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Explain the Limiting the Spectrum
This low-pass filter is known an anti-aliasing filter. These filters are originated at the input to most applications. Since they are required before the signal is sampled, they are approximately always analog filters. It is theoretically possible to make use of the DSP device to remove the aliasing, but this would need a high sample rate. Actually, this is rarely done as it would consume too much of the processing power of the DSP, which we need to carry out other tasks. The ideal anti-aliasing filter characteristics are displayed in the lower half of the above diagram. It is flat along with gain A over the pass band and zero at any other point.
An ideal filter would as well have a linear phase response. Variations from this ideal may have an important effect on performance. For instance, in control applications, a badly planed filter may mean that the system spends all of its time trying to compensate for the filter, rather than trying to keep a constant motor speed. In audio applications, a poor phase response can lead to harmonic distortion and degradation that is frequently audible. For audio applications, commercially available switched-capacitor filters are easy to use and offer a reasonably linear response.
Gaussian derivatives Generate Gaussian kernels for a given scale "sigma", and display the kernel. The size of the kernel should be floor(3*sigm)+1; (i) Write an m-file "
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