at all – verified against the R2026a block dialog – and set_param on a parameter a block does not define is a hard error in MATLAB that aborts the whole generated script.

Notes

• Stateless and algebraic: the output depends only on this sample's input and on the configuration. There is no memory and nothing to seed.
• Bartlett vs. Triangular. Both are triangles and they are not the same one: Bartlett divides by N−1 and reaches exactly zero at both ends; Triangular divides by N (even) or N+1 (odd) and does not. At N = 8 the first entry is 0 and 0.125 respectively.
• Two windows are not normalised to a peak of 1, deliberately, because their defining functions are not: Taylor exceeds 1 near the centre, and DPSS carries unit energy so its peak falls as N grows. Scaling either to match the others would make this block disagree with the function it names.
• Flat Top goes negative. Its five-term sum dips below zero on the way to the ends. That is the window, not a defect, and it is why an amplitude-accurate window is a poor choice for anything that assumes a non-negative taper.
• Every one of the eighteen is exactly 1 at a window length of one, which is what MATLAB's functions return there too – measured on all seventeen that accept N = 1. DPSS is the exception on both sides: its parameter bound cannot be met at N = 1, so this block refuses it and so does dpss.
• No length parameter, by design. Simulink's block has one because it can also run as a source; this one always has an input, so N comes from the port and the two cannot disagree.