Questions tagged [digital-filters]

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21
votes
4answers
29k 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 ...
14
votes
2answers
3k views

Is a high-passed signal the same as a signal minus a low-passed signal?

My question is, if I want to high-pass a signal, is it the same as low-passing a signal and subtracting it from the signal? Is it theoretically the same? Is it practically the same? I have searched (...
8
votes
5answers
1k views

Why do digital filters work?

So I just started reading on FIR and IIR filters and am amazed by how "simple" the theory seems, so far. But what confuses me is, why does filtering work by creating a weighted sum of previous ...
7
votes
3answers
379 views

Protect an IIR filter from being reverse-engineered

I created a somewhat unique IIR filter and I want to protect the filter from being reverse-engineered I think you all know it is quite easy to get all the different weights of an IIR by using impulse ...
6
votes
2answers
19k views

Transfer function of second order notch filter

Can anyone mention the transfer function of second order notch filter to remove the line frequency of 50 Hz, in terms of frequency and sampling rate. Just like for Low pass Butterworth filter as, $$ ...
6
votes
4answers
307 views

Make a signal that fits another the best possible with a limitation in the 2nd derivative

Consider this step function: The signal that "fits" this should look like the following (in green): The corners are now smooth because the maximum second derivative allowed is not infinite anymore. ...
5
votes
2answers
1k views

What is the largest “safe” order for the digital Butterworth filter of a given signal?

Say I want to apply a zero-phase Butterworth bandpass filter, implemented in MATLAB using butter and filtfilt. So, for an order-$...
5
votes
5answers
4k 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 ...
4
votes
5answers
3k views

What's the Q factor of a digital filter's pole?

For the analog S-plane, the Q factor depends on the angle of the complex pole $p$ from the horizontal axis, $\theta = \arg p$: damping factor $\zeta = \frac{1}{2Q}$, and $\zeta = \cos(\theta)$, and $\...
4
votes
5answers
938 views

Why can't a causal digital filter have an infinitely sharp transition between the passband and the stopband?

In DSP book by Proakis and as well as in this pdf, it is mentioned that practical causal digital filters cannot have an infinitely sharp transition from Pass-band to Stop-band. Why is it so? Can you ...
4
votes
1answer
3k views

Exponential weighted moving average time constant

I think it is an easy question but I am stuck. I want to derive that $$ \alpha = -e^{\frac{-T}{\tau}}\,. $$ Can someone provide me with an answer? [EDIT] Sorry guys, this was really a senseless ...
4
votes
1answer
240 views

Problems with implementation of a band-stop filter on an MCU (dsPIC) using fixed-point arithmetic

I'm trying to implement a band-stop (notch) filter on a microcontroller dsPIC33EP64GS506 to filter out a $100\textrm{ Hz}$ component from an input signal. The ...
4
votes
1answer
812 views

Polyphase Filter decomposition. It is not working

So, I want to do a polyphase implementation of a filter bank (I had problems with it since the beginning and I already asked for help to the community in the past, indeed: Norm MPEG-1 Layer III (Mp3) ...
4
votes
2answers
2k views

Digital filters in LabVIEW

I am very new in signal processing and using digital filters. I have to use a low-pass filter to analyze my data in LabVIEW and have a question about it. Any help and advice is appreciated. I am ...
4
votes
1answer
717 views

How to include phase in a sinusoidal Kalman Filter

I start with the equation for sinusoidal motion with an offset and differentiate to get the 2nd order ODE describing the motion of the object. \begin{align} x &= A\sin(\omega t + \phi) + O\\ \dot{...
3
votes
2answers
342 views

Question about zero-phase filter bank

I found what I believe is a valid solution to the following assignment problem but the answer is bothering me. Let $$H_0(z) = 1+2z^{-1}+3z^{-2}+2z^{-3}+z^{-4}\quad\textrm{and}\quad H_1(z)=H_0(-z).$$...
3
votes
1answer
281 views

What's Logic Behind the Construction of Sobel's Filter in Image Processing?

