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A graph of amplitude vs frequency (not time) for a single sinusoid at frequency 0.6 f s and some of its aliases at 0.4 f s, 1.4 f s, and 1.6 f s would look like the 4 black dots in Fig.3. The red lines depict the paths ( loci ) of the 4 dots if we were to adjust the frequency and amplitude of the sinusoid along the solid red segment (between f ...
Reduce high-frequency signal components with a digital lowpass filter. Decimate the filtered signal by M; that is, keep only every M th sample. Step 2 alone creates undesirable aliasing (i.e. high-frequency signal components will copy into the lower frequency band and be mistaken for lower frequencies). Step 1, when necessary, suppresses ...
Effects of aliasing, blurring, and sharpening may be adjusted with digital filtering implemented in software, which necessarily follows the theoretical principles. A family of sinusoids at the critical frequency, all having the same sample sequences of alternating +1 and –1.
In this example, f s is the sampling rate, and 0.5 cycle/sample × f s is the corresponding Nyquist frequency. The black dot plotted at 0.6 f s represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample rate. The other three dots indicate the frequencies and amplitudes of three other sinusoids that ...
A simple illustration of aliasing can be obtained by studying low-resolution images. A gray-scale image can be interpreted as a function in two-dimensional space. An example of aliasing is shown in the images of brick patterns in Figure 5. The image shows the effects of aliasing when the sampling theorem's condition is not satisfied.
In a monochrome or three-CCD or Foveon X3 camera, the microlens array alone, if near 100% effective, can provide a significant anti-aliasing function, [2] while in color filter array (e.g. Bayer filter) cameras, an additional filter is generally needed to reduce aliasing to an acceptable level. [3] [4] [5]
Lanczos windows for a = 1, 2, 3. Lanczos kernels for the cases a = 1, 2, and 3, with their frequency spectra. A sinc filter would have a cutoff at frequency 0.5. The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L(x), called the Lanczos kernel.
Here we provide an example of two-channel filter banks in 2D with sampling matrix = [] We would have several possible choices of ideal frequency responses of the channel filter () and (). (Note that the other two filters H 1 ( ξ ) {\displaystyle H_{1}(\xi )} and G 1 ( ξ ) {\displaystyle G_{1}(\xi )} are supported on complementary regions.)