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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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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34 views

Discrete Fourier Transform - measuring signal at equi-spaced points

I found a really intuitive explanation of Discrete Fourier Transform here. To summarize the author's approach briefly : What if any signal could be made from circular motion (repeating cycles) ? ...
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Why would you use DCT as oppose to DFT for detecting oscillation in a signal?

For my project, I needed to detect the primary oscillation frequency in a signal data. As I googled around, it turns out that DCT is the best tool to find this ...
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59 views

How can I reduce noise errors when detecting DTMF with the Goertzel algorithm?

Thanks a lot to whoever downvoted my question for no good reason. I wrote an implementation of the Goertzel algorithm in JavaScript and made a demo that detects DTMF dial-tones. You can find the ...
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33 views

DFT method for a sequence defined by recursion

I encountered the following interesting computational problem in the field of computational statistical mechanics. https://www.dropbox.com/s/8yimd9uy5u0jrdj/dftpr.pdf thank you :)
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DFT for somthing similar to convolution

I have the following problem: Let x,y be finite real valued sequences defined on 0...N-1 and let g be a non negative integer . define also on 0..N-1. Note that the sum is from 0 to n, not N-1. ...
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26 views

Matrix form of STFT

IS there a Matrix form of the STFT that could be applied to a signal directly, as in the case of DFT? We know the matrix structure of the DFT Matrix. Can we derive that somehow for a STFT Transform? ...
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34 views

2D version of Shift Theorem

What is the 2D version of Shift Theorem?
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Meaning of tight frame in the context of texture synthesis

I am currently reading "A parametric texture model based on joint statistics of complex wavelet coefficients", by Portilla and Simoncelli. In this article, they use the "steerable pyramid" to ...
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37 views

Complex numbers in a frequency domain of a 2D image [duplicate]

I am try to grasp the idea of frequency domain for images. I think get the basics, but now I've stuck with a question that I can't find appropriate answer anywhere. How are frequency domain and ...
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84 views

Intro Question to Signal Processing (Low-Pass Filter)

I have a noisy signal file in Matlab and I have to denoise the polluted signal using a discrete Fourier transform. I'm asked to perform the fourier transform, then take its absolute value. Then ...
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72 views

How can I use time-series transforms for detecting malware? [closed]

I am student of network security, and very unfamiliar with the domain of signal processing. Do pardon my naivety at asking very basic stuff. My work deals with detecting malicious activity in network ...
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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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74 views

Scaling Property in DFT

In below image, we have scaling property of DFT, how the final equation is obtained from the above equation. That is how we are getting the scaling factor , $ \frac{1}{|ab|} $ in the final equation ? ...
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1answer
43 views

Standard representation of FFT of an Image?

Statement 1 : When we take DFT of an image matrix, we get DFT co-efficient matrix. What does the DFT Co-efficients tells about the image? (For example, take the 1st co-eff in the DFT matrix, what ...
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1answer
54 views

FFT analysis of longer data sets

I have a problem with a FFT analysis in MATLAB, which is probably related to my limited understanding of the fundamentals of Fourier analysis. I use MATLAB’s built-in fft analysis function. The ...
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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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36 views

Using Spectral Density To Compute The Autocorrelation Function

I have a spectral density function $S_{xx}$ and I want to compute the discrete autocorrelation function $r_{xx}[n]$ from it but I can seem to figure out how.I have $$ S_{xx} = 3e^{-2jw} + ...
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176 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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82 views

STFT - DFT size of the bins

Having some trouble understanding this concept, really could do with some advice. I want my STFT to have the following parameters: NFFT = 256 ...
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76 views

Change of bin magnitude when phase of signal changes when doing FFT?

I am working on an implementation in which I need to apply an FFT to determine which of 4 frequencies are present in a signal. I am doing a 64 point FFT on a buffer which only is partly filled (the ...
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103 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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79 views

DFT Vs DCT - spectrum differences

When you are transforming a signal in to a frequency domain using both DFT and DCT, say for a function sin(x), how the spectrum will be? will both frequency values (of DCT and DFT) same? Can anyone ...
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61 views

How do I compute the DC component given the other part of the Fourier spectrum?

I often see examples in textbooks where someone constructs a 2D Fourier spectrum of an image by fixing two (symmetric) pixels to a given value, and computes the inverse DFT to get a nice waveform ...
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78 views

How to compute the statistics of the DFT of noise?

I would like to know how to compute the statistics of the discrete Fourier transform of a noise signal. To illustrate what I mean, I will first explain in detail a computation I have managed to do ...
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To what extent can we see signals that fall between frequency bins?

I have a simple problem I would like to figure out for fourier analysis of seismic data. Let us say that we have a signal $z[n]$, of length $N$. If I take its (same size) FFT, I will get $Z[k]$, ...
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Squared dft Coefficient defines?

What does the squared magnitude of the DFT coeffiecient tell me, where do I use it? what does it define? $|X(k)^2| = ???$ I am curious to know because the Amplitude is given by the formula $A_k ...
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119 views

Why is it possible to frequency sweep with just one sinusoid?

