Table of Window Function Details

November 8, 2018

The following are descriptions of all 40 window functions available in the VibrationVIEW and ObserVIEW software packages.

Note: All the metrics on these tables were calculated with N (Window Size) = 4096. The window function images are credited to Bob K/CCO.

WINDOW CHARACTERISTIC EFFECT


MLW
Main Lobe Width
The ideal window in the frequency domain is a single impulse—that is, a window with MLW=0 and SLH=-infinity dB. In any real system, this is not possible as the MLW will be greater than 0. The greater the main lobe width, the more the test signal will be distorted in the frequency domain. As such, the lower the MLW value, the better.


SLH
Side Lobe Height
Side lobes are a necessary albeit unwanted artifact of data windowing (see above). Side lobes cause the data to be aliased (or “copied”) in the frequency domain. As such, the lower the SLH, the better.


SLRR
Side Lobe Roll-off Rate
Side lobes are not ideal (see above) and there is an infinite number of them. However, they roll-off (attenuate with increasing frequency) at some rate (the SLRR). The higher the SLRR, the better (the faster they attenuate the better).


ENBW
Equivalent Noise Bandwidth
Every window listed in this section performs low pass filtering. It is possible to construct a window that performs high pass filtering by the use of “conjugate mirror filters.” As such, white noise (a random signal with constant power spectral density across all frequencies) at the input of the window filter will be attenuated unevenly in frequency at the window output (the noise will no longer be white at the output.)

The ENBW allows users to easily compute the total noise power being passed through the window. For example, if the noise at the input of the window filter is white with constant power spectral density P, then the total noise power at the output of the window filter will be P x ENBW. By Schwartz Inequality, the minimum value of ENBW is 1, which is the case for the rectangular window.

Window Functions

Function Name: Blackman
Use: All-purpose window function

DESCRIPTION
Wide main lobe, but a good roll-off rate

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 12π/N
SLH: -58.2336 dB
SLRR: -18 dB/octave
ENBW: 1.7272
SIMILAR WINDOWS: Hamming, Hanning

 


Function Name: Hamming
Use: All-purpose window function

DESCRIPTION
Sinusoidal shape, wide main lobe reduces frequency resolution. Has the best selectivity for larger signals.

Time Domain (Left) & Frequency Domain (Right)

MLW:   8π/N
SLH:   -43.7547 dB
SLRR:  -6 dB/octave
ENBW:  1.3631
SIMILAR WINDOWS:  Blackman, Hanning

 


Function Name: Hanning
Use: All-purpose window function

DESCRIPTION
Sinusoidal shape, delivers good frequency resolution and reduced spectral leakage. A safe choice when no function has a clear advantage.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   8π/N
SLH:   -31.5565 dB
SLRR:   -18 dB/octave
ENBW:   1.5
SIMILAR WINDOWS: Hamming, Blackman

 


Function Name: Lanczos
Use: Interpolation and re-sampling advantages

DESCRIPTION
Narrow main lobe, but only moderate attenuation. Derived from the main lobe of a sine function.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   6.5π/N
SLH:   -26.5935 dB
SLRR:   -12 dB/octave
ENBW:   1.2994
SIMILAR WINDOWS:   None

 


Function Name: Parzen
Use: Density estimation, machine learning, pattern classification

DESCRIPTION
Best side lobe roll-off rate but gains this at the cost of a wide main lobe and relatively high side lobes for its ENBW

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   16π/N
SLH:   -53.0459 dB
SLRR:   -24 dB/octave
ENBW:   1.9175
SIMILAR WINDOWS:   None

 


Function Name: Bartlett

DESCRIPTION
A simple triangular window, with narrow main lobe and high side lobes

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   8π/N
SLH:   -26.5269 dB
SLRR:   -12 dB/octave
ENBW:   1.333
SIMILAR WINDOWS:  Rectangular, Trapezoidal

 


Function Name: Trapezoidal
Use: Bat chirp analysis, transients

DESCRIPTION
A variation of the rectangular window, with narrow main lobe and high side lobes

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   4.125π/N
SLH:   -13.4122dB
SLRR:   -6dB/octave
ENBW:   1.0212
SIMILAR WINDOWS:  Rectangular, Bartlett

