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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A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on application, the required attenuation within the stopband may typically be a value between 20 and 120 dB higher than the nominal passband attenuation, which often is 0 dB. The lower and upper limiting frequencies, also denoted lower and upper stopband corner frequencies, are the frequencies where the stopband and the transition bands meet in a filter specification.
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.
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. In electronics and signal processing, a filter is usually a two-port circuit or device which removes frequency components of a signal (an alternating voltage or current). A band-pass filter allows through components in a specified band of frequencies, called its passband but blocks components with frequencies above or below this band.
Adaptive signal processing, A/D and D/A. This module provides the basic
tools for adaptive filtering and a solid mathematical framework for sampling and
quantization
The students will acquire a solid knowledge on the processes necessary to design, write and use scientific software. Software design techniques will be used to program a multi-usage particles code, ai
This laboratory work allows students to deepen their understanding of optical instruments, optoelectronic devices and diagnostic methods. Students will be introduced in state of the art optical instru
A fundamental problem in signal processing is to design computationally efficient algorithms to filter signals. In many applications, the signals to filter lie on a sphere. Meaningful examples of data of this kind are weather data on the Earth, or images of the sky. It is then important to design filtering algorithms that are computationally efficient and capable of exploiting the rotational symmetry of the problem. In these applications, given a continuous signal f:S2→R on a 2-sphere S2⊂R3, we can only know the vector of its sampled values f∈RN:(f)i=f(xi) in a finite set of points P⊂S2,P={xi}i=0n−1 where our sensors are located. Perraudin et al. in \cite{DeepSphere} construct a sparse graph G on the vertex set P and then use a polynomial of the corresponding graph Laplacian matrix L∈Rn×n to perform a computationally efficient - O(n) - filtering of the sampled signal f. In order to study how well this algorithm respects the symmetry of the problem - i.e it is equivariant to the rotation group SO(3) - it is important to guarantee that the spectrum of L and spectrum of the Laplace-Beltrami operator ΔS2 are somewhat ``close''. We study the spectral properties of such graph Laplacian matrix in the special case of \cite{DeepSphere} where the sampling P is the so called HEALPix sampling (acronym for \textbf Hierarchical \textbf Equal \textbf Area iso\textbf Latitude \textbf {Pix}elization) and we show a way to build a graph G′ such that the corresponding graph Laplacian matrix L′ shows better spectral properties than the one presented in \cite{DeepSphere}. We investigate other different methods of building the matrix L better suited to non uniform sampling measures. In particular, we studied the Finite Element Method approximation of the Laplace-Beltrami operator on the sphere, and how FEM filtering relates to graph filtering, showing the importance of non symmetric discrete Laplacians when it comes to non uniform sampling measures. We finish by showing how the graph Laplacian L′ proposed in this work improved the performances of DeepSphere in a well known classification task using different sampling schemes of the sphere, and by comparing the different Discrete Laplacians introduced in this work.
We propose an ultra-low-power (ULP) image signal processor (ISP) that performs on-the-fly in-processing frame compression/decompression and hierarchical event recognition to exploit the temporal and spatial sparsity in an image sequence. This approach reduces energy consumption spent processing and transmitting unimportant image data to achieve a 16 × imaging system energy gain in an intruder detection scenario. The ISP was fabricated in 40-nm CMOS and consumes only 170 μW at 5 frames/s for neural network-based intruder detection and 192 × compressed image recording.