Questions tagged [inverse]
The inverse tag has no usage guidance.
25
questions
0
votes
1answer
33 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 ...
1
vote
0answers
52 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 ...
1
vote
3answers
56 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.
2
votes
2answers
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 ...
0
votes
2answers
72 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 ...
0
votes
0answers
61 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?
0
votes
1answer
42 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
votes
1answer
70 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 ...
0
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0answers
24 views
Solving the system response using inverse Laplace transform
I am trying to solve this question but I got stuck when inverting the Laplace transform for this problem. I do not know that whether I do it right or wrong. Moreover, I do not know how to handle the ...
0
votes
1answer
56 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 ...
0
votes
1answer
57 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 ...
-1
votes
2answers
136 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 $X$ ?
0
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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 ...
0
votes
1answer
116 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,
$$H(j\omega)...
0
votes
2answers
164 views
My impulse response does not tend to zero
I am doing an IFFT of frequency response data achieved with Simulation tools.
When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
0
votes
2answers
657 views
Z transform - Inverse System function - Why number of poles and zeros myst be equal?
I know that if a system is causal then the system function H(z) must have :
a) a ROC that spans from the exterior of the most distant pole and
b) the number of zeros must not be greater than the ...
0
votes
1answer
82 views
How can I find the value of Inverse DFT
I have dt signal $x[n]={[6.29, 8.11,-7.46,8.26,2.64,-8.04,-4.43,0.93,-9.29]}$
And I need to give the function value of:
1) sum of $x[n] = \sum\limits_{k=0}^{N-1} X[k] \, e^{-j 3 \pi k/5}$ from k=0 ...
0
votes
1answer
602 views
Is the inverse of a causal system also causal?
If I have a causal system H(z) and I find the inverse of this system:
$$
G(z) = \frac{1}{H(z)}
$$
Is G(z) also causal?
1
vote
1answer
142 views
Problems with IFFT not being symmetrical
I have two signals, a measurement and a reference which I have performed an FFT on. They have both been windowed with a Hanning window, and now I would like to deconvolve these to get the impulse ...
0
votes
2answers
574 views
Is $y[n]=x[n] * x[n^2]$ invertible?
Is the following system invertible or not?
$$y[n]=x[n] * x[n^2]$$ where $*$ stands for the aperiodic convolution operator. I have not been able to find a mathematically sufficient argument for it...
0
votes
2answers
624 views
Inverse system of a system with integral
I am trying to find the inverse system of the following (I tried finding the mathematical inverse function but since it is not the same I am not so sure) . Can someone help me find it?
$$ y(t)=\int_{...
1
vote
0answers
75 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 ...
0
votes
1answer
366 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 ...
1
vote
2answers
2k 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:
$$ x(n) = \frac{1}{2\pi}\int_{0}^{2\pi} \cos^2(\omega)e^{j{\pi}n} d\...
2
votes
1answer
917 views
Is this system invertible or not?
Prove that the following system is invertible.
$$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 ...
