# Questions tagged [fft]

The fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse.

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25 views

### Harmonics below oscillation frequency in the brain

Apologies if this question is trivial, I'm a neuroscientist and would hugely appreciate your help to correctly interpret my analysis. I am recording EEG signals and am manipulating the brain using ...
86 views

### MATLAB: Applying Inverse Fast Fourier Transform to an array of real numbers

I'm trying to understand the difference between applying the Discrete Cosine Transform (DCT) and the Inverse Discrete Fourier Transform (IDFT) to the log Mel-filterbank energies as explained in the ...
54 views

### Torque signal fft

I have the following torque signal picked up with a 10.240Hz sampling rate from a testbench. I am studying its fft which I create on Octave with the following code: ...
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### A Delay Between Two Filtered Chaotic Signals

it is a common practice to use a shift of cross-correlation peak to evaluate a group time delay of two signals (chaotic signals are included). Can one synchronously and equally filter these chaotic ...
98 views

### Getting back the original x axis after IFFT-FFT in Python

I have an analitically generated spectrum $I(\omega)$, x axis represents angular frequency, y represents intensity. The spectrum is centered around some frequency value, which is often called central ...
41 views

### Can the (point-wise) multiplication of two discrete band-limited functions be inherently aliased?

I'm not fully used to the language of DSP, so forgive me if I confuse some of the notation, or if the below is trivial. I'm interested in the case where we want to do the point-wise multiplication ...
65 views

### Why are FFT numbers so high?

My input numbers are close to 10, here is a sample of some: ...
45 views

### Frequency domain multiplication

I am confused why zero-padding in the frequency domain does not result in linear convolution in the time-domain using the relationship: $$corr(a,b) = ifft(fft(a) fft(b))$$ See my process below for ...
36 views

### performing cwt and inverse cwt using fft

I'm currently working on my project related to implementing an speech enhancement algorithm on fpga which uses continuous wavelet with morel wavelet, how can i use efficient fft algorithm to calculate ...
126 views

### how I can use the FFT data to compute the convolution?

First,I have a vector A of length N,through process ...
514 views

### Difference between bandpass filter and using fast fourier transform to extract power of frequency bands

In signal processing, I have heard of two terms: Using band-pass filter to extract some frequency bands. Using Discrete/Fast Fourier Transform (DFT/FFT) to extract some frequency bands. Are these ...
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### Extracting different frequency bands (alpha, beta, gamma) from brain activity data

I am new to signal processing and despite googling about my question, I still couldn't find the solution. I have an Electrocorticography (ECoG) dataset. This consists of recording brain activity from ...
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### Why does spectral accuracy of laplacian decrease with sampling size?

We know that for any real-valued function $f(x,y,z)$ whose Fourier transform is $\mathcal F[f]$, its laplacian can be computed from a spectral interpolant as follows.  \Delta f(x,y,z) \simeq \sum_{...
275 views

### Discrete Cosine Transform (DCT) Coefficient Distribution

I have two images : Original Image Binarize Image I have applied Discrete Cosine Transform to the two images by dividing the 256x256 image into 8x8 blocks. After, I want to compare their DCT ...
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### Image Transformation Functions to Identify if the Text in the Document Originally There or Just Synthetically Overlaid

I have a copy of scanned ancient dirty document and synthetically generated ancient dirty documents. I want to use Discrete Cosine Transform to characterize noise types existing in the document and ...
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### What is the correct input format to perform IFFT on a spectrum?

Say I have response of a band pass $\left(f_1-f_2\right)$ or a lowpass filter $\left(0-f\right)$ and if I want to estimate filter length then I may take the inverse transform of the frequency response ...
33 views

### Acceleometer Noise and FFT

Background: I'm fairly new to signal processing and sensors, etc. I'm working on my thesis, which involves the use of an MEMS acceleration sensor as a vibration measuring device (for rotating ...
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### Discrete-time system: getting the true frequency from normalized frequency

Lеt's say that i have a plot where i can see the spectrum of some discrete signal and let's say that it's x axis is normalized (by normalized i mean $\omega/\pi$ on the $x$ axis). Now, i know that in ...
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### Given a static time domain signal, why does the magnitude oscillate in the frequency domain after FFT?