One way to measure the frequency response of a filter is to input separate cosine/sine wave at the desired frequency, measure the steady state output, stack the inputs/outputs into complex arrays, and ...
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142 views

Discrete Fourier transform

When you perform a discrete Fourier transform (DFT), and compute the DFT coefficients, $c_k$ and $X(K)$, what do these values tell us about the signal it came from?
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59 views

Using goertzel confuses me

I am having some troubles understanding the algorithm. My algorithm looks like this. how come am i able to compute the DFT coefficient using this algoritm. As far as i know $$ X[k] = ...
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117 views

Goertzel algorithm

I am having a hard time understanding why my textbook takes the squared magnitude of the calculated DFT coefficients. I know in DFT, you would normally take the magnitude to get the spectrum, how ...
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1answer
46 views

DFT's Unitary Property

I have doubt, please clear. A transform is said to be unitary transform when the product of the transform matrix and its conjugate transpose (Hermitian) matrix is equal to Identity matrix. DFT for ...
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262 views

1/3 octave spectra from fft

I have got a signal in frequency domain. This is a frequency response function from software, so I can do nothing about it and have to leave it in frequency domain. I want to transfer the data to 1/3 ...
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59 views

magnitude of intermodulation distortion products?

Assuming I have a set of frequencies F, and I pick 2 frequencies f1 and f2 randomly from the set, generate sine waves for them, and pass the signals through a non linear distortion process while ...
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219 views

28-Band Graphic Equalizer in Matlab

I'm trying to design a MATLAB audio player that includes something like a 31-band equalizer. Right now I have the filters working by using the FIR1() function to ...
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243 views

Discrete Fourier Transform: What is the DC Term really?

I am currently toying around with the Discrete Fourier Transform (DFT) in Matlab to extract features from images. I like to fully understand the concepts that I use. I have read several explanations, ...
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106 views

Phase factors for an 32 point fft

I have just started working on FFT and its related phase factors. I have read for an N=2 point FFT, We have two phase factors, one on the positive axis and one on negative axis. similarly for an 4 ...
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213 views

Discrete Fourier Transform for beginners

I want to make image processing programs which talk about homomorphic filter. But when I read some articles, I can't get it. Maybe can anyone help it. I very need this. Sorry about my english. I ...
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62 views

DFT detemine frequencies

I am just begining learning about DFT and I am bit unsure on what is happening mathematically during DFT. I've sampled a signal , a sine wave sin(1000*2*pi*t). And performed DFT to calculate the ...
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STFT and DWT (Wavelets)

STFT can be successfully used on sound data (with a .wav soundfile for example) in order to do some frequency-domain modifications (example : noise removal). With ...
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DFS of a time shifted periodic discrete signal

I'm taking the DSP course on Coursera, and am having trouble understanding one concept. One of the lectures says that if we have a N-periodic(periodic by repetition) signal $\tilde{x}[n]$ for $n = 0, ...
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66 views

Theoretical question on Fast Fourier

I have a question regarding Discrete Fourier Transform and Discrete Time Fourier Transform. Suppose that we have a sequence $x(n)= \{1,2,3,3,2,1\}$. So is it possible to reconstruct the Discrete ...
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114 views

Why only take 205 sample when using a sample rate of 10khz or 8khz?

I've often seen i my DSP book, that when they record a sound, they use a sample rate at 10khz or 8 khz, which makes sense since the fs is 2 times bigger than the sampling signals max freq. What i ...
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329 views

Why do we say that “zero-padding doesn't really increase frequency resolution”

Here is a sinusoid with frequency f = 236.4 Hz (its duration is 10 milliseconds (N=441), at ...
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95 views

Getting an specific frequency component from sampled audio

I have a half second audio data sampled at 44.1 kHz. If I FFT it I get frequency components in 2 Hz increments. Now suppose I want the component of an arbitrary frequency, like 32.45 Hz, how can I get ...
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Why are magnitudes normalised during synthesis (IDFT), not analysis (DFT)?

In most examples and FFT code that I've seen, the output (frequency magnitudes) of the forward DFT operation is scaled by N -- i.e. instead of giving you the magnitude of each frequency bin, it gives ...
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296 views

relationship between block size and detected frequencies in goertzel algorithm

I'm trying to use the goertzel algorithm to detect a pair of frequencies in a signal. The sample rate I'm using is 8000 hz, and the size of the incoming sample buffer is 60 samples. I have a large ...
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253 views

simplest Notch filter in the world

What do you think of this notch / band reject filter for a very very narrow band ? ...
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Phase scaling to 2d DFT

What effect should you get from scaling the phase of the Discrete Fourier Transfrom of an Image and then transforming back into the spatial domain? I am doing some experiments but I can't completely ...
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156 views

How to process video with DFT/FFT - getting the frequency of green color changes?

Goal: I have a video stream from a webcam. I need get frequency of the green color changes on the video. Video color space is RGB The signal looks sinusoidal with a frequency range 0.5 - 2.4 Hz I ...