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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165 views

Underwater Acoustic Positioning

I have to develop an underwater positioning system which has to determine the position of a ROV. Four buoys will be placed on each corner of a swimming pool. Each one of these buoys will be equipped ...
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1answer
174 views

Fourier transform with periodicity at the harmonic frequency

Let's suppose I have a signal F(t) that is periodic, with two periodicities P1 and P2, with P1>P2. Suppose that I know the values of the two periodicities. Using the Fast Fourier transform I can show ...
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2answers
670 views

What does boundary discontinuity in DFT imply?

I have been studying about boundary discontinuity in DFT and why it is not used as transform in image compression. What i understand is that DFT is N periodic and that causes a discontinuity at the ...
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2answers
1k views

Fourier transform of exponent: Delta pulse or hyperbola?

Why do some tables say that Laplace (or Fourier?) inverse of exponential is a time-shifted delta pulse \begin{align} \delta (t) &\overset{\mathcal F}{\Longleftrightarrow} 1\\ \delta (t-t_0) &...
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1answer
57 views

Sine of frequency 0 contains sines of all frequencies at once in it

You know that a sine corresponds to a pulse by J.Fourier transform. The lower is the frequency, the closer is the pulse to the origin. A constant signal is a sine (or cosine, that may be important) of ...
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982 views

Fast Fourier Transform and Clustering of Time Series

I'm making a project connected with identifying dynamic of sales. That's how the piece of my database looks like: There are free columns: Product - present the group of product Week - time since ...
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2answers
1k views

Design Filter Banks for every 100 Hz

I need to study a wave file for every 100 Hz. However, I dont know how can I design filer for each 100 Hz. Let's say 0-100 Hz, 100-200 Hz, ... , ((fs/2)-100) _ (fs/2) Hz. Is it any MATLAB code for ...
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2answers
902 views

Audio compression with STFT

Let STFT[frame, freqbin] be the short-time Fourier transform of some audio data. (here frame is the index in time, and ...
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1answer
2k views

2D version of Shift Theorem

What is the 2D version of Shift Theorem?
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3answers
1k views

Store a FFT with a minimal amount of data

I have an array x of length 1024 (stored as 16 bits integers, named for example np.int16 in numpy/python), i.e. the size of x is ...
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0answers
96 views

question about the frequency of Gabor filters

The Fourier transform of 2D Gabor filters is shown below: F is the radial frequency of the Gabor functions. Another parameter Fm is denoted as highest central frequency. Fr is the constant frequency ...
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2answers
5k views

Disadvantages of wavelet transform

I have a question related to wavelet transform: we know that while the Fourier transform is good for a spectral analysis or which frequency components occurred in signal, it will not give information ...
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1answer
171 views

Malaysia Flight 370 Image Processing

I wish that all those people on that flight were with us, and maybe they still are, as I like to think they are on an island somewhere waiting to us to find them ... however, it does not look good... ...
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Why does the inverse fourier transform of a lowpass filter have complex components in matlab?

I am quite confused whether the following numerical differences i find are just severe round off errors made by matlab, or something i am doing wrong. The following happened when trying to see what a ...
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221 views

Determining Valid DTFT's

Are the following frequency domain signals valid DTFT's (Discrete Time Fourier Transforms)? Answer yes or no, and justify your answer. a) $X(\omega) = \omega + \pi$ b) $X(\omega) = i + \pi$ c) $X(\...
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619 views

understanding complex fft results

i use this for complex fft. Output expected $fft[3].real= 32$ (peak at 3rd bin) $fft[61].real= 32$ ((peak at negative frequency pair of 3rd bin)) All other values negligibly small The input is ...
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1answer
112 views

$\sin (t \omega)$ is not an Energy Signal, then how come its Fourier transform do exist?

The following integral (perhaps fourier tranform of $\sin (t \omega)$ ) is not convergent: $\int_{-\infty }^{\infty } e^{-i t \omega } \sin (t \omega ) \, dt$ As, $\sin (t \omega)$ is NOT an Energy ...
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2k views

Power spectral density interpretation

After reading this question: PSD (Power spectral density) explanation I am still a little confused as to what extra information the PSD gives us over simply taking the magnitude of the fourier ...
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1answer
263 views

Which kernel produces sharper image

kernel A = [ 0 -1 0 -1 4 -1 0 -1 0 ] and B = [-1 0 -1 0 4 0 -1 0 -1 ] i have found the frequency spectrums with ...
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1answer
66 views

problem with Fourier transform

I am reading some paper, and I am having some trouble with some Fourier transform, Suppose that $F(\omega)$ is the Fourier transform of $f(x)$, i.e. where $$F(\omega)=\int_{-\infty}^{\infty}f(x)e^{-...
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1answer
242 views

Is there a closed form expression for main-lobe width increase given a window?

We know that when we window a signal, we increase the main-lobe width. Let 'main-lobe-width' here be the null-to-null bandwidth of the main lobe. Let us further more say that the main-lobe width of a ...
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1answer
102 views

Is there an analogue of coherence between data sets related by a non-linear transformation?

Calculating the coherence (sometimes called magnitude squared coherence) between two signals indicates the presence or lack thereof of a linear transformation between the two signals. Is there an ...
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1answer
125 views

Obtaining the frequency and phase spectra from fourier transform?

