Questions tagged [inverse]

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1answer
400 views

Deblurring 1D Data Using Direct Inverse Filtering

In my assignment I have been given recorded temperature over a period of time (193 Values) and the Impulse Response (5 Values with n=0 corresponding to the middle value). data : data.csv | h = [1/16 4/...
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2answers
182 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
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1answer
1k views

Is this system invertible or not?

Prove that the following system is invertible. $$y(t) = \mathcal{T}\{x(t)\} = \int_{-\infty}^{3t} x(\tau) \,\mathrm d \tau$$ Answer: yes, the system is invertible. I need some hint here, not the full ...
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3answers
267 views

Filter odd or even harmonics with notch or inverse notch filter

Hi i had the following question. I have a signal containing a 200Hz sine wave and it's odd and even harmonics (no other frequencys or disturbing signals are contained). What i'm looking for is a kind ...
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2answers
3k views

Discrete time inverse fourier transform of cosine squared

$$ X(\omega) = \cos^2(\omega)$$ I tried this problem, and I ended up getting $0$, which doesn't make any sense. I integrated: $$ x(n) = \frac{1}{2\pi}\int_{0}^{2\pi} \cos^2(\omega)e^{j{\pi}n} d\...
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3answers
90 views

Invertibility of an ideal differentiator

Is the system $y(t)= dx(t)/dt$ invertible or not? If yes, please determine the inverse system for it.
1
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1answer
471 views

why use svd() to invert a matrix?

In MATLAB, i compared elapsed time to invert a Hermitian matrix using inverse(), svd(), and chol(). svd() took the longest. So is there any reason to prefer svd() to the other two methods?
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2answers
2k views

Z transform - Inverse System function - Why number of poles and zeros myst be equal?

I know that if a system is causal then the system function H(z) must have : a) a ROC that spans from the exterior of the most distant pole and b) the number of zeros must not be greater than the ...
1
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1answer
178 views

Problems with IFFT not being symmetrical

I have two signals, a measurement and a reference which I have performed an FFT on. They have both been windowed with a Hanning window, and now I would like to deconvolve these to get the impulse ...
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0answers
54 views

Calculating DCT in reversed vector

I'm doing an exercise in which I need to show that the DCT of $\tilde{x} = (x_{N-1}, x_{N-2}, ..., x_1, x_0) $, with $\tilde x_m = x_{N-m-1}$, is equal to $ \tilde{X}_k = (-1)^{k}X_{k}$, but I have ...
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0answers
77 views

Normalized LMS with a posteriori Error and Woodburry's Matrix Inversion

I was going through this paper and the author mentioned that we can prove the following using the Matrix Inversion Lemma (AKA Woodburry's Matrix Inversion Identity): Using matrix inversion lemma we ...
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1answer
1k views

Is the inverse of a causal system also causal?

If I have a causal system H(z) and I find the inverse of this system: $$ G(z) = \frac{1}{H(z)} $$ Is G(z) also causal?
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2answers
70 views

how to find the inverse response of a system

For the system described by the differential equation below find its inverse zero-state unit step response $$\dfrac{d^2y(t)}{dt^2}-2\dfrac{dy(t)}{dt}-8y(t)=\dfrac{d^2x(t)}{dt^2}-2\dfrac{dx(t)}{dt}-3x(...
0
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2answers
944 views

Is $y[n]=x[n] * x[n^2]$ invertible?

Is the following system invertible or not? $$y[n]=x[n] * x[n^2]$$ where $*$ stands for the aperiodic convolution operator. I have not been able to find a mathematically sufficient argument for it...
0
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2answers
427 views

inverse fourier transform of magnitude and phase

I stuck this question. Frequency response is written as magnitude and phase and I don't find inverse fourier given signal which as magnitude and phase.How can I solve it ? Can you explain the solution ...
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2answers
845 views

Inverse system of a system with integral

I am trying to find the inverse system of the following (I tried finding the mathematical inverse function but since it is not the same I am not so sure) . Can someone help me find it? $$ y(t)=\int_{...
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1answer
71 views

Fourier Transform: $\omega$ vs $f$ as frequency variable

I try to understand how the Fourier transform changes when I try to compute $X(\omega)$ or $X(f)$. Can someone work me through the maths please for two examples, $x(t) = \exp(j\omega_0 t)$ and $x(t) = ...
0
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1answer
161 views

Is Differentiation as a system, is an invertible system?

is the following system invertible? as I understand it, invertible means finding an inverse function which should return back the original input from an output of the given system. if so I ...
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1answer
178 views

inverse discrete FFT in python, multiple times?

I was wondering what really happens when taking the inverse discrete FFT on some set of numbers, for 3 times? Because looking at it, it looks like we're getting an output that is identically with the ...
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1answer
126 views

Frequency domain Inversion of a signal

I have been trying to calculate the inverse of a sweep (by inverse I mean something that when convolved with my original signal will yield a unit impulse) and although I managed to find a time-domain ...
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1answer
261 views

Inverse system of a box function

I learned about the inverse system. Suppose I have an impulse response $h(t)$ which is a box function. ($A = 1, T = 2$) If I take the Fourier transform and referring the transform pairs, $$H(j\omega)...
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2answers
266 views

My impulse response does not tend to zero

I am doing an IFFT of frequency response data achieved with Simulation tools. When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
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1answer
131 views

How can I find the value of Inverse DFT

I have dt signal $x[n]={[6.29, 8.11,-7.46,8.26,2.64,-8.04,-4.43,0.93,-9.29]}$ And I need to give the function value of: 1) sum of $x[n] = \sum\limits_{k=0}^{N-1} X[k] \, e^{-j 3 \pi k/5}$ from k=0 ...
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1answer
445 views

Programming the IDWT for image processing

I want to program the 2D inverse discrete wavelet transform (only 1 level) in the case of image processing. In the matlab website there's this diagram: now, I want to program the IDWT with haar ...
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0answers
65 views

If you are given an inverse DFT, then how do you convert it back to the DFT without actually computing any DFT?

If you are given an inverse DFT, then how do you convert it back to the DFT without actually computing any DFT?
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1answer
76 views

Build an inverse model for a train of gaussian pulses

I have a stationary signal from a train of Gaussian pulses. My sampling window is too wide (cannot be reduced). In the example 1 ms. So it is not possible to clearly distinguish one pulse from another....
0
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1answer
134 views

Inverse Fourier Transform Dirac impulse with scaled argument

Currently, I am dealing with the sampling problems and I don't understand how to calculate inverse Fourier transform of a scaling impulse function $\textrm{IFT}\{\delta(\Omega T)\} = ?$, $T$ is ...
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0answers
24 views

Inversion problem for big dataset

Suppose my goal is to solve for $x$ in $Ax = b$ using CG method and $A$ is Toeplitz. The problem is that $b$ is extremely large in size and I can't just read in the whole vector $b$ and then solve for ...
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2answers
302 views

How to get the inverse of Filter based on channel

Given a signal $X$, and a channel $h$, and the received signal $Y = Filter(h,1,X);$ What's the inverse of filter, it means if I know $h$, how can I get back $X$ ?