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

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Can I study continuous time Fourier Transform and treat the rest as special cases

Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to Lapace transform, Z transform, DTFT, DFT, Fourier sequence ...
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10 views

Transposing pitch profile of one audio on another

I have one audio file with rap music and one audio with sound record of my friend's reading some text. I want to transpose pitch profile of rap music on sound recording, is that possible? I can ...
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40 views

Skew detection and correction using Fourier transform

I was trying to implement skew correction method for scanned documents using the method described in this paper. The algorithm steps: 1- Threshold the image . 2- Find the fourier transform. 3- ...
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1answer
31 views

Filtering and Fourier Transforming, does the order matter?

I have a signal $x(t)$. I want to find the Fourier Transform of it, $X(f)$, and then extract a narrow frequency range from $X(f)$ by use of a Band Pass Filter (BPF) in frequency domain. Can I instead ...
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18 views

How to equalize frequency contents using filter?

Suppose there is a bounded continuous signal $f(t)$ that can be fourier-transformed into $F(\omega)$ of frequency contents. $|F(\omega)|$ is non-zero for only finite number of frequencies: ...
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7 views

radon fractional Fourier transform or radon Fourier transform code in matlab environment

Does anyone have radon fractional Fourier transform or radon Fourier transform code in matlab environment. I am looking for such implementation eagerly. Thanks in advance.
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33 views

Compute Similarity between Fourier Transforms

I'm looking to compare the Fourier Transforms generated by accelerators and gyroscopes that collected data of people walking. I've looked to see if there is a standard form of comparison, but I have ...
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25 views

Does the enlarged photo benefit from shrinking it?

Take a look at the following diagrams: The original picture: The upscaled (2x, bilinear) picture: In both cases the first item in first row is the input image. There is it's 2d fft next to it. ...
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8 views

Inferring space domain signal from 2D DFT

By just looking at the 2D Fourier Transform of a signal, can it every be known precisely which values in the space domain are zero?
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44 views

What is the 2D Fourier Transform of this function?

$ f(x, y) = \begin{cases} 1,\hspace{30px} x > 0 \\ 0,\hspace{30px} else\\ \end{cases} $ i.e. $f(x,y)$ is a bi-variate function which is zero everywhere to the left of the y-axis and one ...
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23 views

energy and power type signals [duplicate]

How can I determine if the signal $$\begin{array} \\g_1(t)=A\cos (2\pi f_c t), & \frac{-T}{2}<t<\frac{T}{2} \\ 0, &\text{otherwise} \end{array}$$ and: $$g_2(t)=\cos(t), -\infty < ...
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80 views

Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
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1answer
18 views

How to determine stopband of discrete Gaussian, stdev sigma, support N

I would like to analyse a gaussian smoothing kernel with a set standard deviation and support (let's say, in MATLAB, fspecial('gaussian', [5 1], 1.3) so sigma is 1.3 and support is 5) in the DTFT ...
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1answer
20 views

Correction of signal after High-pass RC-filter

I have one question about digital correction of signal after RC filter which is high-pass. Let me explain detail. I have one simple signal conditioner. It has RC filter on the signal input with ...
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0answers
38 views

Difficulties with derivative of convolutions in Fourier domain

I am trying to solve a minimization problem in the DFT domain. I have a formula where both dot products and convolutions are involved. Capital letters are the DFT of 2d images, the overline denotes ...
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4answers
327 views

Difference between DC component and zero frequency component of signal

We know that Fourier Transform of a signal exists if it is absolutely integrable and it exists for periodic signals if impulse functions are allowed. If we consider the fourier transform of ...
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1answer
35 views

How to implement Fourier Descriptor of an image?

I want to implement Fourier Descriptor of an object. I have read link. However, I have some questions about normalizing Fourier Descriptor. First, if I want to normalize the position of the starting ...
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2answers
101 views

Why are there so many windowing functions?

