Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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Create an aliased image in FD

Is there an accurate way to create an aliased image from the Fourier transform of the original image? in other words, i have the Fourier coefficients of an image and i want to make down-sample in ...
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Downsapled and blurred image

I have an image with size $256*256$ then i get the Fourier transform of the image, If i only take the central region of the Fourier transform whose size is $64*64$ and get the inverse FT ,What is the ...
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SVD is not applicable to time series analysis?

I am studying a deconvolution problem for which observations include noise. I am considering using one of several common regularization methods, including Tikhonov's solution, truncated Singular Value ...
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Expression to represent alternating pulse train?

I have a question regarding an alternating pulse train signal, $p(t)$, and a system which looks like this: Immediately, I'm supposed to be able to extrapolate that $$ P_t = P_1(t)-P_1(t-\Delta) $$ ...
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Multiply FS Coefficients by 0 or 1 to get Low Pass Filter?

I have written a bit of code to upsample and interpolate a sample waveform in MATLAB. It's at the point where I have taken a signal, upsampled it 2x and filled in the gaps with 0's, and then I found ...
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Given h(t)~H($\omega$) Fourier transform pair, what is the counterpart of H(-$\omega$) [closed]

Thanks in advance. Any help will be much appreciated.
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Side lobes not visible in FFT of rect function

I was making a plot to show side lobes for different spectral windows and I noticed if I take a simple fft of a rectangle window, I don't see any side lobes. I think I'm just making a simple mistake. ...
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Downsampling a PSD that was generated by zero-padding - worth it?

Let us say we have a signal $y(k)$ that is of length $K$. I can compute its PSD, also of length $K$. Let us say that this length was not good for finding peaks, so I computed a PSD that was of length $...
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Estimating and Improving the accuracy of fourier transform in the low frequency sector

I have a time series file which starts with 1 and then quickly tends to oscillating about 0.001. The time series has a resolution of 0.01s and has 10^6 sequential points starting from t=0. The goal is ...
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Compressive Sensing Incoherence Principle

As people acquainted with Compressive Sensing would know, incoherence and sparsity are two main principles. I've been reading about compressive sampling and developed an interest into the topic. What ...
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How do we know that CTFT of the autocorrelation function is the PSD?

I know that the Fourier Transform of the autocorrelation function is the Power Spectral Density. But how can we arrive at such a result intuitively? Is it just a theorem?
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Fourier Transform & Convolution to get response - confused

in the past couple of years I've always been using Laplace transform for system responses, but today tried to do it with Fourier transform and failed. What am I doing wrong? If we have a signal $x(t) ...
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A little bit better than zeroing bins in order to filter

The topic of zeroing frequency bins before IFFT has been discussed here : Why is it a bad idea to filter by zeroing out FFT bins? It was very helpful to understand why it is a bad idea. What do you ...
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Why can't we just make all wireless networks use integer multiples of base frequency?

I always wondered why transmission capacity depends on bandwidth. For example, let us say that there is an isolated island. In this island, people decide that all wireless networks use frequencies ...
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Theoretical question on Fast Fourier

I have a question regarding Discrete Fourier Transform and Discrete Time Fourier Transform. Suppose that we have a sequence $x(n)= \{1,2,3,3,2,1\}$. So is it possible to reconstruct the Discrete ...
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Shift estimation using fourier transform

If i have two images of the same scene, reference image and a shifted image, the shift can be in x or y directions, i want to estimate the shift using the shift property of the fourier transform. <...
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Calculate cut-off frequency of lowpass IIR-filter

Given a an IIR lowpass-filter in z-space: $ H(z) = \frac{\sum_{i=0}^P b_{i} z^{-i}}{1+\sum_{j=1}^Q a_{j} z^{-j}} $ How to calculate it's 3dB cut-off frequency? I about evaluating it's fourier ...
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Reason of Fast Fourier and Inverse Fast Fourier [closed]

I am not very good at mathematics I was doing some image processing so I came to know about FFT and IFFT I was learning about ...
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Why do we say that “zero-padding doesn't really increase frequency resolution”

Here is a sinusoid of frequency f = 236.4 Hz (it is 10 milliseconds long; it has N=441 points at sampling rate ...
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window for short time fourier transform

When we implement the 1D-short time fourier transform, the formula is as such: $$ Sf[m,l]=\sum_{n=0}^{N-1}f[n]g[n-m]\exp\left(\frac{-i2\pi l n}{N}\right). $$ the window $g$ used is normally ...
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Removing values from FFT result same as filtering?

I don't quite understand why the textbooks say it is impossible to implement an ideal low pass filter. If I was to take the FFT of a discrete signal x[n], with Matlab's fft function I'd be returned ...
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Why Is Super Resolution (SR) Possible?

I've been reading about Super Resolution Image reconstruction (Reconstruction of high resolution image from multiple low resolution aliased images contain sub pixel shifts), and i want to know why SR ...
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What is the frequency of $\cos x -\sqrt 2\cos\sqrt 2 x$?

