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

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How to compute the main lobe width of generalized Hamming windows (i.e. Hann, Hamming, etc.)?

Is there a way to compute the main lobe width of windows of the generalized Hamming window family (i.e. Hann, Hamming, etc.)? By main lobe I mean the first zeros left and right of the center of the ...
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Power Spectrum: Defnition

I am new to the study of time series. Recently I have asked a question about the covariance of real and imaginary part of a real(in time domain) stochastic time series and I have received an answer ...
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DTFT of an infinite sequence

We want to find the DTFT (Discrete Time Fourier Transform) of a infinite sequence of consequtive numbers ones (1) and -ones (-1). The length of ones are 8 as well as the length of -ones (-1). For ...
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28 views

UWB radar to find heartbeat

I have a UWB radar that Im playing with. The problem is that my algorithms at the moment can clearly, reliably and validly pick up 1-2mm movements of a pendulum i've set up. However, when I use it on ...
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133 views

Is there any alternative basis for a fourier-like transform?

Fourier transform of a continuous signal is just the projection of the signal on the sinusoidal family for imaginary part and the same family with phase offseted by a quarter of period for the real ...
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154 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary process in time (in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary ...
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48 views

how to get the phasor(frequency domain) representation of a digitalized signal?

I know that we can get the phasor representation(frequency domain) of a signal through Fourier transform, but the picture above gives a method that can get the phasor representation of a signal in a ...
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40 views

Discrete Fourier Transform and Opposite Convolution Theorem

I am reading the Wiki for DFT. There is a part for circular convolution theorem which sounds a bit odd saying: $$ \mathcal{F} \left \{ \mathbf{x\cdot y} \right \}_k \ \stackrel{\mathrm{def}}{=} ...
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How to get the quaternionic analytic signal of a image?

The 2D discrete image signal's quaternionic fourier transform can be described as F(u,v), and its 2D analytic signal often be described as: $$ F_q(u,v) = (1 + \mbox{sgn}(u))(1 + \mbox{sgn}(v)) F(u,v) ...
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36 views

Why does the periodic signal in time always give a discrete frequency spectrum

I would like to know, why does the periodic signal in time always give a discrete frequency spectrum in FT? I know the equations, but I simply dont understand why is it so. Thanks!
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What happens with signal in frequency spectrum when it is time shifted in time spectrum?

I have some trouble to understand what is going on with signal in frequency spectrum when it is time shifted in time spectrum. I am hoping that somebody will help me to understand that. Thanks you ...
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86 views

Image Reconstruction:Phase vs. Magnitude

Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. Figure ...
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113 views

Intuitive explanation of the Fourier Transform for some of the functions

Does anyone have a mechanism to understand intuitively (and automatically) why the Fourier Transform of certain functions have certain shapes (at least for some functions, not necessarily for all)? I ...
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56 views

Frequency spectrum of a sinc function

I am doing one example from my book as a preparation for exam. The assignment is: It is given that: $$\mathbb{rect}(t)=pf(t) \leftrightarrow PF(f)=2AT_0 \cdot \mathbb{sinc}(2\pi fT_0)$$ you ...
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1answer
10 views

Filtered backprojection implementatoin

I am wondering the detail of the filtered backprojection. Suppose I have a projection file: $p(s,\theta)$=[1 2 3 1 2] Then to get its filtered backprojection ...
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1answer
33 views

How are phase values able to capture motion from video?

I know that the phase spectrum contains most of the structural information about the image importance of phase. But I want to know more about importance of phase spectrum related to video signals. I ...
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36 views

Is it possible to decompose an image into basis images using MATLAB?

I have read that: Using Fourier decomposition any arbitrary image can be represented as summation of orthogonal basis images. I want to see the basis images for any image say Lena or ...
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2answers
120 views

Properties of Spectral Transformations - Allocation (decomposition into even and odd part)

I am trying to understand the Allocation property of Spectral Transformations. I can't. I know that every function can be separated into an even part and into an odd part. My problem is ...
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41 views

Inverse Chirp Z Transform

I am working to understand and use the Chirp Z-Transform. I want to use the algorithm for simple signal processing on data sets that are not a power of two. I need to be able to inverse transform as ...
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1answer
85 views

How do we compare between Spatial Domain and Frequency Domain?

I am doing my academic project in image processing. I have few doubts that i want to ask Which information do we actually get from "phase spectrum" and "magnitude spectrum" about an image? What are ...
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1answer
91 views

What is obtained from the cross correlation plot?

Let’s assume that we have two audio signals, x(t) and y(t) affected by the noise as shown below. And we would like to cross-correlate these two signals and the cross-correlation plot is shown as ...
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1answer
56 views

Inverse DTFT of $e^{-j\omega}$

I've been trying to solve the following problem, but I noticed that I get two different answers by means of two different techniques: Find the impulse response, $h(n)$, of the following system, ...
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1answer
100 views

What is the general feature of a time domain signal that gives a step like spectrum?

