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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57 views
How can a linear operator on DFT vector produce the same vector using only half of the DFT vector?
Suppose there is a DFT vector $\mathbf{X}$ with length N, which presents complex conjugate symmetry around its middle point, i.e., $X(1) = X(N-1)^*$, $X(2) = X(N - 2)^*$ and so forth. $X(0)$ and ...
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2answers
52 views
Conditions for precoding matrix to preserve complex conjugate symmetry on DFT vector
Suppose there is a DFT vector $\mathbf{X}$ with length N, which presents complex conjugate symmetry around its middle point, i.e., $X(1) = X(N-1)^*$, $X(2) = X(N - 2)^*$ and so forth. X(0) and X(N/2) ...
7
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4answers
175 views
DFT-like transform using triangle waves instead of sin waves
We know that DFT (discrete Fourier transform) breaks down a signal into multiple frequencies of sine waves. Does there exist a transform that does the same thing, but for triangle waves?
For my ...
5
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3answers
120 views
Determining the mean of of a sampled signal (improvements to time averaging method)
I am sampling a signal at 1kHz, which is essentially a single-frequency sinusoid with a DC offset (and a small amount of noise). I don't know the precise frequency of the sinusoid (it is at most ...
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1answer
62 views
frequency domain vs cosine wave amplitude
Hey guys, what is the difference between b.) and c.)? Why do we need each of them?
Excrept from: http://www.dspguide.com/ch8/5.htm (scroll below)
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2answers
95 views
How to determine a very low frequency signal?
I have a noisy signal with frequency between 1/3 and 1/5 of the sampling window.
DFT has a very low resolution for low frequency components, what is the best way to find the frequence?
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0answers
55 views
Phase Correlation and Negative Shifts
I am implementing phase correlation algorithm to determine shift between two images.
It generally works, but I am not sure how to interpret the resulting shift.
Pseudocode:
...
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1answer
61 views
retrieving original data from phase and magnitude of Fourier transform
I use this snippet of python code to transform data to Fourier phase and magnitude and then retrieving original data.
...
4
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1answer
72 views
Discrete Fourier Transform a dummy approach
I'm trying to understand how DFT works exactly. However, when experimenting around, I compared both Matlab generated FFT result with a dummy approach result and I get similar result.
However, the ...
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2answers
85 views
What is the basic concept of Fourier transform
I use discrete Fourier transform for digital image processing purposes , but I don't understand basic concept behind it. For example :
What information exists in frequency domain?
What is ...
2
votes
1answer
56 views
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2answers
69 views
Ways to analyze electrical signals without FFT?
I am collecting a 15Hz sine wave at 1500Hz. Therefore, every 100 points of data collected should contain a single complete sine wave. If I sample for 10 seconds, I will have 15000 points of data. If ...
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2answers
123 views
FFT for a single frequency
I was looking for a more efficient way of finding the magnitude and phase of a signal at a certain frequency without performing an FFT because it produces more information than I need and I came ...
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1answer
62 views
Frequency resolution and timestep in DFT
I am learning DFT and I am not sure I understand it correctly. I am just going to write out the process of DFT and I am asking you to tell me if I am thinking the right way.
Suppose we have a ...
2
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0answers
34 views
How to prove that Dilution of a time domain signal results in duplication in Frequncy domain?
While reading a description on FFT from this book, I found the following statement:
...diluting the time domain with zeros corresponds to a duplication of
the frequency spectrum.
How can I ...
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1answer
42 views
Where does convolution fit in DFT?
I am trying to understand where does the convolution fit in Discrete Fourier Transform. I know that convolution is producing a third signal from two other signals. I also know that DFT transforms one ...
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2answers
145 views
Periodicity property of DFT in time and frequency domain
I am trying to understand the periodicity of the DFT. How can this property (both in time and frequency domain) be used and can be helpful while developing on a DSP?
It would be good to see some ...
