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Category# Filtering theory

Summary

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, , computer graphics, and structural dynamics.
There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be:
non-linear or linear
time-variant or time-invariant, also known as shift invariance. If the filter operates in a spatial domain then the characterization is space invariance.
causal or non-causal: A filter is non-causal if its present output depends on future input. Filters processing time-domain signals in real time must be causal, but not filters acting on spatial domain signals or deferred-time processing of time-domain signals.
analog or digital
discrete-time (sampled) or continuous-time
passive or active type of continuous-time filter
infinite impulse response (IIR) or finite impulse response (FIR) type of discrete-time or digital filter.
Linear continuous-time circuit is perhaps the most common meaning for filter in the signal processing world, and simply "filter" is often taken to be synonymous. These circuits are generally designed to remove certain frequencies and allow others to pass. Circuits that perform this function are generally linear in their response, or at least approximately so. Any nonlinearity would potentially result in the output signal containing frequency components not present in the input signal.

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Comb filter

In signal processing, a comb filter is a filter implemented by adding a delayed version of a signal to itself, causing constructive and destructive interference. The frequency response of a comb filter consists of a series of regularly spaced notches in between regularly spaced peaks (sometimes called teeth) giving the appearance of a comb. Comb filters are employed in a variety of signal processing applications, including: Cascaded integrator–comb (CIC) filters, commonly used for anti-aliasing during interpolation and decimation operations that change the sample rate of a discrete-time system.

Linear phase

In signal processing, linear phase is a property of a filter where the phase response of the filter is a linear function of frequency. The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the group delay. Consequently, there is no phase distortion due to the time delay of frequencies relative to one another.

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Nowadays almost all the mobile networks use the 4G and will eventually soon use the 5G. To use this technology, devices need lots of band filters. This is why the Advanced NEMS laboratory of the EPFL is developing a new kind of MEMS resonant device at 5GHz called "Lithium niobate bulk acoustic resonator". The goal of this project is to compare several techniques to create thin walls by several deposition methods into silicon layer in order to allow chain production of those resonators.

2021This thesis describes innovative techniques for reducing speckle noise and improving the intensity profile of the speckle correlation fringes. The methods are based on reducing the range of the modulation intensity values of the speckle interference pattern. After the fringe pattern is corrected adaptively at each pixel, a simple morphological filtering of the fringes is sufficient to obtain smoothed fringes. The concepts are presented both analytically and by simulation by using computer-generated speckle patterns and experimental verifications are performed wherever possible. A new generalized method for designing continuous amplitude-only pupil filters for transverse superresolution using a nonlinear programming method is also presented. The thesis emphasises the principal advantage of amplitude-only filters over their phase-only counterparts, that the side lobe intensities can be highly reduced along with the spot size. A quantitative comparison with continuous phase-only filters as well as the two-zone binary phase filter is shown with respect to spot size and ratio of side lobe to central peak intensity. The work is extended to combine the advantages of amplitude and phase filters in one complex filter that performs better than either phase or amplitude filters designed so far. The performance here refers to having a smaller spot size along with higher peak to side lobe intensity ratio. Using numerical simulation the limitations of phase and amplitude filters are assessed. The experimental verification of the designed combination filter is performed with two LCD spatial light modulators used for displaying separately the phase and amplitude part of the filter. Results obtained from this setup confirm the simulation. Finally, the effect of optical superresolution on speckle correlations is studied. Simulations reveal that using a lateral super-resolution pupil filter more than twice the out of plane correlation length of the clear pupil can be achieved. This means that the measurement range in speckle correlation measurements doubles. To verify the correlation length an experiment is performed using a liquid crystal (LCD) spatial light modulator as a programmable superresolution filter. The results corroborate the simulation.

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