I'm trying to: Generate a sine wave in the time domain (locally within my program at 500 Hz). Analyze it with FFT Print the results in the frequency domain. The expected results are that since the ...
39 views

### Output shape of numpy's rfft function

For numpy's rfft function, the length of the output is about half of N, the length of the input sequence. What is the reason behind this? What are the frequency bins?
78 views

### Phase shifting in frequency domain

I am aware this topic has already been addressed in at least one question here, but despite that I could not find the solution to my problem. Also bear patience with me since I am not a mathematics ...
111 views

### Fast Fourier Transform for varying period (Order analysis)

I am trying to do a fast Fourier transformation on accelerometer data from a shaft rotating at varying speed in Python. What I have done so far: 1: The original plot was in the time domain, and I ...
36 views

### Random 2D noise generated in spectrum domain always have maximum at (1,1)

I want to add a noise made of harmonic functions to my 2D matrix. I thought it could be made by adding random amplitudes to modes in Fourier domain. I keep Hermitian symmetry of the matrix so that the ...
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### How to classify audio files based on their ZCR, energy, and enthropy of energy features?

Let's say I wanna classify the audio files of race car exhaust and normal car exhaust. I attain few features such as ZCR, energy and enthropy of energy from the training set and I wanna build the ...
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### Phase Difference offset when measuring phase difference between different FFT bins

In application where two sensors are used to calculate the phase difference of the incoming signal, what is the the phase difference offset which should be added when taking phase difference from ...
50 views

### Autocorrelation to diagnose faults

I'm attending a very practical course on signals and i have some doubts, i hope to receive answers in layman terms. 1) My prof said i can use the autocorrelation of the output of a process to ...
65 views

### Removing DC Offset (via removing mean) of input and output signals affects their coherence

I have input $x$ and output $y$ signals (fs=10 Hz, length N=10800). I have removed DC offset via the following equation: $x_{normalized} = 100 \frac{(x-\bar x)} {\bar x }$ where $\bar x$ is the mean ...
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### For SNR calculation, should I use FFT|X+iY| or FFT|R|?

I use a demodulator that outputs X and Y quadratures, with the R and Phase which can be calculated. For SNR measurements, when plotting the FFT to find the SNR a signal at a certain frequency, ...
232 views

### Use of Tukey window and its effect on a graph

I am trying to minimise the noise in a spectrum of a variable. I am trying to to divide the time history in equal parts, to do the FFT of this time history parts and to do an average between these fft....
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### Zero padding in frequency domain, any tricks to speedup?

there are many situations when one has to carry some operations on spectra, like splitting a spectrum Z wide in two Z/2 spectra, or vice versa merging two Z sized spectra in a 2Z sized one. The only ...
52 views

### Understanding outputs of image Fourier Transform in Numpy

I am trying to understand the meaning of FFT outputs with respect to images. Take a look at the following example: ...
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### Spectral filtering

I am working with a STFT spectral processing toolkit I wrote in C, now focusing on a module for spectral filtering. In its first implementation, the module simply multiplied an user drawn spectral ...
148 views

### How to detect overlapping peaks in FFT?

I am working with a modular spectral processing STFT toolkit I have written in C. I often need to carry spectral peak detection and analisys (frequency estimation, peak displacement, etc) but I am ...
128 views

### How to manually implement convolution with FFTs?

I'm trying to manually implement a convolution using FFTs and it isn't working as expected. I know I'm probably missing some subtlety with padding, shifting, or conjugation, (all of which I've tried ...
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### Different representations of frequency space of 2D image FFT

I'm learning images processing using FFT. In my test example provided below the input pixel values are clamped 0-1 (0-255), but I do eventually want to process floating point heightfield pixel values....