**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Finite impulse response

Summary

In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
Definition
For a causal discrete-time FIR filter of order N, each value of the output sequence is a weighted sum of the most recent input values:
:\begin{align}
y[n] &= b_0 x[n] + b_1 x[n-1] + \cdots + b_N x[n-N] \
&= \sum_{i=0}^N b_i\cdot x[n-i],
\end{align}
where:
*

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people (7)

Related publications (96)

Loading

Loading

Loading

Related units (5)

Related concepts (29)

Convolution

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function (f*g) th

Digital signal processing

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The di

Low-pass filter

A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency

Related courses (55)

This class teaches the theory of linear time-invariant (LTI) systems. These systems serve both as models of physical reality (such as the wireless channel) and as engineered systems (such as electrical circuits, filters and control strategies).

The goal of this course is twofold: (1) to introduce physiological basis, signal acquisition solutions (sensors) and state-of-the-art signal processing techniques, and (2) to propose concrete examples of applications for vital sign monitoring and diagnosis purposes.

Ce cours aborde la théorie des systèmes linéaires discrets invariants par décalage (LID). Leurs propriétés et caractéristiques fondamentales y sont discutées, ainsi que les outils fondamentaux permettant de les étudier (transformée de Fourier et transformée en Z).

Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochasticity in both the graph topology and the signal itself. To bridge this gap, we examine the statistical behavior of the two key filter types, finite impulse response and autoregressive moving average graph filters, when operating on random time-varying graph signals (or random graph processes) over random time-varying graphs. Our analysis shows that 1) in expectation, the filters behave as the same deterministic filters operating on a deterministic graph, being the expected graph, having as input signal a deterministic signal, being the expected signal, and 2) there are meaningful upper bounds for the variance of the filter output. We conclude this paper by proposing two novel ways of exploiting randomness to improve (joint graph-time) noise cancellation, as well as to reduce the computational complexity of graph filtering. As demonstrated by numerical results, these methods outperform the disjoint average and denoise algorithm and yield a (up to) four times complexity reduction, with a very little difference from the optimal solution.

Digital signal processors are ubiquitous in electronics, with applications ranging from sound processing to software-defined radio. Finite impulse response (FIR) filters are among the components that are used for the processing; the implementation is tailored to the user’s needs, whether they specifically need performance or configurability. Handling numerous channels in a single filter block can be achieved in hardware by running multiple filters in parallels, with a high space expense and controller overhead. This project proposes and discusses an implementation template for a pipeline that simultaneously processes a desired number of channels, while keeping coefficients configurability. The implementation we propose is economic in terms of area while meeting the theoretical timing requirements to process long filters.

2017Sentiment analysis is the automated coding of emotions expressed in text. Sentiment analysis and other types of analyses focusing on the automatic coding of textual documents are increasingly popular in psychology and computer science. However, the potential of treating automatically coded text collected with regular sampling intervals as a signal is currently overlooked. We use the phrase "text as signal" to refer to the application of signal processing techniques to coded textual documents sampled with regularity. In order to illustrate the potential of treating text as signal, we introduce the reader to a variety of such techniques in a tutorial with two case studies in the realm of social media analysis. First, we apply finite response impulse filtering to emotion-coded tweets posted during the US Election Week of 2020 and discuss the visualization of the resulting variation in the filtered signal. We use changepoint detection to highlight the important changes in the emotional signals. Then we examine data interpolation, analysis of periodicity via the fast Fourier transform (FFT), and FFT filtering to personal value-coded tweets from November 2019 to October 2020 and link the variation in the filtered signal to some of the epoch-defining events occurring during this period. Finally, we use block bootstrapping to estimate the variability/uncertainty in the resulting filtered signals. After working through the tutorial, the readers will understand the basics of signal processing to analyze regularly sampled coded text.

Related lectures (193)