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Questions tagged [inverse]

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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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35 views

How to calculate amplitude of inverse DFT?

maybe my question is more math question than signal processing, but as long as it concerns DFT topic I think it's proper to ask it on that forum. Actually I have problem with understanding both: ...
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1answer
92 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
140 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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275 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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0answers
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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
182 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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2answers
600 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
344 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 ...