I'm trying to study a nonlinear system by sending a pulsed signal into the system and look at the response spectrum. The signal I send to the system is something like and the response spectrum from ...
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2answers
58 views

Development of Hilbert transform relationship

In the development of Hilbert transform relationships, Prof. Oppenheim has chosen \begin{equation} ...
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36 views

Noisy Signal auto/cross-correlation

I am trying to understand the basics of the cross/auto-correlation if the noisy signal $y(t)$ which is received from the channel at the receiver. Here at receiver we want to estimate the noise in the ...
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1answer
67 views

Magnitude of gradient in frequency domain

I'm learning some basics of image processing. Recently I've read about image filtering and two-dimensional Fourier transform, because I'm preparing for exam. And I have one question I don't know ...
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432 views

Difference between discrete time fourier transform and discrete fourier transform

I have read many articles about DTFT and DFT but am not able to discern the difference between the two except for a few visible things like DTFT goes till infinity while DFT is only till N-1. Can ...
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48 views

Fourier Transform Form: two sin components & a phase shift & a magnitude for only one term

This is an example from my text book of a continuous signal: $$x_{in}(t)=\sin \left( 2\pi \cdot 1000 \cdot t\right) + 0.5\sin \left( 2\pi \cdot 2000 \cdot t + \dfrac{3\pi}{4} \right) $$ So to perform ...
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59 views

Low Pass Filter in AM Demodulation

I am trying to recover my baseband signal that was AM modulated. I am using the filter command in MATLAB to perform the low pass filtering ...the code is given below: ...
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Is Gabor uncertainty a feature of the Fourier transform, or of nature?

By Gabor uncertainty, I mean the principle of uncertainty as applied to signals — with the result that you can't have arbitrary time and frequency localization. By way of background to my question, ...
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32 views

How to perform a Stockwell Transform on a 2D matrix

I was looking at performing a Stockwell transform on a matrix (or an image as it has two directions - the matrix I am interested in has a spatial dimension and a time dimension, but this should make ...
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1answer
63 views

How moving part pixel intensity values of video frames becomes dominant compared to stationary part intensities in reconstructed frames?

Hello everyone i want to do dynamic texture video sementation using the Fourier transform in MATLAB. I am applying 3-D fft on dynamic texture video frames (using matlab function 'fftn') and ...
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35 views

Autocorrelation - cyclic vs acyclic

In terms of signal analysis (especially frequency decomposition) would it be bad to use cyclic autocorrelation (AC) instead of acyclic/linear AC? My use case: I'm trying to characterize events in a ...
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130 views

Why can't DFT be used when samples are not equally spaced in time?

I found the following comment here The DTFT can be used when the samples are not equally spaced in time, the DFT cannot My initial thought was that this had to do with periodicity of the basis ...
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73 views

Simple FFT filtering vs. e.g. butterworth filtering

I am currently working on functional connectivity analysis of EEG, and need to bandpass filter my data into different frequency bands (Delta, Theta, Alpha and Beta). An important thing is that the ...
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1answer
45 views

Why we need fourier transform of periodic signal although we have fourier series for periodic signal?

I was going through some of the basics of fourier series and fourier transform. And I came across one topic "Fourier transform of periodic signal". But I am not able to understnad why we need to go ...
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86 views

Discrete Fourier transform of complex time series

I am working through previous exam questions for a class I'm currently taking in signal theory, and one problem, although it looks easy, stumps me. PROBLEM Two real $N$-periodic time seires $f_n$ ...
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Fourier Transform in 2D? (image processing) [duplicate]

In audio signal processing, Fourier Transforms are widely used to convert the mono-dimensional signal, expressed in time, into the frequency domain. It is not clear to me how this is extended to the ...
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87 views

Window functions with rippleless spectra

On Wikipedia I found the Hann-Poisson window, and the article claims the spectrum is smooth, but it isn't theoretically smooth, as it turns out. In practice you achieve partial smoothness by jacking ...
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1answer
89 views

Correlation between real and imaginary parts of a Fourier transform of zero mean Gaussian

From this previous post, the real and imaginary parts of the Fourier transform of a zero mean Gaussian are uncorrelated (and i.i.d. Gaussians) This some how seems counter-intuitive. It seems if the ...
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2answers
86 views

FFT for bearing fault analysis

Why is FFT a good method for detection of bearing faults? Why can't we do the analysis in time-domain?
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Estimate the type of wavelet transform in receiver side

Suppose that a signal is decomposed by using discrete wavelet transform (DWT) and transmitted. Is it possible for receiver to find which type of wavelet is applied in transmitter side ? I mean, if ...
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Fourier Transforms and Series for the NON mathematically inclined.

This would most likely be the opposite of this question ( Mathematically inclined Signal and Systems/Signal Processing book? ) I figured I'd ask here if there are any good books that while, ...
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156 views

Difference between Convolution and multiplication [duplicate]

I read that multiplication is convolution in frequency domain. I also understand that convolution is just polynomial multiplication. Can somebody explain what are the advantages of doing convolution ...
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72 views

How to interpret results of Fourier transform by using Python

Connected with this topic , I would like to have some clarifications about the Fourier Transform and the Python tools that make it. Having my data set whose plot is showed in the above link, my array ...
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27 views

Reason for bimodal behavior while low second fourier coefficient

If I have a time series (for eg. for 23 timestamps) and if I plot it and see that it is bimodal, that means it might be having high value of second fourier coefficient (with frequency = 2). But when I ...
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1answer
31 views

How to check if Fourier components are in phase of out of phase?

I have a time series (of 23 timestamps) of which I take the Fourier transform. Now the fourier transform has 23 imaginary values and each has an amplitude and a phase. When I get the phase angle, it ...
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1answer
58 views

Order analysis or order tracking

Last week I've been trying to implement the Order Analysis in MATLAB in vain. I've read a lot of docs about it like this one , but I still can't figure it out. This will be my last shot. Say I have ...
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500 views

When can we write Heisenberg uncertainty Principle as a equality?

We know that Heisenberg uncertainty Principle states that $$\Delta f \Delta t \geq \frac{1}{4 \pi}.$$ But (in many case for Morlet wavelet) I have seen that they changed the inequality to an ...
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130 views

Calculation of cosine in frequency domain instead of calculatin in time-domain followed by a FFT

I got an $N$, in my case 512, point FFT of a real-valued signal. Based on some calculation in my application I determine the parameters $k \in [1, N-1]$, the number of oscillations per period, $\phi ...