# 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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31k views

### How many taps does an FIR filter need?

I am looking to design a set of FIR filters to implement a low pass filter. I am also trying to reduce the latency of the signal through the filter so I am wondering what the minimum number of taps I ...
49k views

### FIR filter with linear phase, 4 types

I know there are 4 types of FIR filters with linear phase, i.e. constant group delay: (M = length of impulse response) Impulse response symmetrical, M = odd Imp. resp. symmetrical, M = even Imp. resp....
6k views

### FIR Filter Design: Window vs Parks McClellan and Least Squares

Are there any advantages to use a window approach over Parks-McClellan (further abbreviated here as PMcC) or Least Squares algorithms for FIR filter design of a low pass filter? Assume with today's ...
5k views

### Why would one use a Hann or Bartlett window?

Suppose we're designing a low-pass FIR filter, and I want to use one of these three windows: Bartlett, Hann or Hamming. From Oppenheim & Schafer's Discrete-Time Signal Processing, 2nd Ed, p. 471:} ...
636 views

### Gaussian FIR filter with no multipliers?

What is the simplest way to implement a Gaussian FIR filter with unity gain coefficients and no multipliers? Please preface your answer with spoiler notation by typing the following two characters ...
27k views

### Why is a linear phase important?

If symmetry conditions are met, FIR filters have a linear phase. This is not true for IIR filters. However, for what applications is it bad to apply filters that do not have this property and what ...
5k views

### Digital filter design basic principles (IIR/FIR)

Although I have a solid experience in designing audio engines and such, I am fairly new to the realm of Digital Filter Design, particularly IIR and FIR filters. In other words, I'm trying to learn as ...
9k views

### Filter Order Rule of Thumb

Is there a rule of thumb for calculating the approximate filter order of a FIR/IIR based on passband vs sample rate? I seem to remember reading about it once in Undergrad. I'd think you could make a ...
4k views

### Convert a FIR to an equivalent IIR

Is there a way to convert a FIR to an IIR filter with the most similar behavior?
25k views

### Why are FIR filters still stable even though they contain poles?

How come FIR filters are always stable? Since they contain poles, shouldn't they be more affected by stability issues than others?
3k views

### Is there a way to derive an FIR filter using an IIR filter?

I know there's a thread similar to this one here, but the OP is asking the reverse of what I'm trying to find here. I've done some research on the web with very few sources coming up with actual ...
1k views

### How to design very narrow, sharp lowpass filters - Only DC needed?

I asked exact the same here one year ago: One year ago question I asked this question again here, because after one year, I have learned more about DSP and am thinking ways to improve it. Filter ...
826 views

### Are SOS structures better for linear phase FIR filters?

I've seen many discussions suggesting that SOS's are often/usually the preferred structure for fixed point hardware filter implementations, since they preserve conjugate pairs, etc., but I've never ...
666 views

### Design a linear-phase FIR filter approximating the magnitude of a given IIR filter

I have a biquad IIR filter from which I want to get a linear-phase FIR. I saw that related question but the OP does not care much about phase. I have troubles getting the exact same magnitude curve ...
2k views

Adaptive IIR filters is not straightforward, and may be unstable. Many people say that adaptive IIR filters use less coefficients than FIR filters. What I'm curious about is how many coefficients can ...
30k views

### Group delay of the FIR filter

For an FIR filter, with symmetrical tap values $h[N-1-n]=h[n]$, why is the group delay $\frac{N-1}{2} T$ (where $N$ is the number of taps of the FIR filter and $T$ is the sampling time)? Why is ...
4k views

### How to design very narrow band, very sharp low pass filters - Only DC needed?

I am using a DSP processor to sample signals at 108kHz and I only want to get the DC part out of it. Such a high sampling rate is used because I want to use oversampling to reduce quantization noises. ...
6k views

### Given the input and the output, how to determine the impulse response?

I would like to find the impulse response, $h[n]$, of an LTI system given the input $$x[n] = [1,-3,2]$$ and the output $$y[n] = [1,-1,-4,4]$$ I know that $y[t]=x[t]*h[t]$, but I am having hard ...
226 views

### How to reliably compute the group delay of a comb filter

I applied the following FIR comb filter in real-time: y[n]=x[n]-x[n-40] Since this is an FIR, the group delay is D=(N-1)/2=20 samples. After applying the filter ...
645 views

### Raised-Cosine Filter - calculating phase response

I want to compute phase response of an raised-cosine FIR filter. I have trouble finding the complex transfer function of the filter in literature (there is a real valued transfer function of frequency)...
309 views

### Obtaining phase and magnitude of 2 spectral components after ADC

I am currently implementing a digital filter to obtain the output of a PID controller. The control loop is carried out by applying a 1kHz sine wave at the input of the system and reading the output ...
1k views

### Minimum phase FIR method

I am trying to make a minimum phase filter (in wxMaxima) according to these steps: first create a "normal" FIR (a simple sinc, wc=0.4, random example, but in the pictures a remez with Octave) ...
717 views

### Help in understanding the formula of Signal-to-Noise-Ratio (SNR) - Part 1

Question 1: Consider an Autoregressive model : \begin{align} y[n] &= y[n-1] + x[n]\\ z[n] &= y[n] + w[n] \end{align} where $y$ is the output observation, $x$ is a random input and $w$ is ...
80 views

### What should be the cut off frequency of a Filter operating on an OFDM signal?

I have a time domain OFDM signal and to this I need to apply different linear filter however I am not sure on the cut off frequency. I am simulating for multiple symbols where each symbol has 1200 ...
710 views

### Removing an unwanted sinusoidal signal using FIR filter

I am learning about the $\mathcal Z$-transform and FIR filters and I do have problem with the following exercise: There is given signal $$x[n] = s[n]+\sin\left(2\pi f_n n\right)$$ where $s[n]$ is a ...
36 views

