Questions tagged [inverse]

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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....
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1answer
29 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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2answers
93 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 ...
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1answer
58 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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0answers
51 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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3answers
48 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.
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2answers
62 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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1answer
365 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
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 ...
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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?
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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 ...
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1answer
52 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
49 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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2answers
129 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 $X$ ?
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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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1answer
108 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
158 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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2answers
597 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 ...
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1answer
77 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
569 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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1answer
140 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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2answers
601 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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2answers
516 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...
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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\...
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1answer
858 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 ...