The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in the frequency and time domains. DFT requires an input function which is discrete and non-zero, such as a sampling from an analogue audio signal.

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How does the OFDM system receiver decide the OFDM symbol length?

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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57 views

recovering phase of sine signal from FFT

I have a simple sine function as $sin(2\pi ft + \phi)$. I want to obtain the phase signal $\phi$. I tried to use FFT to calculate $\phi$. In matlab I do the following ...
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3answers
60 views

Is there a method to compute an average amplitude for 2D sinusoids using the F.C.'s?

I am working on FFT analysis AFM like the one shown below. I am currently at a point where I understand fairly well what an FFT does, and how to think about the information it gives. I currently have ...
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4answers
372 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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49 views

How can I test an implementation of DFT for correctness?

A friend of mine implemented a DFT algorithm for a project we're working on, and we're not quite sure how to test whether or not its correct. We're only in the eleventh grade, so we have very little ...
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16 views

Sinogram Fourier Analysis Doesn't Show Clear Bow Tie Shape

I'm working on finding the center of rotation of a set of test tomographic projections in order to perform 2D reconstruction. I'm trying to implement the algorithm to find center of rotation as ...
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3answers
167 views

FFT on non-uniformally sampled signals

Most fft tutorials use sinusoidal signals for demonstration, which makes the user already know what the fft is supposed to give as an output, but what about real time signals where we don't have any ...
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26 views

How does we choose parameter in SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT,Fs)

I am facing problem in SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT,Fs) How would i choose Window, Noverlap,nfft parameter for spectrogram of children voices sampled at ...
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50 views

Decomposing a DFT into multiple FFT calls

I'm using a good fast FFT implementation (vDSP) that will only work on power of 2 blocks of audio data. Now I have a problem where I would like to be able to apply the calculations to non powers of 2 ...
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2answers
90 views

DFT vs FFT: does odd number works for DFT only?

I am always confused between FFT and DFT. In both algorithm, it has been assumed that the signal is periodic (so my understanding is that, if you have a 20 sample point signal, and you do DFT or FFT, ...
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52 views

I saw this question on one of the sites related to DFT

The analog signal x(t) is band-limited to 40 Hz. Suppose the signal is sampled at the rate of 100 samples per second and that at this rate 200 samples are collected. Then 200 zeros are appended to the ...
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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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38 views

Discrete Fourier Transform of PMF and PDF

I got this explenation: "It is well-known that an image’s histogram is essentially the probability mass function (pmf) of the image (only differing by a scalar). Multiplying each component of the pmf ...
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1answer
32 views

evaluating individual terms of 2D DFT (Goertzel?)

I'm looking for a fast way to do a 2D discrete Fourier transform of an image at many arbitrary frequencies. I know the Goertzel algorithm works for 1D, but is it possible to generalize it in 2D? Or ...
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43 views

How I can optimize the DFT become the FFT?

As title, I am trying to understand fast Fourier transform, but I have a little trouble, that is: The DFT said that we must multiply the matrix 2n x 2n with ...
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2answers
200 views

Deriviation of the “Twiddle Sum” property

I can't seem to understand how to derive the "twiddle sum" property: $$\sum_{n=0}^{N-1}W_{N}^{kn}=N \ \delta[k\bmod N] $$ where $$ W_{N} \triangleq e^{\frac{j 2 \pi }{N}} $$ and $$ \delta[n] ...
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58 views

The Phase Information of the DFT

As known, we can get a 'phase spectrum' from the DFT of a input signal. Assume, we do a DFT on a given equal interval sampled 50Hz AC signal, the signal is a complete whole cycle, but the start sample ...
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54 views

Discrete Fourier transform of even function

I have a cosine function - Hence it is even. Considering only the real parts of the DFT, on performing DFT, I am getting something like this. Could anybody tell me where I am going wrong: DFT: ...
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109 views

FFT: Removed padded zeroes?

I have an application where I do this: DFT->Filter->IDFT on a range For computational performance I'm zero-padding my FFT to a power of two, but when I ...
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137 views

Horizontal banding (flickering) due to electronic rolling shutters

It is a well-known artifact that in CMOS cameras with electronic rolling shutter, horizontal banding (flickering), i.e. brightness intensity variations, are observed when the image is recorded under ...
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1answer
62 views

Discrete Fourier Transform: Prove that only N distinct values of {X(k)} can be computed

Please can anyone answer this question: The Discrete Fourier Transform (DFT) is a sequence of $X(k)$ in frequency domain of the time sequence {$x(n)$} of $N$ terms. The periodic property of the DFT ...
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1answer
82 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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16 views

Are there condition numbers associated with the STFT, DWT?

Recently I learned that the DFT has good numerical stability since it can be represented as an orthogonal matrix, which has a condition number of 1. Is it possible to represent the STFT and DWT as ...
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56 views

applying convolution theorem swaps quadrants

For educational purposes I implemented the DFT and inverse DFT for images using OpenCV. Applying the DFT to an image and taking the inverse DFT of the spectrum yields the original image, so this ...
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24 views

Analytical expression for convolution of two 2D DFTs

I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size ...
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70 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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3answers
100 views

Why does an 8 point DFT behave differently from a 16 point?

