**680 filter-design questions.**

Question 1
$$
H(e^{j\omega})=\sum_{n=0}^{N-1}h[n]e^{-jn\omega}
=\mathbf{c}^H(\omega)\cdot \mathbf{h} \tag{1}
$$
$$
=\mathbf{h}^H\cdot\mathbf{c}(\omega) \tag{2}
$$
$$H(\mathbf{h})=\sum_{k=1}^Kh[k]e^{...

I have raw values that are coming directly from a sensor (on the fly). I do a quick calculation on these values and I end up with a graph like the bellow image.
I would like to be able to detect ...

I have studied convolutions and filters a long time ago. Today, I am trying to review the basics using some notes of mine, but I am finding difficult to solve easy problems. Since I don't have ...

I'm wondering if we can measure 3-D length only by our smart-phone's accelerometer. And we all know these low cost IMUs are not accurate.
You can model accelerometer's error this way:
$$ a = f*a' + g ...

Where to learn about "analog prototype filters"?
I've heard about them, but I'm unsure about what they really are and how they're constructed.

I was planning to develop Android / iOS applications that enable users to measure 3D length using their smartphones.
According to this question, you need to know at least the time-varying bias that ...

I ran a finite-difference simulation and the behavior of an output signal, $s$, in time, $t$ (sampled with period $\Delta t$) behaves approximately as in the figure below. It is well-described by a ...

What happens if the noise has no zero mean? I mean, if the exercise is something like:
$$y(k) = A x + \eta(k)$$
When I have zero mean, I start from:
$$y = A x$$
$$\Rightarrow \hat{y} = A \hat{x}$$
...

I am given $|H(\omega)|$, I wonder if minimum phase stable causal filter is unique and how to calculate it.

For a given narrowband Gaussian filter with a specific central frequency and filter width, I need corners of a bandpass Butterworth filter whose amplitude response is close enough to the Gaussian ...

For converts any causal LTI digital filter into state-space form,there is the following procedure :
1-The general causal IIR filter
$$
y[n] = b_0 u[n] + b_1 u[n-1]+... + b_N u[n-N]- a_1 y[n-1] - ...

If a practical filter can't remove all unwanted frequency components like ideal filter, does that mean unwanted frequency component are still present after filtering?
how can we use such distorted ...

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 ...

I'm looking construct a stable pole-only filter where the feedback coefficients start with a block of zeroes, i.e.
\begin{align}
a_0 &= 1\\
a_i &= 0, \textrm{ for}\ 1 \le i \lt k\\
a_i &\...

I hope to design 1st order highpass filter from transfer function. In the example of 1st order lowpass filter, I first get the coefficients of numerator and denominator in the variable 'b' and 'a'. In ...

I would like to approximate a moving average filter with an IIR filter of much lower order than the tap-length of the moving average filter. Optimality shall refer to the $L_2$ norm of the impulse ...

It is widely known that matching a FIR filter of fixed length to a band model is an unconstrained QP-problem. The MATLAB function firls() implements a solution to ...

I understand to an extent various filter like low pass filter, high pass filer, Wiener filter Kalman filter etc. I also understand some of this filter will decorrelate/uncorrelate the signal. The ...

I am attempting to design a matching filter from long sequences. I want to do this in the time domain. I have 3 inputs. Let's called it p,s, and r. The matching filter is to be designed between p and ...

I believe that there is no connection between the sampling frequency used for converting an analogue filter to digital filter and the one used to sample a signal that the filter will be used on. But I ...

I try to understand the 'arbitrary' what does it meant?
I had read many references ,such a one it is 'begin the process with a transfer function of your choice' ,in other reference :related by the ...

I am running a BPSK flowgraph in GNU Radio which is based on RRC pulse shape. I noticed that the BER is quite poor when the number of taps is low. However, using the number of taps around $20\times ...

So it recently dawned on me that Bessel filters, despite being listed along with the other common types, are really an oddball that belongs in a different "class", and I'm trying to learn more about ...

I was reading Winder's Analog and Digital Filter Design and the section on Bessel filter.
I was hoping to see a complete derivation of the Bessel filter theory, but Winder's book gives only
\begin{...

