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

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Implementing the Naive Discrete Fourier Transform (Not FFT)

So, I am trying to implement the Discrete Fourier transform and its inverse for the purposes for gaining a better understanding of how it works. The two functions are inverses of each other. (modulo ...
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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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Difference between Convolution and multiplication

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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42 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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22 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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24 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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33 views

Order analysis or order tracking

I've been trying the last week to implement the Order analyse 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 ...
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437 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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77 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 ...
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69 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
95 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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156 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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77 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 whereas others say that it is a (pole) hyperbola rather than a delta-pulse?
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44 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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94 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
62 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
68 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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20 views

get similar picture from wavelet transform

my today's question is related to previous question about wavelet, ...
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34 views

2D version of Shift Theorem

What is the 2D version of Shift Theorem?
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162 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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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 ...
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37 views

Disadvantageous of wavelet transform

i have question related to wavelet transform:we know that while Fourier transform is good for spectral analysis or which frequency components occurred in signal,it will not give information about at ...
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98 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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49 views

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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61 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) ...
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65 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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56 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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61 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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63 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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51 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 ...
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58 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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32 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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20 views

Finding Signal Energy of a continuous signal in the time domain

I have a quick concern regarding an assignment that I'm working on. Currently, to find the signal energy of a continuous signal, we're converting the signal to the frequency domain through a fourier ...
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1answer
30 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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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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101 views

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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65 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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70 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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87 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 ...
3
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1answer
72 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
61 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 ...
3
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2answers
149 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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0answers
27 views

How to acquire the `mainlobe` width to be less than the separation between two components that we wish to distinguish?

How does the mainlobe width of your window affect your ability to resolve the two components? Suppose a safe choice is to ...
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1answer
68 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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74 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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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
84 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
30 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
70 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
58 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 ...