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1answer
43 views
Parameter extraction from DFT results, possibly with leakage effects
Let's start with a simple temporal law, that I want to analyze in the frequency domain :
$x(t)=\frac{1}{2}(A+Bcos(2\pi \nu_0 t+\phi_0))$, with :
$A=4$
$B=10$
$\nu_0=10^8$
$\phi_0=10^8$
I made a ...
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2answers
102 views
FFT amplitude or magnitude
Can I use the word amplitude instead of magnitude when I describe FFT bins? I dont see any similar word in my language.
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2answers
128 views
How to separate the upwards-propagating from the downwards-propagating waves?
I've got a real 2D image of propagating waves in both directions. How can I separate this image into one with the upward-propagating waves and one with the downward-propagating ones?
This example has ...
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0answers
80 views
DFT, cepstrum, LPC for feature extraction
I am a newbie in speech processing and experimenting to get a feel. I have extracted some speech segments using a window function and I want to find distance between a pair of segments. First, I took ...
2
votes
1answer
88 views
Goertzel algorithm: Relationship of magnitude
I've written a quick test app that uses the Goertzel algorithm to determine if a given frequency is present in the signal. This is to pick up DTMF tones and various other signals. The app appears to ...
3
votes
1answer
74 views
Chirp z algorithm clarification
I am attempting to implement a chirp z algorithm to handle random sized DFTs, and I can not seem to obtain any meaningful results. I have gone over several write ups and "think" I have a handle on ...
5
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2answers
264 views
How does subpixel image shifting using DFT really work?
I am trying to assess the quality of several image interpolation methods for an application that involves generating subpixel-shifted images. I thought I could compare the results of a subpixel shift ...
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1answer
160 views
DFT as convolution question
I have tried to make this question as readable and consistent as possible. The short of it, is that I am trying to ascertain how one gets from the math equation shown, (which I understand), to the ...
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2answers
78 views
Filtering + Images [duplicate]
Possible Duplicate:
What does frequency domain denote in case of images?
I am studying applications of low and high pass filters in images. However, first I'm trying to understand what ...
2
votes
1answer
342 views
Time domain interpolation using FFT with zero padding on the end
I've got a situation where I'd like to use an FFT to do interpolation in time on some complex data (I need to go to the frequency domain anyways to window my data).
The notional way of doing this ...
4
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1answer
147 views
Failed to implement Goertzel algorithm in Python
After some questioning on stackoverflow, I tried to implement a Goertzel algorithm in Python. But it doesn't work : https://gist.github.com/4128537
...
4
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1answer
85 views
Determining the type of filter on an image
I have the following mask where the origin is marked in bold text
$$ \left[ \frac{-1}{4}~~~{\bf\frac{1}{2}}~~~\frac{-1}{4} \right ] $$
After computing the DFT, the result is:
$$ \frac{1}{2} - ...
3
votes
1answer
43 views
Mapping the value of a sample in a 2-D DFT to cycles/pixel
If I have an image and its 2-D DFT of that image, what is the mapping between the value of the DFT at (u,v), and the frequency in the spatial domain in the x and y components, in cycles/pixel? I want ...
3
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1answer
159 views
What is the meaning of the DFT? [duplicate]
Possible Duplicate:
Real Discrete Fourier Transform
What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series?
Discrete Time Fourier Transform ...
3
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1answer
82 views
Circular Time Delay in signal, effect on phase spectra of DFT
If you circularly shift a signal x[n]= [-3 -2 -1 0 1 2 3 2 1 0 -1 -2 ] to the right by M=1 compared to M=2, the phase spectra has a lot many zeros when M=2 compared to M=1.
here, I am talking about ...
4
votes
3answers
594 views
Why is the FFT “mirrored”?
If you do an FFT plot of a simple signal, like:
t = 0:0.01:1 ;
N = max(size(t));
x = 1 + sin( 2*pi*t ) ;
y = abs( fft( x ) ) ;
stem( N*t, y )
1Hz sinusoid + DC
...
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2answers
623 views
Comparing Image FFT with Sine wave FFT
So, When we take the FFT of any Composite or Single Sine Wave we get exact frequency on x-axis of the plot.
The point where we get the original frequency in FFT is depend upon the Sampling Rate and ...