 


Function Name: Rectangular
Use: Periodic signals that are perfectly spaced or for signals shorter than the length of the window

DESCRIPTION
Simple box waveform, typically results in leakage due to discontinuities

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 4π/N
SLH: -13.3239 dB
SLRR: -6 dB/octave
ENBW: 1
SIMILAR WINDOWS: Trapezoidal, Bartlett

 


Function Name: Kaiser 1
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   4.25π/N
SLH:   -14.7171 dB
SLRR:   -6 dB/octave
ENBW:   1.0046
SIMILAR WINDOWS: Chebyshev, Saramaki

 


Function Name: Kaiser 2
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   4.75π/N
SLH:   -18.6075 dB
SLRR:   -6 dB/octave
ENBW:   1.0472
SIMILAR WINDOWS:  Chebyshev, Saramaki

 


Function Name: Kaiser 3
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   5.5π/N
SLH:   -28.4232 dB
SLRR:   -6 dB/octave
ENBW:   1.366
SIMILAR WINDOWS:  Chebyshev, Saramaki

 


Function Name: Kaiser 4

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   6.5π/N
SLH:   -30.1532dB
SLRR:   -6dB/octave
ENBW:   1.2467
SIMILAR WINDOWS: Chebyshev, Saramaki

 


Function Name: Kaiser 5
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   7.5π/N
SLH:   -36.8982 dB
SLRR:   -6 dB/octave
ENBW:   1.359
SIMILAR WINDOWS:  Chebyshev, Saramaki

 


Function Name: Kaiser 6
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   8.625π/N
SLH:   -44.0897 dB
SLRR:   -6 dB/octave
ENBW:   1.4668
SIMILAR WINDOWS:  Chebyshev, Saramaki

 

 


Function Name: Kaiser 7
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height.  Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW:   9.75π/N
SLH:   -55.9526 dB
SLRR:   -6 dB/octave
ENBW:   1.569
SIMILAR WINDOWS:  Chebyshev, Saramaki

 

 


Function Name: Kaiser 8
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height.  Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 11π/N
SLH: -59.0503 dB
SLRR: -6 dB/octave
ENBW: 1.657
SIMILAR WINDOWS: Chebyshev, Saramaki

 


Function Name: Kaiser 9
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height.  Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 12.125π/N
SLH: -66.7879 dB
SLRR: -6 dB/octave
ENBW: 1.7576
SIMILAR WINDOWS: Chebyshev, Saramaki

 


Function Name: Kaiser 10
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 13.625π/N
SLH: -78.8358dB
SLRR: -6 dB/octave
ENBW: 1.8451
SIMILAR WINDOWS: Chebyshev, Saramaki

 


Function Name: Kaiser 11
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height.  Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 14.625π/N
SLH: -89.6442 dB
SLRR: -6 dB/octave
ENBW: 1.9288
SIMILAR WINDOWS:  Chebyshev, Saramaki

 


Function Name: Kaiser 12
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 15.75π/N
SLH: -90.6277 dB
SLRR: -6 dB/octave
ENBW: 2.0092
SIMILAR WINDOWS: Chebyshev, Saramaki

 


Function Name: Kaiser 13

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 17π/N
SLH: -109.6578 dB
SLRR: -6 dB/octave
ENBW: 2.0865
SIMILAR WINDOWS:  Chebyshev, Saramaki

 


Function Name: Kaiser 14
Use: Modular window function, all-purpose window

DESCRIPTION
Balances amplitude accuracy, side lobe distance, and side lobe height. Increasing the coefficients results in a wider main lobe and more attenuation on the side lobes.