Question Considering that $1\over{2\pi}$ is the frequency of $\cos x$ and also of $\cos x - 2\cos 2x$, what is the frequency of $\cos x - \sqrt 2\cos\sqrt 2 x$? Thoughts Perhaps "frequency" isn't ...
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Relationship between filters, Fourier magnitude, and frequency

I'm just beginning to study Fourier transforms and I'm having trouble getting this concept down. I know what a low/high pass filter does to a signal. What is the relationship between Fourier ...
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Stationary processes and their power

The top answer to this question: Power spectral density vs Energy spectral density states: However if random process is stationary, then it is for sure that it has some finite power over some ...
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Comparison between Fourier transform, short time Fourier transform and wavelets

What is the difference between the Fourier transform, short time Fourier transform and wavelets?
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General question about DFT

I am learning Fourier analysis and without any teacher, just trying to read books on my own. I think I have made some decent progress but they are a couple of points which are still very unclear to me ...
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Intuitive interpretation of Laplace transform

So I am getting to grasps with Fourier transforms. Intuitively now I definately understand what it does and will soon follow some classes on the mathematics (so the actual subject). But then I go on ...
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MACE correlation filter - any suggested values of of u?

I am trying to understand the MACE correlation filter as per the paper Mahalanobis, A., Kumar, B.V.K.V., Casasent, D.: Minimum average correlation energy filters. Appl. Opt. 26, 3630–3633 (1987) ...
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How is it possible to find the Fourier transform of unit impulse function?

Since Fourier transforms are applicable to only periodic functions, and unit impulse function{..0,0,1,0,0..} doesn't seem periodic, is this possible? Is it like we are considering unit impulse ...
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1-D Fourier Transform Of A 2-D Image But At An Arbitrary Orientation

If one has a 2-D array and would like to take the 1-D Fourier transform along a direction $\theta$ degrees off the horizontal, is there a better/faster way to do this rather than rotating the image by ...
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Error Propagation through an IFFT

I'm not sure how to approach this problem. I will describe what I am trying to do, and what some of my matlab outputs look like. I'm not trained in signal processing or anything, so please be ...
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fourier transform to the power of two

Could someone explain to me why the computation speed for the fast Fourier transform increases by padding the series with zeros to the point that its length is close to a power of 2? This is common in ...
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Why does circular symmetry of complex envelopes mean that $\mathbb{E} \Big[\mathbf{x}[i] \mathbf{x}^T[i] \Big] = \mathbf{0}$?

I am making my way through this paper here, and I understand everything up to equation 16, and I am stuck here. Long story short, the vector $\mathbf{x}[i]$ here is an $N$ by 1 vector, consisting of ...
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What is the physics behind the width of a main lobe?

We know that the square window gives the lowest main lobe width possible, and that other windows after that trade main lobe width for side lobe height. I also understand that the main lobe width is ...
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What is the essential bandwidth with the given function?

Let the function be $$ f(t) = e^{-3t} u(t -1) $$ The criterion is set at 70% of the total signal energy. I know how to find total energy, but not how to find the the $W$ (or frequency) at which the ...
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Can I apply Fourier Transform to a non-time-indexed signal?

Say I have a signal that is not x-indexed. That is, the x-axis of the signal is the distance traversed by car and the y-axis is the heading direction of the car at the corresponding distance. Can I ...
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What information is lost, if any, in normalizing Seismic/Earthquake time-frames in an STFT to equal variance?

This might be more of a statistical question, but let us assume that we take a spectrogram, or STFT, where time is on the x-axis, and frequency is on the y-axis in this matrix. What information might ...
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How to choose a phase for the deconvolution of an autocorrelation?

Say I have a function, $C=C\left(x\right)$, whose fourier transform is denoted by $c=c\left(k\right)$, i.e. $C\left(x\right)=\sum_{k=-\infty}^{\infty}c\left(k\right)\chi\left(x\right)$, where $\chi\...
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Where does homomorphic filtering stand in regards to DSP applications?

I am studying my Oppenheim and Shaffer book, (New Edition), and the last chapter deals with something called homomorphic filtering. I have read the wiki and some other websites about it, but they do ...
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Energy Spectrum of a signal after FFT in Matlab

I have a vector of signal x(t) with its time vector. I want to obtain a frequency representation of the signal, in particular the energy spectrum of x(t). Can someone please show some light into ...
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When to use the DTFT vs the DFT (and their inverses) in analysis?

In many of my readings, whenever some author speaks about working in the frequency (transform) domain (of a digital signal), they often times take the DFT, or the DTFT, (and of course their ...
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Estimate phase using STFT in Matlab?

My signal oscillates back and forth on the interval [-1, 1] at varying frequencies, with some added higher frequency noise components (example data shown below). I want to to estimate the phase of the ...
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Is the discrete Gaussian kernel an eigenfunction of the DFT?

So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right? But this isn't true for the sampled Gaussian in the DFT because the tails of the ...
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What Are the Suggested Resources for Extensive Knowledge About the Fourier Transform (DFT, FFT, etc…)? [closed]

I would like to improve my knowledge about Fourier Transform related subjects. What are the recommended resources in order to self study about it?
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A kind of Phase Retrieval problem

I know there are lots of papers proposing algorithms for the problem of reconstructing a signal from modulus of its Fourier Transform (so-called Phase Retrieval Problem). Also, recently it is studied ...
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How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where ...
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Similarity in absolute value of nearby DFT coefficients

Is there any approximate relation in FFT coefficients? For example, consider time domain signal $x_n$. Its $N$ point (assume $N$ to be even) DFT is given as $X_0,X_1,...,X_{N-1}$ Can I say something ...
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Right algorithm for fourier transform on physical heights

I have data from a LIDAR unit that I would like to get the spectral density of. Unfortunately, the only thing I remember from my Fourier analysis class are the methods that I know will not work. The ...