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Questions tagged [inverse]

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39 views

How to check if a NON LTI System is invertible?

$T\left\{x\left(t\right)\right\}=x\left(t\right)cos\left(\omega t\right)+1$ Can I say that? or there is another way? $x\left(t\right)=\frac{T\left\{x\left(t\right)\right\}-1}{cos\left(\omega t\right)}$...
121 views

Why not overlap save for inverse stft

Since STFT uses overlapped sections of the input signals and compute DFT, it resembles overlap-save method used for block convolution, instead the overlap-add method for block convolution uses non-...
• 31
136 views

Inverse $\mathcal{Z}$-transform of a shifted Dirac delta function $\delta(z - z_{0})$

I'm looking for the inverse $\mathcal{Z}$-transform of a shifted Dirac delta function in the $z$ domain, i.e. $$x[n] = \mathcal{Z}^{-1} \{ \delta(z - z_{0}) \} = \ldots$$ Does an analytic/closed-...
451 views

Is it possible to predict the peak value of a time-domain signal from its frequency-domain spectrum?

As the question states, is it possible to predict the peak value of a time-domain signal given its frequency-domain spectrum? Since the time-domain signal is just the sum of the individual sinusoids ...
• 296
1 vote
781 views

Can someone explain the phase spectrum of a sinc function?

The Fourier transform of a sinc function will result in a rect function. Suppose I have a discrete time-domain sinc function with a frequency of $\omega_0 = 0.1$ Hz and amplitude of $A = 10^{-3}$: If ...
• 296
54 views

How to compute the ifft of a constant value?

I am clearly missing something obvious here because I am trying to do something that ought to be very simple: compute the ifft of a continuous signal. My understanding is that the ifft of a continuous ...
• 296
1 vote
404 views

Inverse Fourier Transform of $\omega ^2$ in $[-\omega _0,\omega _0]$

I've been learning about signals for a while now, and I'm just starting to learn about Continuous time Fourier transforms. In this particular case, we were asked to get the inverse Fourier Transform ...
102 views

Non-causality deepness of inverse system

Assume I have a FIR, stable and causal system. I want to know the deepness of non-causality on the inverse of my FIR system. It's obvious that the system is non-minimum-phase, since minimum-phase ...
34 views

Determining invertibility of weird system

Student here, As an academic exercise, is the system $$y[n] = x[n-1]x[2n]$$ Invertible? I thought it was since you could find an infinite multiplication series for y[n] that allows you to recover x. ...
1 vote
92 views

How can one infer the input signal $x[n]$ from the output $y[n]$ of an LTI system with known Gain and Phase Response

I have the gain response of an amplifier and its phase response curves, in an appropriate frequency range. I also have a set of output (from the system) discrete data $y[n]$. How would one go about ...
• 131
274 views

Taking The Inverse FFT And Extrapolating For Future Predictions In R

This is what I am trying to achieve: See how the increasing number of harmonics are creating a good fit? I am trying to find the components of a given wave (discrete samples), and then to make brief ...
40 views

Acausal form of $Z^{-1}\left(\frac{1}{z-a}\right)$

We know that $Z^{-1}\left(\frac{z}{z-a}\right) = a^nu[n]$ if $|z| > |a|$. In addition, $Z^{-1}\left(\frac{1}{z-a}\right) = a^{n-1}u[n-1]$ if $|z| > |a|$. This is the delayed version of the first ...
212 views

Convolution theorem for inverse DTFT

in trying to understand the convolution theorem for DTFT, I'm faced with the following problem which I can't get my head around. First, let me state the convolution theorem for the DTFT as follows: \...
• 225
1 vote
150 views

• 162
2k 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?
• 111
1k 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
79 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
151 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.
525 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 ...
1 vote
2k 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 ...
74 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?
1 vote
119 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....
• 111
1 vote
587 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 ...
• 111
610 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 ...
• 1,314
245 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 ...
794 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 $X$ ?
• 639
28 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 ...
542 views

106 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 ...
• 131
587 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 ...
• 165
1 vote