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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Image processing, recognizing a small feature in a larger image

I am trying to write an image processing program to recognize bubbles in oil. It has been suggested I try computing the convolution of the image and an image of a typical bubble. i.e. : ifft(fft(a)....
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877 views

How to calculate the energy levels of frequency intervals of an audio signal?

Using the Fourier transformation I can translate a signal from the time-domain to the frequency-domain. If I divide the frequency axis into intervals, how can I calculate the audios signals energy for ...
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What is the role of complex exponential?

What is the role of complex exponential $ e^{jθ} $ in Fourier Transform? Is it different in the continuous and in discrete time domain?
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Question about the Haar Wavelet transform

I'm trying to detect the presence of a sinusoid in 1/f noise conditions using the STFT and the DWT with Haar wavelets. I find this interesting phenomenon that I'm not able to explain (see plot at 1) ...
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FFT of random binary data

I am trying to make sense of FFTs and binary data. Say I have a series of random binary data, which is measured with a repetition rate of 400Hz (interval time of 0.0025s). I have a total of 12489 ...
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584 views

How to convert a sound file to any other data format which can be manipulated

I know this is very basic question and i am new to this site. But can anybody help me with my question. How to convert a sound file to other data format say using some type of transform (FFT or DFT) ...
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179 views

Approximation using a Fourier transform with low pass filter

I need to approximate a function f, but I cannot do so with frequencies that exceed 1kHz What is the best approximation I can get? Is taking the Fourier transform then zeroing any term above 1kHz the ...
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390 views

How can I find the amplitude of the 20 Hz frequency component of a signal faster?

I have a time varying discrete signal x(t) sampled at 5ms rate. I need to find the amplitude of the 20 Hz frequency component for each sample. What I do today is that for each sample I do a Short-time ...
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What is $F(0)$ is “dc” component in the context of image processing?

It has always been said that $F(0)$ is the "DC component" in fourier transform. However, I don't get what it means to say that $F(0)$ is "DC" in the context of image processing. The zero in this ...
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1answer
264 views

Which Approach Is Better for Decomposing an Image into High Frequency and Low Frequency Components?

Which approach is better or there is mathematical justification for using Bilater filter and Fourier Transform to decompose a image into High Frequency and Low Frequency Component. Both Bilateral ...
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269 views

How can I detect clicks/ticks in a wav file?

I have a long recording of a train (here is a small sample) there are a number of clicks as the wheels go over joins in the tracks. I would like to detect the location of these. Looking at the ...
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Understanding Walsh coefficients

I am working with Walsh coefficients. I know the intuitive understanding is almost that that they are the degree of connectivity, but it is there a better way of thinking about it? What is the ...
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Discrete Fourier transform in a multidimensional space

I want to measure the frequencies at which a point oscillates in a multidimensional space, let's take the example of a point on a 2d-surface. For now, I naïvely split the signal in two, along the ...
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About the fourier transform of Periodic Signal

I cannot understand some part of the period signal's Fourier transform. Here this my note's methods, For periodic signal with period $T_0$, define as $s_{T_0}(t)$ as $$ s_{T_0} (t) = \begin{...
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466 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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Global Transforms besides the DFT?

This is a simple question. Fourier analysis gives us the DFT, which is known as a global transform of a signal. In contrast, the Discrete Wavelet Transform (DWT) has a plethora of wavelets, all of ...
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Finding out modulation index and DC offset

I have a question form my teachers, and I cannot understand why I can find out the modulation index form the figure. The question provide a Figure like this: And the information signal is a ...
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1answer
949 views

How do I find the power of a specific frequency at a specific sample of a discrete time varying signal?

EDIT: First off let me explain that I understand that frequency makes no sense for a single sample. What I am actually talking about is the power spectrum within a short time window around a specific ...
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1answer
246 views

What are the uses of those three types of wavelet transformations?

In my studies of wavelets, there appear to be 3 different families of them: The Continuous wavelet transform The Discrete wavelet transform The Redundant wavelet transform They are all based on the ...
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How to find the envelope of a wide-band signal?

I would like some feedback on possible techniques that one may use to determine the envelope of a broad-band time domain signal. I have heard anecdotally, that it is not as straight-forward as it ...
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What happens if we change the limits of integral in Fourier transform?

By definition of Fourier transform $$X(\omega)=\int_{-\infty}^\infty x(t) e^{-j\omega t} dt $$ Now what will happen to the answer of transform for example in case of $x(t)= \cos(\omega_0 t)$ if ...
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What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?

At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
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279 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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Covolution of DTFT [duplicate]

Possible Duplicate: Convolution and DTFT $x_1(n)=x_2(n)=1$ where $0 ≤ n ≤ N-1$ 1)The linear convolution of the signal gives a triangle how you write it in mathematical form? The DTFT of the ...
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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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1answer
987 views

FFT of color images incorporated into an Object Recognition method?

Is there any instance where Fourier transforms of color images have been used in conjunction with other object recognition method? Any instance of usage of Fourier transforms in color images? I ...
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Obtaining the Impulse response from the frequency of a discrete system

I have the following discrete system's transfer function (Z domain): $$h[z] = {z \over z - \frac{1}{2} }$$ I need to obtain the following: The frequency response. The impulse response. The fourier ...
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112 views

Vestigial Filter problem?

