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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Which frequency bins give the best interpolation for the derivative of a function?

A function $u:[0,2\pi]\to\mathbb R$ sampled over $N$ equidistant points $\theta_j=(2\pi/N)j,\, j = 0, \dots, N-1,$ can be interpolated by a set of functions $\{u_{k_0}\}$ enumerated by integers $k_0\...
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49 views

Fourier Transform of finite time series

I have some signal 𝑠(𝑑) which is real data i.e. finite. The time runs from βˆ’π‘‡ to +𝑇. The signal amplitude is large at 𝑑=0 and small (β†’0) at the ±𝑇 limits. I can do a finite (discrete) Fourier ...
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46 views

What is the form of the spectral derivative in the all-positive-frequency notation in DFT?

The Discrete Fourier Transform (DFT) of a function $u:[0,2\pi] \to \mathbb R$ sampled over $N$ equidistant points $\theta_j = 2\pi j/N,\, j = 0, \dots, N-1,$ is defined by $$ \tilde U_k = \frac1N \...
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43 views

Solving equation with convolution

I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$: $$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$ where $\ast$ is the convolution. I know $A(f)$, $B(f)$,...
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30 views

FFT freqency bin center in R

I'm trying to do a spectral analysis in R. I learned it in Python from Allen Downey's ThinkDSP book. What is the R equivalent of the Python numpy function, numpy.fft.fftfreq? If you provide a window ...
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48 views

How does one interpret an element of the “transfer matrix” used to calculate frequency domain granger causality (via VAR models)?

I am attempting to gain a better mathematical understanding for how autoregressive models can be used to infer frequency-domain granger causality. All freq. domain measures of causality that utilize ...
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62 views

Frequency Domain Signal to Noise Ratio

I am doing some research on low-cost air pollution sensors. I'm measuring the "ground truth" with a single low-noise sensor, and I'm trying to use it to calibrate a low-cost sensor that has high noise....
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57 views

How do I make sense of the cosine wave having Fourier Transform coefficients which have infinite magnitude?

To illustrate my question better, consider the Fourier Transform of an aperiodic (as a periodic cosine wave has a Fourier Transform not Fourier Series) cosine wave $$f(x) = \begin{cases} \cos(2\pi ...
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52 views

How to find a Matched Filter Transfer Function from large signal sample

Lets say I have a system where I have a small sample of a signal with no noise $\hat{x}(t)$ and a lot of a similar signal with noise $y(t) = \hat{x}(t) + n(t)$, and from $\hat{x}(t)$ I want to create ...
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25 views

How to search for irregular signals: Fourier, DWT or k-means?

See my notebook here I want to search for irregular time signals in a data set of ~3 500 000 time signals. By eyeballing I have found hundreds of flat and oscillating signals, but just a few that are ...
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29 views

How can I relate my amplitude from a FTT to the actual signal?

Sorry for disturb you guys, I've been playing with this the last days. I am computing signals of a wave produced with a wavemaker. Cause I have several sensors (wave gauges) I am sensing the same wave ...
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49 views

Is the whole data needed for the fast fourier transform with an ongoing signal?

I sample an signal with around 840k values a second, to check the spectrum around <400kHz. But i can't save the whole data as it is just to much for my microcontroller. I know that for the ...
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42 views

Graph Fourier transform: the adjoint notation for the eigenbasis matrix

I already asked this question here but there is no response. I'd like to ask this question in signal processing domain. It is well-known that for a real symmetric matrix $L$ (here, graph ...
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56 views

What is the significance of y-axis in Lomb-Scargle Periodogram?

What does the y-axis of Lomb-Scargle periodogram represent? Periodogram obtained by Fourier transform contains information about the original data's amplitude, but the so-called "Lomb-Scargle power" ...
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61 views

Proof that DFT does not require more than N points

I'm trying to show how the discrete Fourier transform (DFT) arises from the equation for the continuous-time Fourier Transform. I've run into an interesting caveat which I can't seem to find an ...
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63 views

Is it possible to extract peak locations in the time domain using help from fourier/wavelet analysis?

