Questions tagged [finite-impulse-response]

A finite impulse response (FIR) filter is a type of a signal processing filter whose impulse response is of finite duration.

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Does a FIR filter always perform a convolution operation?

I've come across this question in textbook. I guess it's basically asking are there any input or impulse response conditions that a FIR filter won't be able to compute. I can't think of any.
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How to find the impulse response from the following input/output relation

Suppose we have a system defined with input $x(t)$, and output $y(t)$, related by $$ y(t) = \sum_i \alpha_i(t)x(t-\tau_i(t)) \tag 1 $$ This is a linear system, (according to the textbook), so we can ...
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Frequency Sampling Filters (FSFs) NOT the Frequency Sampling Method

A class of digital filters called Frequency Sampling Filters (FSF) has been mentioned in a side note by Richard Lyons in another related question comparing IIR digital filter design using mapping ...
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Minimum Phase - All Pass Decomposition For Large Linear Phase Filters

UPDATE: I am looking for a robust approach to decompose linear phase FIR filters with 100s of coefficients into its minimum phase and all pass components. I originally thought determining all the ...
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Mapping of Classic Filters for Digital Filter Design

Of the four classic analog filter types: Butterworth, Chebyshev, Elliptic and Bessel- are any of these relegated to obsolescence for purposes of digital filter design in comparison to optimized ...
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How to calculate magnitude of frequency response?

I'm trying to write a function in Python that calculates the magnitude of an FIR filters frequency response. I tried doing it by first calculating the Fourier transform with np.fft.fft and then ...
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Causal inverse of $h[n]=\delta[n]-\alpha\delta[n-1]$

Find the causal inverse of $$h[n]=\delta[n]-\alpha\delta[n-1]$$ we have $h[0]=1$ and $h[1]=-\alpha$ also $h[n]=0$ for $n>1$ From the formula $$ h_i[n]=\sum_{i=1}^n\frac{h[n]h_i[n-i]}{h[0]} $$ we ...
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strange waveform after highness FIR filter

I was trying to apply FIR filter on the ECG signal: a bandstop for 45-55 Hz for noise removal and a highpass filter for moving baseline wander. But after that, the ECG signal show strange waveform at ...
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How to get the difference equation from impulse response?

I'm trying to solve a problem about filter design. We want to design a equalizer filter which have the following frequency response : How can i get the difference equation from the impulse responce ...
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Combination of type I FIR linear-phase systems

Let $h_1[n]$ and $h_2[n]$ be impulse responses of type I FIR linear-phase systems with lengths $M$ and $N$. What can be said about the phase response of the following filters? $h_3[n] = h_1[n] + h_2[...
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Radar Pulse Shaping Filter

For communication signals, a Root Raised Cosine (RRC) filter is often used as the pulse shaping filter. What kind pulse shaping filters (prototypes or window functions or tapers) are used in radar ...
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Equivalence between the linear phase of FIR filters and the (anti)symmetry of the coefficients

According to the Matt L.'s answer to this question, real-valued and causal FIR filters have a (generalized) linear phase response if and only if their coefficients satisfy (anti)symmetry condition. ...
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Python FIR Notch filter applied on both + and - frequency but only need + frequency

I have posted a summary of what I am seeing, I just made a pulse train and testing a notch filter on it as an example only. I also have a complex baseband signal centered on 0 Hz, this complex ...
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How does zero forcing equalizer work for consecutive pulses?

If in a digital communication system consecutive pulses are sent over a channel, to avoid ISI, a raised cosine filter is used for pulse shaping. If I understand correctly, then this graph taken from ...
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Filter Synthesis Formula to implement ZOH

$$h_n = \frac{1}{2\pi}\int_{-\pi}^\pi H_d(\omega) e^{jn\omega}\,\mathrm d\omega$$ I am attempting to design a FIR filter using the formula above for coefficients. Where $$H_d(\omega) = \frac{\sin \...
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Pulse-shaping FIR filter

I understand that pulse-shaping is performed to limit the bandwidth of the transmitted signal, but I would like to know how pulse-shaping can be implemented using an FIR filter.
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Multi-thread Audio Processing With C and JACK