Many windowing functions are listed here in the Mathematica documentation. I tried using a few to reduce leakage when computing a Discrete Fourier Transform. From what I could tell it made little ...
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1answer
50 views

What is the difference between multiplying a delta and a step versus convolving a delta and a step?

Seems both will produce another step. there is no difference? Thanks
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309 views

Why is the Fourier transform of a Dirac comb a Dirac comb?

This doesn't make sense to me, because the Heisenberg inequality states that $\Delta t\Delta \omega$ ~ 1. Therefore when you have something perfectly localized in time, you get something completely ...
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2answers
70 views

A clarinet has no even harmonics. What would produce no odd harmonics?

According to this link, the waveforms of clarinets do not have even-numbered components in their harmonic series: A closed cylindrical air column will produce resonant standing waves at a ...
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16 views

“Normalizing” PSD of unequal window lengths

I am acquiring time-varying data with unequal sampling (nature of the source). When building a spectrogram, I have the algorithm choose sample blocks that are are -nearly- the same length -but, they ...
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2answers
70 views

Is there a better Fourier Transform-based algorithm to use in Image recognition

I have been trying to use the Fourier transform in recognizing images of the same size 200x400. I have tried many different ways to do that such as: Performing the Fourier on the full image and ...
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1answer
43 views

Energy calculation in frequency domain

I was just wondering... The formula I learned to calculate the energy of the signal is expressed in the time domain: $E_x^{\text{time}} = \sum_{n=-\infty}^{\infty} |x[n]|^2 $ Then, what does the ...
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1answer
46 views

Discrete Time Fourier Transform to Frequency Domain

I failed to do this question on the exam and finding it very difficult, I would be glad if you can help me solve it. How shall I start?
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1answer
55 views

Do signals with a Fourier transform with discontinuities or zero amplitude (in some frequencies) have Laplace transform?

I am reading a book on Laplace transform, and in the section on the convergence of Laplace transform for various signals the following theorem is stated, without any proof : If a signal's Fourier ...
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1answer
88 views

Removing periodic noise from image using Fourier transform

I'm trying to get rid of some periodic flicker noise through post-processing of the recorded images. The reason for these artifacts is that the electronic rolling shutter of the camera reads each line ...
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1answer
105 views

Fourier transform possible on non-rectangular part of an image

Dear Signal Processing readers, I want to introduce 'noise' into parts of images. Until now, I worked with rectangluar images for a similar purpose and did the following, using (inverse) Fourier ...
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63 views

Fourier descriptors: trying to classify objects

Describing my background: I have around 33 items labeled. For example, 3 pictures of the contour of a basil plant, 4 pictures of the contour of earphones, 7 of a mug, etcetera. I'm trying to ...
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1answer
42 views

Filtering Passband Signals using Complex Baseband Filtering

So I'm given a pass band filter with specific transfer function $H_p(f)$, I want to implement this via baseband processing. I already know how to take the input signal $u(t)$ and process it such that ...
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1answer
38 views

How to narrow the frequency band of a wavelet

I have a ricker wavelet with a dominant frequency of 15 Hz. The fourier transform shows its frequency band is almost to 50 Hz. How can I narrow the frequency band of this 15 Hz ricker wavelet? I ...
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1answer
92 views

Psudocode implementation of true envelope

I am trying to implement the algorithm described in this paper, I'll quote the relevant portion: http://recherche.ircam.fr/equipes/analyse-synthese/roebel/paper/trueenv_dafx2005.pdf Let $V_i(k)$ ...
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1answer
79 views

Conceptual question on FFT/IFFT (IFFT existence)

I was reading "Discrete and continuous Fourier transforms: analysis, applications and fast algorithms" written by E.Chu and, at some point, I found something that I could not completly understand. ...
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2answers
78 views

Using only positive frequencies in fourier domain, How will it affect the ifft?