I have a 50 Hz sine wave sampled at 1600 Samples/second.I'm computing the 16 point DFT.So my fundamental frequency is 100 Hz. I then decimated the 1600 samples to 400 samples.I then computed the 8 ...
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27 views

Limit of DFT from zero to N-1:

Why do we take the limit of DFT from 0 to N-1? If signal exists from let say -5 to 8. Then what will be the limit and how will we calculate DFT?
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39 views

DFT independent variable as fraction of sampling rate

When the frequency domain's independent variable is labeled as a fraction of the sampling rate, the values along the horizontal axis always run between $0$ and $0.5$, since discrete data can only ...
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22 views

When working with DFT of a real sinusoid why is the discrete time input taken over -N/2 to N/2, as opposed to 0 to N?

I know that when we take the input from 0 to N, the frequency component in the mth bin is the same as that in the N-mth bin, and when we take it from -N/2 to N/2 then the mth bin value is same as -mth ...
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65 views

2D FFT vs 2 Pass 1D FTT

We know that the 2D FFT can be performed by taking the FT along the rows and then taking the FT along the columns. I'm wondering how theoretical performance compares to the direct 2D FT case, which ...
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36 views

DFT of a pressure signal from space domain to wavenumber domain

When I do the DFT of the following signal: I get the following DFT which doesn't capture any peaks at all: Why is this? I'm not really able to identify what the error is?
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39 views

Size obtained by applying Linear convolution

We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a ...
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409 views

Cooley-Tukey Implementation of FFT in Matlab

For my course I need to implement a 30 point Cooley-Tukey DFT by transforming it into a 5x6 matrix. I have tried to implement using the following Matlab code: ...
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2answers
66 views

Purpose of Phase Information

I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency ...
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1answer
39 views

Frequency of the wave in frequency domain

If we have a 1-dimensional wave in time domain, it can be represented in frequency domain with x axis indicating the frequency of the wave and y axis indicating amplitude/magnitude of the wave. But ...
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74 views

Explain Shift property of DFT

Please check the link What effect does a delay in the time domain have in the frequency domain? Here it is said that if you delay your input signal by D samples, then each complex value in ...
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3answers
92 views

What is a translation property in DFT

Hi someone please explain me the translation property of DFT. I am not able to understand it neither from Gonzalez nor from internet. I have done extensive study on this but not able to get it. Really ...
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1answer
140 views

What is the significance of the DFT in SC-FDMA systems? [closed]

Long term evolution (LTE) systems use single-carrier frequency division multiplex (SC-FDMA) in the uplink. In such a system, there is a DFT block and a sub carrier mapping block before the IFFT block. ...
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191 views

Recursive version of DFT as presented in Cooley-Tukey paper

The seminal paper of Cooley and Tukey provides an iterative method for computing the DFT for a sequence of length $N$. Specifically, they mention a method which utilizes the fact that $N$ can be ...
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29 views

Determining effect of powers of DFT matrix conjugate on input without multiplying

Suppose I have a DFT matrix $F$ of dimensions $N \times N$ where $N$ is a power of $2$. I convert it into a unitary matrix $\displaystyle U = \frac{F}{\sqrt{N}}$ and compute $S = U^* U^* $. $S$ ...
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23 views

Variation in Signal Power in Mimo system

I am exploring methods for reducing computations required by MUSIC (Multiple Signal Classification) Algorithm. Most of the computational power is spent on calculating SVD. My approach is to take ...
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77 views

Incorrect Frequency results when using Multiple Signal Classification (MUSIC)

I am using MUSIC (Multiple Signal Classification) to determine Direction Of Arrival (DOA) and frequency of signals impinging on an Antenna Array. I am using a function ...
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53 views

Interpreting magnitude of DFT results

I'm working on creating a simple program to render spectrograms like this one. In this plot, the X-axis is time, the Y-axis is frequency, and the color represents the magnitude of the DFT at that ...
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162 views

Autocorrelation and FFT : avoid zero-padding

Some posts evocate the computation of convolution or cross-correlation using FFT and zero-padding the temporal signal. I want to compute the autocorrelation of a 3D array using FFTW (2 dimensions are ...
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76 views

Instantaneous power estimation by discrete hilbert transform - how far does it smooth?

In my research area, instantaneous power in a specific frequency band is commonly estimated by the following procedure: Apply a bandpass filter on the raw signal (e.g. 80-90Hz bandpass). Estimate ...
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55 views

Multiply filter kernel by sine

1)Suppose that we have low-pass filter with cf equal to 0.1. How frequency response would look like if I multiply filter kernel by sine with frequency say 0.3? How this is related to converting ...
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116 views

please give the reason why every notation for DFT is valid?

$X$ represents sample in frequency domain and $x$ represents samples in time domain. NOTATION 1 $ X[k] = \sum\limits_{n=0}^{N-1} x[n] \ e^{-j \frac{2\pi}{N} n k} $ $ x[n] = \frac{1}{N} ...
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2answers
134 views

About frequency resolution [duplicate]

The frequency resolution of DFT is $\Delta f = \frac{1}{T_{0}} = \frac{1}{NT} = \frac{f_{s}}{N}$ where $f_{s}$ is sampling frequency, $T_{0}$ is sampling time, $N$ is number samples, and $T$ is the ...
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245 views

Why does the DFT assume the transformed signal is periodic?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur). Now, if you look at ...