4
votes
1answer
139 views
Why idft(dft(a) * dft(b)) not equal to convolve(a, b)?
I'm a little confused... I always thought the DFT of a convolution was equal to a product of DFTs, but when I tried this in Python:
...
2
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0answers
35 views
how to break the input signal into segments while calculating DFT [duplicate]
Possible Duplicate:
breaking the input signal into segments while calculating DFT
Im reading a book about DSP and there is an example about investigating the sound that travel through the ...
5
votes
1answer
167 views
Z-transform of a downsampler
In this paper or multirate filtering, the author establishes the following mathematical relationship. Let $y_D$ be the output of a downsampler such that
$$y_D[n] = x[Mn]$$
where $M$ is the ...
3
votes
3answers
702 views
How to demodulate an AFSK signal in software
I am trying to transmit binary data from one device to another over an audio channel (speaker/mic). I use AFSK (Audio Frequency Shift Keying) as in Packet Radio, with $1200 \text{ Baud}$ and two ...
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1answer
317 views
DFT of complex signal using Goertzel algorithm in C
I am implementing a BFSK frequency hopping system with TX and Rx modules. I am using Goertzel Algorithm at the receiver end to demodulate the data i.e. to determine the carrier frequency of the ...
2
votes
1answer
2k views
Difference between linear convolution and circular convolution for a kernel
If I understood correctly (and this page should confirm: http://www.cs.ioc.ee/~khoros2/linear/convolution-teo/front-page.html)
if I convolve linearly (the usual point-to-point multiplication and ...
4
votes
3answers
569 views
Discrete Fourier Transform Symmetry
I was reading the chapter on discrete Fourier transforms in Lyons' book -- Understanding Digital Signal Processing -- and could not understand the last paragraph about symmetry.
There’s an ...
6
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3answers
403 views
FFT for line detection
I am trying use the FFT in a different way then most people ask about. I want to be able to take a picture of a graph with regular repeating vertical lines, and to process the image to determine how ...
2
votes
1answer
241 views
Sliding DFT: I think my results are accurate, but I can't buy a swap-swap IDFT
I've got a sliding DFT implementation that appears to be working (judging from an output plot). I would like to be able to invert this implementation using the standard tricks of swapping the real and ...
3
votes
3answers
224 views
What's the best criterion for determining a frequency peak?
I'm writing an algorithm that analyzes results of discrete Fourier transform (DFT). The algorithm should detect amplitude peaks in predefined ranges of frequencies. This is an example of such a peak:
...
12
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1answer
245 views
DFT with geometrically-spaced bins?
The traditional Discrete Fourier Transform (DFT) and its cousin, the FFT, produce bins that are spaced equally. In other words, you get something like the first 10 hertz in the first bin, 10.1 through ...
30
votes
6answers
3k views
What does frequency domain denote in case of images?
I was just learning about the frequency domain in images.
I can understand the frequency spectrum in case of waves. It denotes what frequencies are present in a wave. If we draw the frequency ...
2
votes
1answer
193 views
Express a wave as a sum of cosine
I started off with this:
$$ x = 5 \cos(200 \times 2 \pi t ) + 10 \cos( 400 \times 2 \pi t)$$
by performing a 1024 point DFT on it. Then I performed IDFT on the complex values obtained through DFT. ...
2
votes
1answer
299 views
Calculate harmonics using DFT from real points
I have a real data of 144 points, when I perform 144-point DFT on this data, I get $X$ with real and complex values. I want to calculate harmonics using these $X$'s. The $X0$ and $X72$, added together ...
3
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1answer
92 views
Creating an array whose DFT is all whole numbers
I'm working on a simple FFT implementation and currently running some unit tests. Long floating point numbers in C and assembly become very hard to keep track of, and this whole thing is error prone. ...
6
votes
1answer
792 views
Real Discrete Fourier Transform
I am trying to understand the real DFT and the DFT and why the distinction exists.
From what I know so far the DFT uses $e^{i2\pi kn/N}$ for basis vectors and gives the representation ...
