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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Is it possible to do single vehicle tracking using Fourier transform?
I am working on a project in image processing which is based on importance of phase only reconstruction of a signal obtained using Fourier transform.For more information about phase only ...
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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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how to compute a discrete fourier transform on fragmented data
I have a list of collected data points that I need to take a DFT of, however with the problem that about one quarter of the data points in the middle are missing, and so even though the existing data ...
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What should the amplitude be when plotting 1-sided Amplitude Spectrum?
I have a continuous signal x(t) such that
$x(t)=12cos(6\pi t)+6cos(24\pi t)+3cos(30 \pi t)$
and is asked to sketch a 1-sided Amplitude Spectrum of the signal x(t) if sampled above the minimum ...
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158 views
2-d circularly symmetric low-pass filter
For a square pixel grid, the ideal 2-d low-pass filter with a horizontal and a vertical cut-off angular frequency $\omega_c$ in radians has an impulse response (kernel) $h_{\small\square}(x, y)$ that ...
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From MFCC to Machine learning. What are the steps?
I was able to get a dataset with MFCC coefficients. However, depending on the length of my sound file I get a different sized matrix. As in, 13 (13 MFCC coefficients) by XXX, where XXX will vary ...
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Is it possible to decompose an image into basis images using MATLAB?
I have read that:
Using Fourier decomposition any arbitrary image can be represented as
summation of orthogonal basis images.
I want to see the basis images for any image say Lena or Cameraman, ...
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169 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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Fourier Transform Computer Vision Textbook
I am required extremely fast to fill the gap and learn Fourier Transform with application in Computer Vision.
It was easy to find mathematical aspects of Fourier Transform, but I am more interested ...
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How to get coefficients for sine/cosine function from complex FFT?
I'm working on a control system that measures the movement of a vibrating robot arm. Because there is some deadtime, I need to look into the future of the somewhat noisy signal. My idea was to use the ...
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Deriving the integration property of the Fourier Transform
I want to derive the property of the Fourier Transform that states that if $X(j\omega) = \mathcal{F} (x(t))$ then $$\mathcal{F} \left( \int_{-\infty}^{t} x(\tau) \mathrm{d} \tau \right) = \frac{1}{j\...
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MP3 Filterbank + MDCT: Why?
What is the rationale for the two-step process the MP3 format performs, first decomposing the input into 32 subbands of 6/18 samples each then performing MDCT on each subband individually?
Why not ...
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How do optical anti-aliasing filters work from a frequency domain perspective?
To prevent aliasing caused by the finite number of pixels on a sensor, a blurring filter is commonly used. How does that work from a frequency domain perspective? What is the transfer function of such ...
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3D wiggle plot for an analytic signal: Heyser corkscrew/spiral
Just reading The Analytic Impulse, A. Duncan, 1988, I met the name "Heyser corkscrew" for the first time in my DSP life, for a 3D display of a cisoid or complex exponential $e^{i\omega }$ (often ...
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How does taking the absolute value of a complex signal reflect in the frequency domain?
I have a frequency-domain representation $X(e^{i\omega})$ of the complex discrete one-dimensional signal $x[n]$: $X(e^{i\omega})=\mathcal{F}\{x[n]\}$. Is there a frequency-domain transformation of $X(...
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Why is level of power spectrum dependent on FFT resolution?
I created a sinusoidal wave in some noise, and plotted the power spectrum of the signal using two periodogram estimates (welch procedure). One estimate is 'high resolution' - i.e. it uses a longer ...
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1-D Fourier Transform Of A 2-D Image But At An Arbitrary Orientation
If one has a 2-D array and would like to take the 1-D Fourier transform along a direction $\theta$ degrees off the horizontal, is there a better/faster way to do this rather than rotating the image by ...
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Kernel Convolution in Frequency Domain - Cyclic Padding
I don't know whether this is the right place to post this, but I suppose it is.
I know that frequency multiplication = circular convolution in time space for discrete signals (vectors).
I also know ...
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How does causality (i.e. unit step) affect the DTFT of a sine or cosine wave?
Tables of common Discrete-Time Fourier Transform pairs list the transform of a sine wave:
$ \sin(\omega_0\ n) $ and its transform:
$ -j\pi\ [d( \omega\ - \omega_0\ ) - d( \omega\ + \omega_0\ )] $
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Periodicity of a constant signal!
This can be a very silly question, but I'm quite confused:
If we take the Fourier transform of any constant signal, we get an impulse at zero, which says that its frequency is zero and, hence, it is ...
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Motivation of time-frequency analysis
Can anyone give me an example of two signals with different temporal waveforms having the same Fourier transform (FT)?
Would the inverse Fourier transform still be able to recover correctly each ...
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Proof of complex conjugate symmetry property of DFT
According to the Proof :
\begin{align}
X_n &= \sum_{k=0}^{N-1}x_ke^{-j\frac{2\pi k n}{N}}\\
X_{N-n} &= \sum_{k=0}^{N-1}x_ke^{-j\frac{2\pi k (N-n)}{N}}\\
&=\sum_{k=0}^{N-1}x_k e^{-j 2\pi ...
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Does DFT produces the same output as FFT?
In my journey about learning what / why / how of DFT, I tried to implement a DFT on MATLAB and then I compared its output with fft output and then I noticed it was ...
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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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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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A system that perfoms Fourier Transform operation - is it an LTI system?
If a system takes input as the time domain signal and outputs the frequency domain signal, is such a system an LTI system?