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 18.25π/N
SLH: -118.4404dB
SLRR: -6dB/octave
ENBW: 2.1611
SIMILAR WINDOWS: Chebyshev, Saramaki

 


Function Name: Chebyshev 40
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 7π/N
SLH: -40.1168dB
SLRR: 0dB/octave
ENBW: 1.4563
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 50
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level. Flat side lobes. The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 8.75π/N
SLH: -50.1403 dB
SLRR: 0 dB/octave
ENBW: 1.4109
SIMILAR WINDOWS:  Kaiser, Saramaki

 


Function Name: Chebyshev 60
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 9.875π/N
SLH: -60.245 dB
SLRR: 0 dB/octave
ENBW: 1.5187
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 70
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 11.375π/N
SLH: -70.168 dB
SLRR: 0 dB/octave
ENBW: 1.6333
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 80
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level. Flat side lobes. The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 12.75π/N
SLH: -80.3373 dB
SLRR: 0 dB/octave
ENBW: 1.7418
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 90
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 14.5π/N
SLH: -90.3681 dB
SLRR: 0 dB/octave
ENBW: 1.844
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 100
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 15.625π/N
SLH: -100.1973dB
SLRR: 0dB/octave
ENBW: 1.9409
SIMILAR WINDOWS:  Kaiser, Saramaki

 


Function Name: Chebyshev 110
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 17.125π/N
SLH: -110.5814dB
SLRR: 0dB/octave
ENBW: 2.0332
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 120
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 18.875π/N
SLH: -120.2028dB
SLRR: 0dB/octave
ENBW: 2.1214
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 130
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level. Flat side lobes. The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 20π/N
SLH: -130.2188dB
SLRR: 0dB/octave
ENBW: 2.2062
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Chebyshev 140
Use: Modular window function

DESCRIPTION
Provides minimum main lobe width for a specified side lobe level.  Flat side lobes.  The variable parameter implicitly controls the height of the side lobes (e.g., 40 – > -40 db).

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 21.5π/N
SLH: -140.4674 dB
SLRR: 0 dB/octave
ENBW: 2.2878
SIMILAR WINDOWS: Kaiser, Saramaki

 


Function Name: Saramaki 1
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB. β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 4π/N
SLH: -13.3227dB
SLRR: -6dB/octave
ENBW: 1.002
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Saramaki 1.5
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB. β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 6π/N
SLH: -31.5163 dB
SLRR: -6 dB/octave
ENBW: 1.1923
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Saramaki 2
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB. β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 8π/N
SLH: -44.542 dB
SLRR: -6 dB/octave
ENBW: 1.4076
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Saramaki 2.5
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB.  β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 10π/N
SLH: -52.9516 dB
SLRR: -6 dB/octave
ENBW: 1.589
SIMILAR WINDOWS:  Kaiser, Chebyshev

 


Function Name: Saramaki 3
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB.  β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 12π/N
SLH: -65.9015 dB
SLRR: -6 dB/octave
ENBW: 1.7477
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Saramaki 3.5
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB.  β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 14π/N
SLH: -86.0196 dB
SLRR: -6 dB/octave
ENBW: 1.891
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Saramaki 4
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB. β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 16π/N
SLH: -98.9664 dB
SLRR: -6 dB/octave
ENBW: 2.0228
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Saramaki 4.5
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB.  β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 18π/N
SLH: -114.0496 dB
SLRR: -6 dB/octave
ENBW: 2.1457
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Saramaki 5
Use: Modular window function

DESCRIPTION
Provides minimum side lobe height for a specified main lobe width, while maintaining a roll-off rate. Beta determines the distance of the first null from the main lobe peak. determines the side lobe level with respect to the main lobe peak in dB. β = -0.0389S + 0.4509

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 20π/N
SLH: -122.2238 dB
SLRR: -6 dB/octave
ENBW: 2.2614
SIMILAR WINDOWS: Kaiser, Chebyshev

 


Function Name: Flat Top
Use: Amplitude resolution, when it is more important to find the exact amplitude, rather than the exact frequency, of the signal

DESCRIPTION
Delivers the most accurate amplitude resolution

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 20π/N
SLH: -69.0129dB
SLRR: -6dB/octave
ENBW: 3.7703
SIMILAR WINDOWS: None

 


Function Name: Exponential
Use: Impact testing and burst random excitation

DESCRIPTION
Very narrow main lobe, consistent but poor attenuation

Time Domain (Left) & Frequency Domain (Right)

CHARACTERISTICS
MLW: 8.875π/N
SLH: -15.4337dB
SLRR: -6dB/octave
ENBW: 1.4414
SIMILAR WINDOWS: None

 

 


 

Time Domain Graphs


Frequency Domain Graphs