I have been stuck on this question for a while now. It has to do with vestigial sideband. I wasn't sure if I should be dividing $H(\omega)$ graph values by 2 because only the positive side of the ...
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292 views

Signal Processing using Fourier Transform

So I'm trying to understand how MRI machines work. I understand all the concepts of it, the parts, what they do, how the machine works, etc. The part I'm having trouble with is the fourier transform ...
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Fourier transform of cosine to the power of 3

How can I find the Fourier transform of $$ f(x) = ( \cos(x) )^3$$ I know that for $ g(x) = \cos(x) $ $$\mathcal F \Big\{ g(x) \Big\} = \mathcal F \Big\{ \cos(x) \Big\} = \pi \Big [ \delta(w-\pi / 2)...
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Impulse Response / Frequency response Question [closed]

I have a major question. Please take a look. I have this differential equation (DE): $$ \frac{d^2y(t)}{dt} +\frac{dy(t)}{dt} +4y(t)= \frac{dx(t)}{dt} +2x(t) $$ And I have to find impulse response (...
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FFT spectre graph measurements y-axis

I am very new to this things. Sorry for probably stupid question. I don't understand what units and meaning have the values on Y-axis of Fourier Transform graph? On X-axis it is Frequency (Hz). Pretty ...
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Need an Identity for CTFT Polynomial Raised to an Exponent

I need to the find the inverse continuous time Fourier transform for unitary angular frequency of the following signal: $e^{a\omega^2 - b\omega + c}$ where $a$ and $b$ and $c$ are real numbers and I ...
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Choice of Gaussian kernel parameters when lowpass filtering before image resampling?

I need to decimate a signal by a factor of q. More specifically my signal is a 3D "image": $\ I(x_i,y_j,z_k)$, which I need to downsample by a factor of two in the z direction. I want to do lowpass ...
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Use fourier transform to calculate image pixelation coef in python

I want to calculate a coef of image pixelation to remove bad pictures from a bunch of files. Some pictures results from bad compression and we can see a lot of pixelation on them like img a here: ...
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Calculating the system output using frequency response

Given an input signal $$x(n)=\cos(6\pi n +\frac{\pi}{6})$$ and system $$y(n)=0.5x(n)-0.1x(n-1)$$. In this case, the coefficients of the difference equation are $a_0=1$, $b_0=0.5$, and $b_1=$. The ...
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length of window and overlap rate in STFT

I want to use STFT to analyze my signal and am wondering what are differences between two solutions: Use short windows (for ex. 256 samples window) Use longer windows (to get higher resolution in ...
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1answer
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Interpreting the inverse fourier transform from a graph

I'm given a graph of the fourier transform of some function $x(t)$. The graph is labelled $F(X(\frac{\omega}{\pi}))$ on the y-axis and $\frac{\omega}{\pi}$ on the x-axis. The graph is plotted only ...
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What's wrong with this code for tomographic reconstruction by the Fourier method?

I've been playing around with tomographic reconstruction algorithms recently. I already have nice working implementations of FBP, ART, a SIRT/SART-like iterative scheme and even using straight linear ...
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FFT, How to decide if there is a signal among noise?

I have sets of data of different deep sky objects. My job is to check for any periodicity. I use IDL to run an FFT and wavelet methods to check for a signal. To test my code I ran the IDL built in ...
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1answer
715 views

What features describe audio signals? (Besides frequency and amplitude)

I recorded sounds with a microphone and I try to distinguish them in my Java program. The frequency works quite good, but if I look at the fourier transforms it seems like there should be more ...
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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: ...
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151 views

Techniques to deriving DTFTs

Are there general techniques to derive DTFTs? Given a bandlimited function $x(t)$, how do I find $$X(\omega)=\sum_{n=-\infty}^\infty x[n]e^{-i\omega n}$$ Generally, it is easier to derive the ...
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Variance of periodogram estimate of the power spectrum

I have been reading chapter 13.4. ("Power Spectrum Estimation Using the FFT") of the Numerical Recipies Book. Some things related to the expectation value of the "periodogram estimate of the power ...
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How can I use the fourier transform of a sequence of x-ray scan images to segment it?

Sorry if this question seems to trivial, but I am a bit of a novice when it comes to signal and image processing and I need some guidance. I have a 3D stack of about 256 grey scale images, each ...
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Signal Reconstruction after fourier transform

I'm working from an example posted here. I understand the steps to acquire the fourier transform and can clearly see the spikes at normalized frequencies at 15 and 40 Hz from the 0-centered ...
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periodic spectrum?

I'm relatively new to signal processing, so please excuse me if this is a trivial question. Why is the spectrum of a frame of speech samples periodic? What is the meaning of a periodic spectrum? And ...
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Intuition behind the scaling property of Fourier Transforms

The Fourier transform of $f(ax)$ is $\frac{1}{|a|}F(\frac{u}{|a|})$. So the frequencies are scaled horizontally but the magnitudes are also scaled when the graph of $f$ is scaled horizontally. On the ...
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Why Do I Get This Crackling Noise on Zeroing out the High Frequencies?

I recently started playing with the Fourier transform (after spending a few weeks learning about the mathematics behind it). I decided to try hacking together a low-pass filter on the following sound ...
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Can edge detection be done in the frequency domain?

Can we take advantage of the fact that high frequency components in the FFT of an image generally correspond to edges, to implement an edge detection algorithm in the fourier domain? I did try ...