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

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Fourier Transform of a Distcrete Sequence Periodic?

Why do we say that the Fourier transform of a discrete sequence is continuous, for example here Fourier transform converts every discrete sequence in continuous spectrumMy first question is for the ...
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Puzzle to puzzle you:image

Suppose 3 1D Signals x(t), y1(t) and y2(t) are given as x(t)=sin(40*pi*t); y1(t)=.5*sin(40*pi*t) and y2(t)=x(t)+y1(t). Left side =Right side Here,values of x(t)and y1(t)i.e.(Right side) are given ...
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12 views

frequency domain image analysis for recognition purposes

There are many areas like, gait analysis, where we recognize persons by analyzing their silhouettes taken while they are at different stages of their walking where analysis also carried on in ...
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109 views
+50

Fourier Decomposition

Hello everyone have a look at this video of Fourier Decomposition of an image(otherwise you can also refer the image which shows few plots of different extracted waves from an image) . We also know ...
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110 views

Finding the Harmonics contained in an Image?

I am beginer in image processing. Any signal whether it is 1D,2D or any multidimensional signal can be represented using combination of number of sine and cosine wavesforms (harmonics). Similerly any ...
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60 views

Dominating frequency in a “clear” 50 Hz signal

I am trying to find out the dominating frequency of a signal with a frequency of 50 Hz (sampled at 200 Hz - every 5 milliseconds). The python code I am using to do this is the following (based on ...
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1answer
32 views

How to choose between taking the real part or the absolute value of an inverse discrete Fourier transform?

I kind of expected this to of been asked before, so if this is duplicate please point me in the right direction, however I couldn't find anything. I am currently experimenting with low pass ...
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1answer
67 views

Intuitive explanation of cross-correlation in frequency domain

According to the cross-correlation theorem : the cross-correlation between two signals is equal to the product of fourier transform of one signal multiplied by complex conjugate of fourier transform ...
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1answer
96 views

Shift in Time-Domain after FFT-Convolution

To my understanding, multiplying a signal in the frequency-domain is equal to a convolution in the time-domain. I wrote a small python program, but i always end up with a shift in the time domain. ...
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36 views

Simulation of a pressure field developed by a song

Greetings! What I am doing: In short, I want to write a program that is fed a song as a wav file, and spits out an animated contour plot indicating the relative pressure/loudness/quantity indicating ...
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1answer
18 views

How does the OFDM system receiver decide the OFDM symbol length? [duplicate]

I am trying to understand how the receiver decides the length of OFDM symbol in time domain before it goes into DFT process at the receiver. The complete OFDM symbol (with Cyclic Prefix added) is ...
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2answers
138 views

Physically what is phase term means for multidimensional signal?

I want to ask very basic question related to multidimensional signals like an image or a video signal. What is phase term means for multidimensional signal like an Image or video signal(like for ...
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2answers
162 views

Whether phase congruency and phase coherence terms are same or different?

I am beginner in Image processing.I am studying the importance of phase in signal.Can anybody explain what is phase congruency ? Also,I am confused between terms i.e. phase congruency and phase ...
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1answer
57 views

Normalize Fourier Transform For Video Game

I am in the process of developing a video game where I would like to sync a character's mouth with an audio clip of their speech that is playing. I found this great website that shows the profiles of ...
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4answers
390 views

What's the exponential term in Fourier Transform mean?

We know that Fourier Transform $F(\omega)$ of function $f(t)$ is summation from $-\infty$ to $+\infty$ product of $f(t)$ and $e^{-j \omega t}$: $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ ...
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43 views

Exact formula for alias of Discrete Fourier transform for periodic sigals

Suppose that $f(t): \mathbb{R} \to \mathbb{C}$ is a $T$-periodic signal, with highest frequency $f_h$. Now suppose that our sampling rate frequency is lower than $f_h$, and is not any multiples of ...
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9 views

implementing bandwidth filter in R

I am reading this "how to" in R: http://www.inside-r.org/howto/time-series-analysis-and-order-prediction-r I am confused about the tutorial's implemented band pass filter. In particular, here's the ...
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29 views

MFCC from DFT (FFT)

I want to write an speaker recognition application (based on some password recorded few times for the authorized person). I've decided to do it with C++ and BASS library (http://www.un4seen.com/). I ...
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33 views

Help with Fourier transform [duplicate]

Firstly I must say that I'm beginner in field signal processing. I'm familiar with Fourier series but I have some hard times in learning Fourier transform. Why we use it? What's purpose of Fourier ...
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25 views

How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

Suppose there is signal $f(t)$ that is continuous and periodic. It is known that this $f$ is $T$-periodic. (but it's not necessarily a single cosine $f(t)$.( I'd like to make the mean of samples be ...
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1answer
55 views

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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77 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
32 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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35 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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26 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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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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45 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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85 views

Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
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19 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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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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441 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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40 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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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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54 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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344 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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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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“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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72 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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48 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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48 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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56 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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111 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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140 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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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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48 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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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 ...