I'm currently trying to create a NUPOLS (Non-Uniformly Partitioned OverLap Save) convolution reverb processor using C and JACK. According to the literature I've consulted; this is equivalent to ...
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Impulse Response and Frequency Response of a FBLMS filter

Suppose I work with sampling frequency FS and block length of L. I implemented the Frequency-domain Block LMS (FBLMS) algorithm ...
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FIR filter attenuation in the passband

OK, so I am designing a 2 kHz bandpass FIR filter using the following parameters: Fa = 1900 Hz Fb = 2100 Hz Fs = 50 kHz M = 33 pts Att = 40 dB I calculated the coefficients using this online tool (...
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Amplitude and phase compensation of analog filter

My analog filter perform much needed antialiasing and input protection. Unfortunately, the filter adds undesired changes in the gain/phase across frequency. For example, here is an example of ...
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Impacted of a conjugated filter

What is the effect of using a conjugated FIR filter? I have a use case where a weight vector, x, can be estimated using the least squares approximation: $$Ax=b$$ $$ A^HAx = A^Hb$$ $$ x = (A^HA)^{-1} ...
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Do we guess the cut off frequency when passband edge frequency and stop band edge frequency are given? FIR Filter design-LOW PASS FILTER

Say passband edge frequency=0.25 $\pi$ Stopband edge frequency=0.35 $\pi$ What is the cut off frequency? Do we average these 2 frequencies and write the answer or what is the procedure to find cut off ...
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Writing the specifications of digital filter, am I correct?

Design the FIR filter using suitable window for the specifications-: $0.899\leq |H (e^{j\omega}\;)|\leq1\;for\; |\omega| \leq0.2\pi$ $\; |H(e^{j\omega}\;)| \leq 0.01, \text{ for } \; 0.4\pi\leq \...
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Is a second order low pass or high pass fir filter possible?

I'm learning about filters and obviously the first kind of filters I came across were low pass and high pass filters: $$\frac{1}{2}(1+z^{-1})$$ is a low pass filter and $$\frac{1}{2}(1-z^{-1})$$ is a ...
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How to estimate multidimensional linear response function from measured input and output signals?

Problem definition: I measure N sources of noise $x_i$ and one output signal $y$ which contains real signal $y_0$ plus noise from all these sources $x_i$ transformed by linear response functions $h_i$ ...
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Where can I find a solved numerical example of FIR digital filter design using Kaiser window?

I am studying for digital signal processing exam. And I need to learn about Kaiser window numerical for it. It is pretty important. I searched the whole internet but could not find 1 example of Kaiser ...
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How would I approach implementing a windowed sinc filter with changing cutoff in real time?

I moved this out of another question, where I'd put it to give more context, and answered it here for the next reader. ELI5 how to implement a windowed sinc FIR filter in real time for an audio ...
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What is a simple method, if any, to calculate a variable IIR filter for audio effects in real time?

Question edited based on first answer which raised a lot of good points about what problem I'm trying to solve. Also reordered some things to stick context of how I did this with FIR so far at the ...
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FIR filtering returns "static" signal

//PROBLEM I'm trying to filter EEG trials from an array in which each trail has dimensions [8x125] = [number of channels x samples@250Hz], but the resulting signal looks static and wrong. Why is this ...
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Notch Filter via Bernstein Polynomial

Context: In the review article [1], the authors explain that we can model the frequency response of an FIR notch filter using Bernstein polynomials. The paper shows the details, but at the end of it, ...
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NLMS algorithm greatly attenuating signal

Im writing an NLMS MATLAB program to remove powerline noise from ecg signals. I sweep through tap widths and learning rates which get the best SNR values. Some of the combinations produce great SNRs ...
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Determine the lattice coefficients corresponding to FIR filter with system function

And sketch lattice structure $H(z)=1+ \frac {13} {24} Z^{-1}+ \frac {5} {8} Z^{-2}+ \frac {1} {8} Z^{-3}$ This is my engineering assignment question from Digital Signal Processing subject on the topic ...
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How do large tap counts effect FIR Filters for block data?