I am going to do some kind of transformation and transform a data to another domain, and again back to the first domain. For this, I take a fourier transform of the data and separate the positive part ...
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88 views

Normalization purpose in signal processing

What is the purpose of normalizing the signal? If we have two signals on hand, how is it used when comparing these two signals?
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75 views

Converting raw I/Q to dB

I am getting I/Q data from a software-defined radio. I want to do some stuff on signals in the data, but only if it exceeds a certain range. What is the general procedure to get dB (dBm, or ...
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34 views

Spectral method for correct first derivative?

I'm trying to take the first derivative of a non-peroidic function. I'm getting a good result for periodic signals, but a bad result on a ramp like signal. How do I get an accurate 1st derivative ...
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1answer
74 views

Implications of $X( -j\omega ) = X^*(j\omega)$

What are the implications of: If $x(t)$ is real and $x(-t) = x^*(t)$, then $X(-j\omega) = X^*(j\omega)$ and $X(j\omega)$ is real. I am trying to understand it and I would like to research it ...
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43 views

Fourier series qn determine the fourier series coefficients

Can someone please help me with this Fourier series question: Determine the Fourier series coefficients of $x(t)$ given as $x(t) = > \cos4t +\sin8t+3$?
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1answer
66 views

non-equispaced DFT bandwidth

I need to construct Fourier transform of non-equispaced data. That is, I have signal $s(t)$, $t\in[0,T]$ sampled at non-equispaced points $t_k$, $k=0...N-1$ with sample values $s_k = s(t_k)$. For ...
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1answer
31 views

why is the DFS of a delta function equal to 1

I have a x[n] = $\delta$[n]. By formula is should be $$ X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn} X[k]= \sum_{n=0}^{N-1} e^{-j2*pi*kn/N} $$ The formulae isn't showing for some reason. I took a ...
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2answers
78 views

Instantaneous frequency vs fourier frequency [closed]

Lets consider a pure sine signal at $\nu$ that is chopped using square pulses (like a burst mode on signal generators). My understanding is that instantaneous frequency is $\nu$ when oscillations are ...
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41 views

Aliasing in the Short time Fourier Transform of a pulse

When attempting to take the Short Time Fourier Transform of a pulse, at the end of the pulse I'm running into problems. The signal looks like this at the end (it is a simple $sin^2$ pulse envelope, ...
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1answer
35 views

What happens to the fourier transform of sample result of $30kHz$ sinusoidal signal when sampled with sample frequency $44.1KHz$?

As the title says,w hat happens to the fourier transform of the sample output of $30KHz$ when sampled with sample frequency $44.1KHz$? I do not get how alias can appear, because fourier transform of ...
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14 views

What is the best way to construct time-domain data to minimize harmonics?

I'm attempting to use a Fourier transform in order to detect the frequency of particular types of discrete events. The events themselves are by their nature completely discrete with no duration. ...
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1answer
62 views

STFT: why overlapping the window?

For STFT, we impose window of certain size onto the original signal, then we perform fft on each window. The uncertanty about frequency and time is determined by the width of the window, however, I ...
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14 views

Short Time Fourier, What happen when window is outside the sample points

I am trying to compute STFT on the following signals..... such that they have 15 cycles of (1/50) second sine wave, with Fs=10000. The algorithm for STFT I am using is :STFT algorithm Then I set ...
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61 views

Fourier transform of triangular function

Determine $X(\omega)$. $g(t)$: I understand how to create a box from [-1,1] of amplitude 1/2. $x(t) = g(t) * g(t)$ $X(\omega) = G(\omega)G(\omega)$ the solution I am seeing says that $G(\omega) ...
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29 views

Constant-Q transform - summing complex DFT coefficients vs. summing DFT magnitudes

The constant-Q transform computes a spectrum on a logarithmic frequency axis. When analyzing music signals, this can be a more meaningful representation than the Discrete Fourier Transform (DFT), as ...
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3answers
365 views

Conceptual question on FFT and chirp signal

If I take the FFT of a sinusoid I will get a plot whit all the energy of the signal concentrated at the sinusoid frequency. But what happens if I have a signal in which the frequency keeps ...