For a question on my homework, I am given f(t) = e^(-a*abs(t)) and asked to find the Fourier transform of the function. I understand how to do that part, but then ...
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2answers
2k views

Getting bpm of song with fft [duplicate]

I would like to get the bpm of a song analyzing the spectrum of the volume. Doing a fft what I get is a peak at the origin and of course that can't be the frequency corresponding to the bpm, so I do ...
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3answers
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Understanding the Gabor filter function

I need to implement a script for generating features from an input image by using the Gabor filter. I have no past experience of wavelets and I'm just learning Fourier analysis (I understand the basic ...
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125 views

discrete fourier transform in Matlab - theoretical confusion

I have a periodic term $V(x) = \sum_K \exp(iKx) V_K$ where $K =2\pi n/a$ where $a$ is the periodicity of the term and $n =0,1,2,3....$ Now I want to find the Fourier coefficient $V_K$ corresponding ...
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1answer
462 views

What does an image of Fourier Transformation of an image tell us?

First time studying image processing... I just don't understand what does fourier transformed image of an image describe? For example consider given following pictures, The first one is the image, and ...
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3answers
758 views

FFT method input argument have to be $2^n$ ?

Does FFT method input argument have to be power of 2, i.e, $2^n$ I just realized there are many algorithm for FFT implementation,...
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1answer
129 views

Correction of a signal through a transmitter

I am inquiring as to a practical way to solve a problem I have. Basically, I need to transmit a signal, $x[n]$, through a seismic transmitter. (It will go through a D/A, etc). The transmitter that ...
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1answer
148 views

Suggestions for FFT based tools to analyze music - Preferably MATLAB/free software packages [closed]

I am interested in analyzing full length songs for general features of the track which are not otherwise apparent. For e.g., I want to look at various parts of the song with time-frequency plots/...
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2answers
15k views

Difference between DFT and Z-Transform

I have searched this question but couldn't find the answer in this network. I know this is very confusing question for DSP beginners. Both DFT and Z-transform work for Discrete signal. I have read ...
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1answer
624 views

How to calculate IDFT this signal? [closed]

$X(jw) = 1 + \frac {jw+3}{jw+4}$ what is the IDFT of this signal?
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1answer
1k views

Fourier Transform of Morlet wavelet Fucntion?

as you know the Morlet Fucntion is given by: $\frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_c}$ The Fourier transform of this equation is: $e^{-\pi^2 f_b(f-f_c)^2}$ (is it right)? First I ...
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3answers
290 views

Doubt : Derive DFT from CFT

In the below screenshot I was unable to understand how the equation 4.3 is derived from the above equation.. How $x(nT)$ has become $x(n)$ ? Please clear my doubt and suggest some link to understand ...
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2answers
391 views

Need to learn wavelet, suggest steps and resources [closed]

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and Orthonormality – ...
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1answer
116 views

Frequency Response Notation

Why do people sometimes write $H(e^{j\omega})$, some others use $H(\omega)$ and even others use $H(f)$ with $\omega=2\pi f$ to describe the frequency response of a filter or a spectrum? Is there any "...
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1answer
1k views

How to evaluate expressions without explicitly computing a discrete fourier transform?

Hello DSP guru nation, I am trying to learn this part but I dont seem to understand. if I have a finite length sequence, and a n-point DFT of it (in an interval)... is it possible to evaluate ...
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1answer
202 views

Frequency Axis problem in a DTFT

I have a doubt related to calculating the Discrete Time Fourier Transform (DTFT) by hand. Specifically in how calculate the frequency axis of the spectrum. My signal has N values and was sampled at FS ...
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2answers
4k views

Convert frequency response to impulse response

I am running an acoustic simulation. I put in a frequency and get out a complex number; the frequency response for that frequency. I wish to generate a 1024-sample impulse response (supposing my ...
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2answers
1k views

Help understanding FFT Phase: code and results provided

I'm trying to figure out how FFT's phase works. Here's my code: ...
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2answers
231 views

make a threshold frequency based on percentage of frequencies less than that?

Using MATLAB signal processing toolbox, I have created signals like dirichlet, chirp and etc and and obtained their fourier and cosine fourier transform. Now I want to find the frequency where for ...
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2answers
378 views

Is $O (N \log N)$ FFT speed the fastest we can ever attain?

I am wondering about whether or not there is a theoretical limit as to the speed at which we can compute a DFT. We all know that the FFT executes in $O (N \log N)$ time. However, is this a lower bound ...
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3answers
5k views

Zero-pad before or after windowing for FFT

What's the correct way. Should I zero-pad a signal before or after applying a windowing function?
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3answers
555 views

Analyse audio/music frequencies without STFT, at 1/f temporal resolution, using probe phasors at logarithmically-spaced frequencies, O(N log N)?

First, some background: The STFT is the best general-purpose tool I know of for analysing a (musical or other) signal into its component frequencies. For many purposes the STFT works fine, but there ...
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3answers
1k views

What does the negative sign mean in the image frequency domain?

When I transform an image from the spatial domain to the frequency domain, some frequencies are negative. What is the meaning of the negative sign? For example:
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1answer
93 views

Get spectral picture from a wavelet transform

According to my previous question, I have changed the generate command to: y=generate1(100,1000,1); and got the following picture: Now I want to test a wavelet ...
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2answers
393 views

Inverse Fourier Transform

It's well known that convolution in the spatial domain is equivalent to multiplication in the frequency domain. i have multiplied the Fourier transform of an image F with H. where H is the FT of a ...
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1answer
77 views

Spectral structure of sinusoidal model

Let us consider the following code: ...
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1answer
918 views

How to prove $cos(t) + cos(\pi t)$ is non periodic function? Also can I represent this signal using fourier series?

I would just want to prove $\cos(t) + \cos(\pi t)$ is non periodic. I don't know where to start it. Also I know that individually these signals ie $\cos(t)$ and $\cos(\pi t)$ are periodic with ...
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2answers
955 views

Working around FFT windowing?

I have the following problem, that I ran into recently, when calculating the spectra of data that I obtain from a measurement technique, we are using in our group. In short what we do in the ...