I am using the ARM CMSIS DSP library for a signal processing application. I find good filter performance when using tap counts that are in excess of 10% of the length of my data block. I understand ...
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Accuracy of time-domain filters and frequency domain filters

I am trying to calculate the Hilbert transform using 3 different method: scipy.signal.hilbert function, time domain filter, and frequency domain filter. The test ...
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FM demodulation using complex differentiation

I'm trying to implement the complex differentiation discriminator which is taken from Software-Defined Radio Using MATLAB, Simulink, and the RTL-SDR. The final result is $$s(t) = \frac{s_q'(t) s_i(t) -...
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Find coefficients of optimal Wiener filter of length 2

I need to find the coefficients (impulse response) of a FIR Wiener filter with length equal to 2. I have a gaussian white noise signal that is generated using the Standard Normal Distribution (mean = ...
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Half-band FIR Filter desired output

I am a trying to implement the Receiver Signal Path of the ADRV9009 in Verilog, starting with the 2 half-band filters. These are the coefficient of the two filters: This is the result that I got. My ...
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Arbitrary phase FIR filter design

I would like to design an FIR filter using the frequency sampling method with nonlinear phase specifications. For example, between $0$ and $\frac{f_s}{4}$ a phase of $180^\circ$ and between $\frac{f_s}...
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Low Pass Filtering, Welch's Method, ENBW

I am working on using Welch's method (https://www.osti.gov/servlets/purl/5688766/) to estimate a Power Spectral Density (PSD). This algorithm involves scaling a set of averaged FFTs by the equivalent ...
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Why is z (and not ω) the variable of interest for discrete time systems?

A continuous time domain system is well described by the Laplace transform. It allows to express any continuous signal x(t) as the integral sum of weighted complex and exponentially growing/decaying ...
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Who first coined "Direct Form I" and "Direct Form II"?

I see "Direct Form I" and "Direct Form II" commonly in literature to refer to FIR / IIR implementation from the filter transfer function, and reference it myself, but where did ...
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Is parallel structure applicable in realizing FIR filters?

This may sound weird but can FIR filters be realized by implementing it in parallel form like in IIR? I know that FIR can be realized in cascade, but I can't seem to find any resources that realize ...
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how to get N point FIR filter( convolution) output when input and impulse response are both N points ? ideally convolution results in length N+N-1

x[n] -> Input Signal of length N h[n] -> Impulse response of length N y[n] = x[n]*h[n] (convolution to get the output of this FIR filter) Ideally length of y[n] should be N+N-1 but is it ...
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Convolving a LP FIR filter with a HP FIR filter

I currently feed a sampled audio input signal into a 511 tap highpass FIR filter, the output of which is then fed to another 511 tap lowpass FIR filter, resulting in a very narrow bandpass filter ...
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Amplitude / gain of difference of 2 known FIR low-pass filters

Given a discretely sampled sinusoidal signal (frequency $1/40$), and 2 Simple Moving Averages (SMA), better known as FIR low-pass filters of order e.g. $10$ and $21$, it can easily be calculated what ...
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Can simple FIR/IIR filtering recover/estimate a signal plagued with low SNR white noise?

I'm trying to design a filter to restore the original signal from strong noise (low SNR). I have tried low pass FIR and it could work well as the amplitude of original signal is much higher than the ...
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Implementing FIR Hilbert Transformer in Python

I want to implement FIR Hilbert Transformer in Python using window method. I'm new to digital signal processing so please point out to me all mistakes you notice. Ideal Hilbert transformer is ...
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Frequency domain filtering: must filter coefficients always be conjugate symetric?

While trying to do frequency domain filtering of audio signals using windowed overlap-add methodology, I came across some pre-calculated frequency domain coefficients. I noticed that the coefficients, ...
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halfband filter

I am not familiar with this halfband filter implementation: input is feed into two paths: the upper path is simply same as input, say x0, x1, x2, etc. The lower path is a halfband filter coefficients (...
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Differences in transforming a sinc FIR filter from lowpass to highpass using spectral inversion and spectral reversal

I have designed a lowpass sinc 1023 tap FIR filter with a Blackman window and this works fine. I understand there are then two ways to transform this lowpass filter to a highpass one. One is spectral ...

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