I am basically very new to this image processing field. I am presently working on edge detection on colour images. While learning the basics of edges and edge detection in images, I encountered image ...
3
votes
2answers
184 views

Find the transfer function of the difference between IIR and FIR filter

I am using a filter following equations from papers. It is basically the difference between exponential moving average and simple moving average. $$L[n]=\frac{1}{\alpha_L}f[n]+\left(1-\frac{1}{\...
3
votes
1answer
3k views

Butterworth band pass filter

I am trying to build a Butterworth bandpass filter. My intent is to have a pass band between $250\textrm{ Hz}$ and $1000\textrm{ Hz}$. However the plot doesn't look right, as can be seen from the ...
3
votes
1answer
3k views

Difference between $\tt freqz()$ and $\tt plot(abs(fft()))$ in MATLAB

I've plotted the response of a high-pass filter x=[1 -1]; freqz(x) gave me where as the magnitude plot for the ...
3
votes
1answer
49 views

How do I interpret this block diagram correctly?

I am reading notes ahead of the class and have encountered this particular slide: While I completely agree with the first block diagram, I am at a loss trying to understand how the second block ...
3
votes
2answers
398 views

What happens when linear phase is critical? [duplicate]

I am studying the topic digital filters. And in the slides it said,"if linear phase is not critical, Infinite Impulse Response (IIR) filters yield a much smaller filter order for a given application". ...
3
votes
2answers
4k views

How does transition width of a low-pass filter affect a message which is well within the pass-band?

I'm taking a communication systems course and we use GNURadio in the lab. In an exam, we had a simple question where we were asked to demodulate a Dual Side Band (with carrier) AM signal in GNURadio. ...
3
votes
1answer
968 views

Why is there little emphasis on phase distortion?

I have a question regarding the frequency response of digital filters. Specifically the phase aspect of the frequency response. Why do we not seem to care about the nonlinear phase response in ...
3
votes
2answers
984 views

The history of FIR filters

Does anyone know the name of the first DSP (sampled data) practitioner who discovered that real-valued symmetrical-coefficient FIR filters exhibit linear phase in the frequency domain?
3
votes
1answer
77 views

Is it possible to design a band-pass filter with fewer taps than a series HPF + LPF?

I am digitally filtering a signal that is streaming live. The goal is to reduce the filter delay as much as possible while maintaining the quality of some measurements based on the filtered signal. ...
3
votes
2answers
3k views

Transposed Direct Form II VS Direct Form II IIR filters?

I read in "Discrete-Time Signal Processing" Reference, in transposed Direct Form II filters section, that it implements zeros first then poles(unlike Direct form II which implements poles first), ...
3
votes
1answer
758 views

How does parallel structure implementation of IIR speed up the process ? What happens in case of FIR?

I was learning about digital filter structures and there I came to know that parallel implementation of IIR filters speeds up the process and I understand that.But what I am not convinced of is that ...
3
votes
2answers
252 views

Question about decimation/downsampling

I am using an on-chip SAR adc where for some reason I can only get accurate signal reconstruction and filtering when I sample at almost 100 times my desired sampling frequency. Specifically, the ...
3
votes
1answer
185 views

Relationship between wavelet shape and wavelet filters

MATLAB has a library of wavelet functions, showing their "continuous forms" as well as the the decomposition and reconstruction filters. In decimated wavelet transform the filter size remains the ...
2
votes
2answers
321 views

Numerically Stable IIR filter

I am making an IIR Filter and I am running into problems with stability with higher orders. The values go off to infinity as soon as it starts. So far, I've been using MATLAB to generate my filters ...
2
votes
2answers
6k views

Complex low pass filters

I am searching for documentation on the behaviour of complex low pass filters, and their application in telecommunications. Thank you
2
votes
3answers
214 views

Detect valleys of a signal

I have raw values that are coming directly from a sensor (on the fly). These values are coming from a wearable sensor installed on a cows neck. When the cow ruminates (meaning that it chews food that ...
2
votes
2answers
2k views

What is the optimal filter?