### What exactly is stored in the buffer array in the code below? Is it the values of x[n-k] or something else?

What exactly is stored in the buffer array in the FIR Filter code below? Is it the values of x[n-k] or something else? ...
43k views

### Filter order vs number of taps vs number of coefficients

I'm learning DSP slowly and trying to wrap my head around some terminology: Question 1: Suppose I have the following filter difference equation: $$y[n] = 2 x[n] + 4 x[n-2] + 6 x[n-3] + 8 x[n-4]$$ ...
1k views

### How can I design a very narrow filter?

Suppose I've got an audio signal sampled at $48000$ Hz, and I'd like to design a low-pass filter that isolates everything below ~$60$Hz. In the digital world, this is a low-pass filter with the ...
5k views

### Vector length output of discrete time convolution

Suppose that the impulse response of a discrete time filter is $h[i]$ where $i=0,1,2,...,N-1$ and the input sequence to the filter is $x[i]$ for $i=0,1,2,.., M-1,$ what would be the length of output ...
433 views

### Force Linear Phase for a FIR Filter Synthesized Using Berchin's FDLS?

As a follow-on to this post, how would you force linear phase for a FIR filter you synthesized using Berchin's FDLS?
8k views

### Where can I get an open source implementation of the Parks-McClellan optimal FIR filter design algorithm?

Background: Often times I am doing some sort of signal processing task that requires a unique filter. Usually at this point I go to MATLAB and generate a new unique filter using $\tt firpm()$. The ...
3k views

### FIR filter design by the Fourier transform method

I am having some problems understanding how the Fourier transform method is used to determine the FIR filter. As far as i have understood, you start by using the ideal impulse reponse for the ...
96 views

### Can I set a constraint on the first tap of an FIR filter such that its inverse is stable?

Let's say I have the following FIR filter $h[n]$, so the output $y[n]$ for an input $x[n]$ is $$y[n] = \sum_{k=0}^{m-1}x[n-k]h[k]$$ The inverse of this filter is given by the IIR difference ...
572 views

### FIR to linear-phase FIR

I am trying to convert an FIR impulse into linear-phase FIR impulse, I need to remove the phase response, so when it is applied to a sound it only changes the amplitude response. Here is my code ...
5k views

### Causal and non-causal systems in real world

Causal systems are defined as the systems whose : Output depends on present as well as past inputs and the impulse response; and sometimes depends also on the past outputs (in case of recursive ...
4k views

### Downsampling lowpass filter for audio: FIR or IIR?

I'm working on a real-time audio processing project in which I have to downsample a 44.1 kHz to a yet-to-be-determined lower sampling rate essentially for reducing computational complexity. I'm ...
3k views

### What exactly is Savitzky-Golay differentiation filter?

I could understand Savitzky-Golay filter as being smoothing filter, but then there also seems to be Savitzky-Golay differentiation filter, though for some reason, details do not seem to be clear. So ...
679 views

### Transform linear-phase FIR to minimum-phase FIR

Given a FIR filter (non-causal) with phase zero and real coefficients given by $$H(z) = \sum_{n=-M}^{M}h[n]z^{-n}$$ with ripple $\delta_2$. How can I obtain a filter $H_{{\rm min}}(z)$ of minimum ...
794 views

### Multi-Stage digital FIR filter vs Single stage FIR filter. Which is better?

Can anyone provide an insight to select a filter structure out of multi-stage and single stage FIR filter?(it will be great help if references are also provided) Let's say I have to make 50 tap filter....
9k views

### Determining the Filter Coefficients of an FIR Filter

I need to find the filter coefficients of an FIR filter that will block sinusoids of frequency $200\ \rm Hz$ if the sinusoid is sampled at $1.2\ \rm kHz$. I feel like this is a fairly simple problem,...
231 views

### should this be viewed as an impulse response or step response

I'm trying to teach myself the relation between simple discrete ODE's and the impulse response-step response concept. Getting back to the question: I don't expect anyone to read the whole thing but I'...
610 views

### Is an FIR filters 'transition width' frequency dependent?

I was recently brushing up on some FIR filter design and was browsing the Wikipedia page. A claim in the article caught my attention: The main disadvantage of FIR filters is that considerably more ...
854 views

### Given an FIR filter coefficients, how can I find coefficients of its equalizer filter?

I have an N-tap direct form complex FIR filter with known coefficients [c0 c1 .. cn]. I want to find the coefficients of its equalizer filter which when cascaded ...
2k views

### Check if a filter is IIR or FIR

I have the following equation: $$H(z) = \frac{z^3+5z^2+3z+1}{10z^3}$$ I want to find out whether if its IIR or FIR. Here is the steps I have gone so far: H(z) = \frac{1}{10}\frac{z^3+5z^2+3z+1}{z^...
2k views

### FIR-Decimation and Low-pass filter (taps vs number of input points vs number of decimation stages)

I am new to digital filters and trying to understand parameters behind them. Scenario I am trying to get DC value from signals sampled at 100kHz sampling rate. such high frequency is used due to ...
480 views

### Design of FIR Filters with Arbitrary Magnitude and Phase Responses

I found many information in this thesis "Algorithms for the Constrained Design of Digital Filters with Arbitrary Magnitude and Phase Responses",i want to understand it. This question is a ...
5k views

### What Is the Transfer Function of a Moving Average (FIR Filter)?

To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ...
157 views

### Convert a Park McClellan FIR Solution to Achieve Stop-band Roll-off

Often it is more desirable to have a roll-off versus frequency of the rejection in the stopband; for example resampling filters where all the alias image locations fold into the first Nyquist Zone. ...