For if the input time domain signal can be represented as a linear ...
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Online DFT Algorithm
I have a discrete audio stream $x$ that needs to be processed in real-time. Specifically, as the each new sample is received, I would like to compute a Fourier transform of the last $n$ samples of the ...
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What is phase congruency?
I am beginner in Image processing.I am studying the importance of phase in signal.Can anybody explain what is phase congruency ?
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What happens with signal in frequency spectrum when it is time shifted in time spectrum?
I have some trouble to understand what is going on with signal in frequency spectrum when it is time shifted in time spectrum.
I am hoping that somebody will help me to understand that.
Thanks you ...
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Finding maximum using DFT
I'm trying to find an efficient way to compute maximum of a signal using its DFT. More formally:
$$\max\left\{ \mathcal F^{-1}\left(X_k\right)\right\}, X_k\text{ is the DFT of the signal and } \...
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Differentiation of sine in Fourier domain
The derivative of $\sin(\omega_o t)$ is $\cos(\omega_o t)$.
The Fourier transform of $\sin(\omega_o t)$ is $\frac{\pi}{j}[\delta(\omega-\omega_o) - \delta(\omega+\omega_o)]$.
Differentiation in the ...
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Energy calculation in frequency domain
I was just wondering... The formula I learned to calculate the energy of the signal is expressed in the time domain:
$E_x^{\text{time}} = \sum_{n=-\infty}^{\infty} |x[n]|^2 $
Then, what does the ...
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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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How do we know that CTFT of the autocorrelation function is the PSD?
I know that the Fourier Transform of the autocorrelation function is
the Power Spectral Density. But how can we arrive at such a result intuitively?
Is it just a theorem?
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Relation between samplingrate and frequency
I am working on Fourier Transformation, and applying this for recognizing an audioclip.
I have a 9 second long audio clip of a guitar strumming an A-Minor.
The audioclip has a sampling rate of 44100 ...
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How condition for existence of Fourier transform is valid?
The condition for Discrete time Fourier transform to exist for function $f(n)$ is given as
$$\sum_{-\infty}^\infty |f(n)| < \infty.$$
In case of continuous Fourier transform the difference is ...
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Conjugation in Fourier Transform
I have a very simple question.
In Oppenheim book, it says that:
If CT Fourier transform of $x(t)$ is $X(j\omega)$ then, CT Fourier
transform of $x^*(t)$ is $X^*(-j\omega)$.
What I can't ...
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disadvantages of FFT, it can not extract enough frequencies without enough samples
Let's say sampling rate is $Fs = 44\mathtt{kHz}$, now I have $N = 2048$ samples, then I can get $N/2 + 1 = 1025$ frequencies.
I'm confused by Matlab's FFT documentation that says the frequencies are ...
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3answers
281 views
Determining the period of a discontinuous function
I'm new to the field of DSP.
I'm trying to determine the period and shift of the function. I've tried using FFT, but haven't had much luck. Seems like it should be simple.
Signal (pastebin of ...
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Chop out frequencies outside human hearing range
I have a bunch of audio files all sampled at 44100 Hz sample frequency. I am trying to remove all the frequencies which are outside the human hearing range (I use the following as reference: Frequency ...
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How Much Zero Padding Do We Need to Perform Filtering in the Fourier Domain?
Consider an $M\times N$ image $f$ and an $G \times K$ filter $h$. Given that convolution in the spatial domain corresponds to multiplication in the Fourier domain, then we can perform a convolution of ...
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2answers
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Convolution in frequency domain
Simple math question. The convolution theorem states that multiplication in time domain is equal to convolution in frequency domain and vice versa. There is a condition that the signal has to be ...
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Are the FFT coefficients symmetric in image processing?
On page 11 of Fundamentals of Image Processing by Ian T. Young, Jan J. Gerbrands, Lucas J. van Vliet (pdf) the results of the Fourier transform are shown (Figs 4a and 4b) and it appears to me (please ...
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Derive Frequency Representation of Impulse Train Function
I want to walk through the derivation of the frequency representation of an impulse train.
The definition of the impulse train function with period $T$ and the frequency representation with sampling ...
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Is there a name for the procedure of taking the FT over separate consecutive small time-blocks?
Suppose we have a continuous time-interval $I=[a,b]$, and a signal $x \colon I \to \mathbb{R}$.
A procedure that is sometimes carried out (e.g. when doing bispectral analysis) is to partition $I$ ...
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Centered Fourier transform
What is the difference between the non-centered and centered Fourier transforms? In other words, when should you use one instead of the other?
Non-Centered: $\quad \displaystyle X_1(f)=\sum\limits_{n=...
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Can you decimate / downsample a signal in frequency domain just like you can interpolate / upsample it?
To interpolate a signal I can just zero pad it in the frequency domain. If I want to decimate the signal, can I just discard some part of the frequency domain?
So in MATLAB this works:
...
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what is nyquist rate of $h(t)\cdot h(t)$ and $h(t)\circledast h(t)$
Let's say we have $h_c(t)$ as a continuous-time signal with bandwidth $B$ and we would like to sample it.
To be able to reconstruct it correctly, the sampling rate must be greater than $2B$.
Now ...
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1answer
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Derive DTFT of $x[2n]$
If the DTFT of discrete sequence $x[n]$ is $X(e^{j\omega})$, what is the DTFT of $g[n] = x[2n]$?
I see the textbook answer is
\begin{align*}
G(e^{j\omega}) &= \frac{1}{2} \left( X(e^{j\omega/2}...