I am currently working on a problem on filtering. In fact, let's suppose a signal that is expressed as : $r(t) = z(t) + x_i(t)$, where $z(t)$ is a smooth function and $x_i(t)$ is white Gaussian noise. ...
2
votes
2answers
92 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 ...
2
votes
1answer
198 views

How determine the delay in my signal practically

I am trying to practically determine filter group delay so that I can try to reduce or adjust for it. I have tried all kinds of methods but still can't get the right result. I know that theoretically ...
2
votes
1answer
460 views

Using Matlab's filter() function for solving difference equation with initial conditions

I am trying to solve a difference equation with initial conditions using Matlab's filter function: $$y[n]=\frac12y[n-1]+x[n],\qquad y[-1]=1\tag{1}$$ For $x[n]=6u[...
2
votes
3answers
2k views

What is the filter with the less phase shift?

I have to analyze a dynamic signal but there is too much noise so I applied low pass filter but then there is too much phase shift.So what is the most reactive filter I can apply to my signal ? Best ...
2
votes
1answer
445 views

Concepts: Ideal and Non Ideal Channel Resulting in Inter Symbol Interference

I am following the book: Blind equalization and Identification by Zhi Ding and Ye Li. In Chapter 2, the concept of T spaced equalizers is presented. It is mentioned that the output of the channel is $...
2
votes
1answer
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) ...
2
votes
1answer
46 views

Applications for the Maximum Phase Filter

A maximum phase digital filter has all zeros outside the unit circle, and has the maximum phase and therefore longest delay for a given magnitude response. Besides the possibility of needing a ...
2
votes
3answers
919 views

How to determine if an IIR filter is causal or non-causal?

It may sound impractical, as only causal system are passively realizable, but what I am facing is a general statement made regarding recursive digital filters: for them to be stable, the poles should ...
2
votes
2answers
4k views

Why analog anti aliasing filter is used before analog to digital converter when there is already a digital filter after ADC?

Normal data acquisition consist of: Analog anti aliasing filter( Sampling frequency : $5\textrm{ kHz}$) ADC - Digital Filter - (Sampling : 200K samples /sec) Digital low pass filters Filters DAC ...
2
votes
2answers
354 views

DAC to Analog Filter to ADC

As the order of filter needed for digital information gets higher, it takes longer to process and requires more memory. Maybe analog filtering could be of use here. I know that the words analog and ...
2
votes
2answers
993 views

Resampling a digital sound signal

As a non maths-pro, I'm looking for some pointers. I am rewriting the audio core in my emulator to improve accuracy, and am getting a bit stuck on the specifics of the technique. I am trying to ...
2
votes
1answer
1k views

Calculation frequency response of digital filter with known structure

Short question What are main stages (steps) of calculation frequency response of digital filter by their structure? Detailed question Let suppose that there is discrete FIR filter with known ...
2
votes
1answer
137 views

Is multirate signal processing involved in ADSL?

Telecom companies offer different data rates for home/office purposes depending on the money they pay. How are the telecom people able to control the flow of data of different cables? Say supposing ...
2
votes
1answer
50 views

Polynomial division to separate FIR and IIR in cascade

I have a FIR filter $L(z)$ and an IIR filter $H(z) = \frac{B(z)}{A(z)}$ which are cascaded together as $L(z)H(z) = L(z)\frac{B(z)}{A(z)}$. For specific reasons I want to calculate a parallel topology ...
2
votes
1answer
237 views

Why is interpolation a time varying system

I was reading about interpolation (Interpolation and Decimation of Digital Signals - A tutorial Review, Ronald E. Crochiere) and found that Interpolation filter is a time varying system. Can someone ...
2
votes
1answer
603 views

Sobel and Prewitt operators decomposition

I was reading in the wikipedia page of Sobel operator and Prewitt operator that is possible to decompose these two operators (quote form the Formulation paragraph): "as the products of an ...

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