The signal I'm studying has fundamental frequencies of 20 and 60 cycles per minute (shown in the Periodogram graph). It is straight forward to extract the peaks in the time domain belonging to the 20 ...
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22 views

Detecting changes in signal due to server delay

I'm currently working on an application that can be used to determine when a signal changes due to a server delay. Essentially, I have an API that is used to output data to a UI. However, for reasons ...
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69 views

Python FFT outptut

I have a (real) array of data and am trying to analyze its frequency components. I've been using NumPy's FFT routines, but I realized there is something I don't quite understand: why does the output ...
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229 views

Plot Frequency Spectrum of Binary Sequence in Matlab

I am new to Matlab and I am trying to implement a section of a published paper, the basic idea of the part that i am implementing is to show the frequency spectrum of camera aperture. The shutter ...
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124 views

Matlab FFT not producing symmetric spectrum

I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset. ...
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59 views

Using MATLAB to plot the input and the magnitude spectrum of the signal

I have an aperiodic signal $v_{out} = e^{-t} u(t)$ (real exponential signal) from discharging capacitor. I was trying to plot using MATLAB 15 seconds of this signal in time domain? I am thinking how ...
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106 views

Finding n Amplitudes by DFT, what is correct normalization

Please forgive me if this has already been asked. Let us assume an example with $x(t) = \sum_{i=1}^N A_i \sin(2\pi f_i t) $ under a given sampling frequency $f_s$, frequencies $\omega_i$ and ...
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37 views

Is there a way to find a picture inside another picture, using only 2D Fourier Transforms of both images?

Can Fourier Transforms of both images tell anything about "likeliness" of two pictures? If yes, how precise? Can it still work if only several pixels are different or can it tell they are same if one ...
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42 views

Wide-Band Lorentzian FDTD Algorithm

I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $g_i(f_i)$ ($f$ is for frequency) or $g_i(\lambda_i)$, into $\tilde g(t)$ for ...
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121 views

Reducing noise on several Transfer Function measurements

INTRODUCTION I want to obtain the transfer function of certain system (a ground "path", in this case) using an impact hammer for the excitation and one accelerometer (measuring vertical direction ...
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56 views

Scipy Welch's gives different first element

I've re-implemented Welch's method and want to compare it to scipy.signal.welch. However, the first two and last elements of the resulting array are different. My ...
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37 views

Voice classification

I'm working to prepare research article for my project. While preparing for it, I've gone through the topics like Gaussian mixture model and Fourier transform for voice classification problems. I've ...
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120 views

Performing inverse DFT after taking conjugate of the result of DFT

The following is a question I got in my school assignment. Pick an image and follow the operations Multiply image by (βˆ’1)x+y. Compute the DFT. Take the complex conjugate of the ...
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54 views

Lowpass-filter necessary before DFT?

I'm trying to distinguish eletrical engines by the magnetic field they create. I have no idea whether this is a smart idea, it's possible at all, whatsoever. However it brought me to a basic question ...
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1answer
129 views

Distortion in sound after multiplying frequency spectrum by constant

I make a simple sound equalizer that operates in frequency domain and lets user to adjust frequencies in sound by using 4 sliders. The first one responsible for 0 - 5kHz, the fourth one for 15-20kHz. ...
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231 views

Mirrored Spectrogram Mp3

First of all sorry if this is a stupid question, but I am an absolute beginner in this field and have been trying for days now. I'm working on a java program that uses fft to analyze audio files. To ...
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322 views

Finding the Period of a Signal by Its DTFT Data

find period of DTFTs where vertical lines represent Dirac deltas
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2answers
436 views

Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
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70 views

how to guess what the interference source it could be

At work, we are in an industrial area, and there is always a signal that I receive inside my office which interferences with my tests. This signal is in the 433 MHz and when I see the spectrum, ...
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348 views

PHAT filtering for cross-correlation yields wrong results while simple cross-correlation does OK (Python)

I work with two signals, the second being perfectly delayed and attenuated, with no reverberation. I implemented cross-correlation algorithm, which yields me these results: Here is my code for these ...
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88 views

Find cepstrum of a function with dirac function

$$x[n] = d[n] + a\cdot d[n βˆ’ N_p]\ ,\ \ |a| < 1$$ I need the complex and real cepstrum of this function as well as what would happen for $N=N_p/6$ for the DFT approximation $$x_p[n] = \frac{1}{N} ...
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353 views

output shape of STFT

I cant figure out why our output image is 257 * 32 , 32 I know why , but 257 I cant understand ? this is the exact word of this paper wich applied STFT on 3 channel of eeg signal : Short time Fourier ...
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3answers
2k views

Correct magnitude spectra of a cosine DFT?

I've just started my course on DSP and haven't laid my hands on MATLAB yet. I was wondering if the plot of the magnitude spectra was correct for the below shown $x(n)$:
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176 views

Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals

If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away? Suppose we are given the ...
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317 views

Hilbert Spectrum vs. STFT

If I wanted to plot a spectrogram of a signal, I would by default use the Short Time Fourier Transform. However, the Hilbert transform does something similar: it lets us calculate instantaneous ...
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1answer
276 views

Phantom harmonics when using cosine windows why do they appear and how to avoid them?

Given an L order cosine window, it is possible to show that the width of the main lobe is given by: $$\omega_w = \frac{2 \pi L}{(2N+1)}$$ Where $L$ is the order of the window, $N$ is the maximum ...
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261 views

Convolving with the frequency response of a filter

With scipy I can use signal.butter and signal.lfilter on a time signal. Performing a Fourier ...
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1answer
478 views

Why the energy is a good feature extraction for detect disturbances in signal processing?

To detect disturbances in signal processing a common step is to extract signal characteristics to analyze them, among these characteristics it is recommended to use the signal energy. Why energy is ...
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96 views

DTFT of $ f[k] = 3^k u(-k-1)$

Find the Discrete-time Fourier transform of $ f[k] = 3^k u(-k-1)$ (then sketch it and find its magnitude & angle). It doesn't fit any templates on the Fourier table, and I don't see how one ...
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40 views

Reduce impact of outliners for frequency analysis by increasing signal length?

I am working on a project to detect drivers drowsiness with EEG signals. I am using the frequency values retrieved by FFT. I have some outliners (artifacts) in my signals, which I don't want to remove ...
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503 views

Time-dependent Fourier Transform (TDFT)?

In my DSP course we are learning right now about the Time-dependent Fourier Transform (TDFT), but I can't find any information about it online. My professor said that it is similar to the Short-time ...
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261 views

FFT in different coordinate systems

Is there a transformation that will enable one to calculate the FFT in an arbitrary coordinate system? What I am interested is the following two cases: The space is Euclidean and infinitely ...
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54 views

Numerical Fourier transform for exact frequency

Mathematically, suppose I have a function $f(t)=\sum_k c_k e^{-i \omega_kt}$, where $\omega_k$ may not fall in $[0,2\pi]$. With an analytical Fourier transform, I can get a sum of delta functions ...
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112 views

Confusion in understanding the Proof of DTFT

While understanding the proof of DTFT from Signals and Systems by Oppenheim, I have confusion in understanding few steps. $$ x'[n]=\sum_ {k=<N>} a_ke^{jk(2\pi/N)n}$$ $$ a_k= \frac{1}{N} \sum_ {...
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231 views

Image processing: High pass filter to remove lowest 16 frequencies

How can I remove the lowest n frequencies of an image? Are the lower frequencies around the centre of the FFT result?