Frequency broom
The frequency broom is an element of test images and is used to assess the horizontal and vertical resolution of a reproduced television image . The name refers to the similarity with a bush or rod broom.
A frequency broom consists of narrow sectors or triangles lying next to one another, which are alternately white and black and whose tip converges towards a common point. The pattern becomes blurred towards the tip because the light and dark areas that are close together can no longer be displayed separately. The lower the resolution of the image, the larger the area in which the pattern is blurred.
The representation of the frequency broom with perpendicular triangles is mainly determined by the bandwidth of the television signal and the electronics; for this, in addition to the frequency broom small, the bandwidth is specified in MHz . As soon as the sectors are so narrow that they blur into a uniform gray area, the bandwidth is reached.
The frequency broom with horizontal triangles provides information about the resolution of the picture tube (focusing). The frequency information here does not relate to the spectral components present in the real television signal. These are the frequencies that would be transmitted if the frequency broom were rotated by 90 °. The resolution given as the number of lines for some test images is more meaningful here (“Z” in the example image). The brooms near the picture corners are used to assess the blurring of the edge of the picture tube.
The moiré effect can also be visible in reduced images of frequency brooms : near the tip, it appears as if the sectors were curved. It is an interference between the spatial frequency of the original and the spatial frequency of the discrete sampling .
In more recent, electronically generated test images, the frequency brooms for determining the bandwidth have been replaced by frequency packets (or wobble bands); the brooms with horizontally lying triangles have been omitted because they only affect frequencies whose transmission is not in question.
The frequency broom as a theoretical model
isolated horizontal frequency broom
Frequency brush after discretization
the same frequency broom after an attempted reconstruction, right of the middle there is aliasing and incorrect reconstructions at lower frequencies
Horizontal frequency brushes are considered here, i.e. those that provide information about the vertical resolution. Vertical frequency brooms are of course to be treated completely analogously.
If you look at a vertical section through the signal, you get a square-wave signal with an increasing vertical spatial frequency to the right (and decreasing expansion, since the number of strokes remains constant). If this exceeds the vertical resolution of the recording, transmission or display, correct reproduction is no longer guaranteed. Typically, the left part of the broom is displayed correctly, and the resolution of the display can be read off from the horizontal position where the first irregularities appear, in the above examples approximately from the center of the image. Traditional sampling knowledge recommends a previous low-pass filtering up to the highest supported frequency to prevent such artifacts.
In the first image shown here, the critical resolution is the vertical resolution of the saved thumbnail or, if enlarged, the saved image. We are initially not assuming a square-wave signal, but a sinusoidal signal, as this of course mathematically facilitates the assignment to a specific vertical frequency.
As with the television signal, the limitation of the resolution is realized by discretization. In the image shown, 15 vertical pixels (original size) correspond to one line, so the horizontal width of the correctly reproduced area is significantly reduced by the discretization.
To demonstrate the extent to which the original signal can be reconstructed in each case, we use the Nyquist-Shannon sampling theorem . This means that if the spectrum of the vertical section is limited to the frequency band up to half the vertical sampling frequency, a complete reconstruction of the signal by means of vertical convolution with the sinc function (Si function or also gap function) is possible. If we try this reconstruction on the example under consideration, we get the result shown above. One can clearly see the edge from which the requirement of the sampling theorem is no longer fulfilled, since the vertical spatial frequency of the cut becomes too high.
When transitioning to square-wave signals, it should be noted that these also contain the third, fifth, etc. harmonic . The reconstruction is made considerably more difficult because the signal is (theoretically) not even band-limited. The figure on the right shows the reconstruction for a signal that only approximates the square-wave signal up to the fifth harmonic. You can see how the display quality gradually deteriorates towards the right, since fewer and fewer harmonics can be correctly reconstructed.