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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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 $1/...
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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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296 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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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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194 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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43 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: $f_1,f_2,.....
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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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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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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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Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
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1answer
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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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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 cut-...
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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 $\text{...
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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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217 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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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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2answers
277 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 then ...
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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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414 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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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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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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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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486 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 ...
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464 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 have ...
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321 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 $V_i(k)$ be ...
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1answer
233 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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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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795 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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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 anything)...
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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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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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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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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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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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0answers
278 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
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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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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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3answers
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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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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 changing?(...
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Regarding Bode plots; $H(s)$ and $H(j\omega)$

In circuit analysis, I understand the use of Laplace Transforms to obtain the impedance of a linear RLC circuit, ie transforming from the time domain to the frequency domain. In most texts I have seen ...
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How do I take the real part of this bandpass filter system's output?

I'm stuck on a final step in this problem. Essentially, there are the two systems above, which we'll call System 1 (Fig. 4.26, with ideal lowpass $H(jw)$) and System 2 (with $H_1(jw)$). The question ...
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Why is a negative exponent present in Fourier and Laplace transform?

could anyone explain why there is a need of negative exponent in fourier and laplace transform.I looked through the web but I couldn't get anything.Does anything happen if a positive exponent is ...
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Fourier Transform Problem - absolute value, time-saving tricks, etc

I am given the following signal: $$[e^{-at}cos(w_{o}t)]u(t),\ a>0$$ Then I am told to find the Fourier Transform, which tells me I need an answer of the form: $$X(jw)=\int_{-\infty}^\infty \! x(...
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1answer
242 views

DSP interview question: use of the identity in development of a significant transform

I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform? How the simple identity $$xy=\frac{1}{2}x^2 + ...
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1answer
314 views

Why doesn't JPEG use 1D DCT for image compression?

I know that JPEG uses 2D dct and splits the images in 8x8 blocks. Why doesn't it simply split the image in one-dimensional vectors in $\mathbb{R}^{64}$? Wouldn't it simplify the math? My guess is that ...
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2answers
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How does taking the absolute value of a complex signal reflect in the frequency domain?

I have a frequency-domain representation $X(e^{i\omega})$ of the complex discrete one-dimensional signal $x[n]$: $X(e^{i\omega})=\mathcal{F}\{x[n]\}$. Is there a frequency-domain transformation of $X(...

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