I am working on a school project on converting a 6th order butterworth high pass filter to digital filter using bilinear transformation.
Just got a couple conceptual questions need to be clarified ...

I am new to DSP and filter design. I have developed a code in C++ to calculate FIR coefficients using Parks-McClellan algorithm. The inputs to calculations are:
Filter type (Low-Pass, High-Pass)
...

I am trying to design a Nth order continous time Butterworth filter in state space, with pole placement technique.
...

I want to implement Butterworth low-pass filter. Thanks to this question, I have found out that the filter coefficients can be generated using Tony Fisher web-site or using his code. But the problem ...

A digital low pass Butterworth filter that has been designed using Bi-linear transformation has been a pole at $z=0.6$. It is also known that the filter's attenuate (at digital frequency) $\omega = 1....

I have learned the Butterworth filter, normally it is used for low pass design. And the amplitude response is:
$$|H(jw)|=\frac{1}{\sqrt{1+(\frac{w}{w_{c}})^{2n}}}$$
mentioned in this Butterworth ...

I am having trouble understanding the exact derivation of the butterworth filter and how it results in the output of the poles. I have researched multiple lecture series and textbooks and this is my ...

I have the strain signal of a lateral beam of a car measured at sampling rate 1,200Hz from data acquiring system. Even after using temperature compensation in strain gage, we are getting drift. So I ...

I want to design a FIR filter by using 'cfirpm' function , which can i use the group delay and grid frequency,
my code is :
...

IIR filters can be designed using different methods,such as:
Analog Prototyping
Direct Design
Generalized Butterworth Design
Parametric Modeling
https://www.mathworks.com/help/signal/ug/iir-filter-...

If anyone has a copy of this book could you please shed some light here: I was trying to reproduce the example shown in Chapter 5, section 5.3.1 Window Design Method's Figure 5-19 which illustrates ...

I noticed, when I try to fit filter coefficients to a given complex transfer function with the output error method, implemented for example in the MATLAB function ...

In the case of frequency domain FIR filter design, the error function given by :
$$E(\omega)=H(e^{j\omega})-D(e^{j\omega}) \tag{1}$$
is a linear function with respect to the unknown filter ...

I have access to the step response of a system and I want to find its poles and zeros without knowing the order of the system.
Consider an example of a step response of the system shown in the ...

Consider Multidirectional Scratch Detection and Restoration in Digitized Old Images Research Paper.
In section 4.1 (Preprocessing), they gave us a formula of the kernel,
$$ H(u, v) = \frac{1}{1+0....

I'm working with signals with variable sampling rate (the time space between samples is not constant). I know the delay between samples but I don't wont to interpolate the signal.
Is there a way to ...

I come from Computer Science so please pardon for my possibly wrong terminology.
I need to design a filter which has coefficients
$$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...

The goal is to create an LTI filter which is exactly, or approximates, damping of harmonic modes.
The equation of course is:
$$\frac{d^2 x}{dt^2} + 2 \xi \omega \frac{dx}{dt}+\omega^2x=0$$
This can ...

The complex function $ D (e^{-jw})$ is defined on the domain of approximation $\Omega$ .In most cases the domain $\Omega$ is the union of several disjoint frequency bands which are separated by ...

What are disadvantages of root raised cosine pulse shaping filter in digital communications and why does it need to be improved?
Links:
Square Root Raised Cosine Fractionally Delaying Nyquist ...

Trying to implement the LoG with different kernel size and sigma.
Been reading this post:
Introduction to IP : Laplacian of Gaussian?
Which mention a scale factor of approx 482 for a 9x9 size kernel ...

The wavelet transform has a problem as it gives poor time resolution for low frequencies and poor frequency resolution for high frequencies according to uncertainty conditions.
This appears well ...

- filters
- matlab
- lowpass-filter
- infinite-impulse-response
- fir
- discrete-signals
- signal-analysis
- bandpass
- frequency-response
- image-processing
- python
- highpass-filter
- digital-filters
- noise
- fft
- frequency-spectrum
- finite-impulse-response
- audio
- phase
- fourier-transform
- transfer-function
- filtering
- convolution
- adaptive-filters
- butterworth

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