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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What to do for the right FFT in Matlab (two peaks and incorrect amplitude)?

This is the FFT I'm using. But two peaks (did not expect the one in the beginning) are occurring and the amplitude is not as specified (expecting a value of 2). Any help is much appreciated! ...
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Why does the frequency in the DFT have to be an integer?

I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ...
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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, ...
32 views

Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
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I want to get impulse response of causal system

I want to get impulse response of this causal system on first photo. So I got frequency response on second photo from this system. and now I am trying to transform this frequency response to impulse ...
267 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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Graph signal processing

What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
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DFT (FFT) of a Real Even Function Doesn't Yield Real Only DFT Signal

There are a lot of similar questions already, but I can't find one answering this problem. I used the following MATLAB code to perform the FFT on a Lorentzian input signal ...
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Accuracy of time domain signal when one frequency is absent

Suppose the known frequency spectrum of a signal is: $$G(n\Delta f)=9,4,3,5,1,6,...$$ where $n=0,1,2...$ and $\Delta f=1$ Hz If, for some reason, we cannot sample $G$ at $n=0$ (i.e. $G(0)=9$ is not ...
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In a periodogram, why is the modulus squared of the DFT taken rather than the DFT itself? [duplicate]

Why can't you just take the DFT itself? And how accurate is this method in spectral density estimation? Are there cases in which it is very accurate?
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How to Calculate the number of DFTs taken in a STFT

Given variables of window size (W), overlap (O), and length of the Signal (S) (in my case, length of a song) and I am trying to determine an equation that gives me the number of DFTs that would be ...
299 views

Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
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STFT amplitude normalization, librosa library

So librosa.core.stft returns a complex single sided spectrogram. My question is: What normalization of the amplitude values should I perform afterwards? I believe I have to multiply the amplitude ...
109 views

Question about time shifting property

I know that time shifting property of discrete-time Fourier Transform states that $x[n]\leftrightarrow X(e^{j\omega})\implies x[n-n_0]\leftrightarrow e^{-j\omega n_0}X(e^{j\omega})$ So given a signal ...
196 views

Bandwidth of Information Signal

I have trouble finding the bandwidth of a signal. Say I have an info bearing signal m(t)=sinc(2t/pi). I found the fourier transform of the sinc function and found that the angular frequency was 1/pi. ...
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Discretization of Sinusoidal Signals

How do I should sample two continuous sinusoids of $f_1$=1/4 Hz and $f_2$=1/2 Hz at a 1 Hz rate? Can i recover both if i bandlimit after sampling at a 1/2 Hz limit?
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Should scipy.signal.coherence be 1 for single input and output signals?

I am trying to calculate the coherence between input and output signals. I thought I could work with a single input and a single output time series and calculate the coherence $\gamma^2$ between them. ...
257 views

Signal squared in time domain

In some publication I have found a formula that for some reason squares signal in time domain. I am analyzing it now. What should be the Fourier transform of a signal that was squared in time domain? ...
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CMV: COLA constraint is not necessary

In the literature on the short-time Fourier transform (STFT) it is often stated or implied that the constant overlap-add (COLA) constraint must be satisfied in order for the STFT to be invertible. ...
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Wikipedia equation for DFT seems to be bad?

I was writing a simple fourier transform implementation and looked at the DFT equation on wikipedia for reference, when I noticed that I was doing something differently, and after thinking about it ...
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Understanding Magnitude Spectrum of Images [closed]

I am facing problem in reading Fourier domain of a given image. I don't understand what to interpret from it. For instance, consider this image. Ok, so there is a dot in the middle, with some ...
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Why Derivative/Integration in time domain act as Highpass/Lowpass filter in frequency domain respectivly? [closed]

It is one of Fourier transform properties
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Demonstrate that $x(t)$ and $\hat{x}(t)$ are orthogonal

I have to demonstrate that a function $x(t)$ and his Hilbert's transform are orthogonal, it is said: $$\int^{\infty}_{-\infty} x(t) \cdot \hat{x}(t) dt = 0$$ I have tried the exercise using Parseval'...
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Why is the size of the output of the FFT of a signal is same as the size of the input signal?

I am kind of new to the DSP domain. I was trying to get the frequencies associated with a signal by performing FFT over it. I used numpy.fft.fft for this. ...
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Understanding where the constant $2/N$ comes from in Fourier transformation

I'm implementing Fourier transformation in my analysis and I wanted dig a bit deeper on the reasons why the absolute value of Fourier transformation is usually multiplied by the constant $2/N$ to get ...
240 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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Applications of Power Spectral Density [closed]

I have a class covering Power Spectral Density but I have no idea why it matters. Could someone provide some examples of its use? Thanks
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Fourier Transform Units

It is documented that 'one' of the units of the Fourier Transform [of $x(t)$ volt] is volt per Hz. That is $X(\omega)$ components will have units of volt per Hz, where $\omega$ is the angular ...
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Fast Fourier Transform MATLAB [duplicate]

I dont understand one thing when I use the function fft(x,N) in matlab, where x is the signal which I want to calculate the fourier transform and N is the number of samples. What I dont understant ...
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New to audio processing, why is my data so lopsided when I try to break into frequency ranges?

I have a wav file audio data, I broke it up into 1024-length windows (no overlap), and performed fft on each one. If I visualize this data it actually looks pretty good, but the problem is that the ...
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FFT - second and further divides and conquers - need help

​ ​Hello, I would like to ask you for help in understanding Fast Fourier Transform. Most articles about FFT describe a simple DFT example with N=8 number of samples. They divide it on half, to evens ...
310 views

Why look at power spectral density for stochastic processes?

I have been told that for deterministic signals, it makes sense to look at their respective Fourier transforms/spectra. For stochastic processes on the other hand, I am supposed to work with power ...
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Characteristic and moment generating function of a random variable interpretation

I have been studying about moments and cumulants of a random variable. Even though the definitions of characteristic and moments generating function are very similar (only the sign in the exponential ...
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Fourier Transform Signals - Time Transformations

I was going over some review problems and came across an interesting one. Using the techniques of (linearity, time shifting, and time scaling) what are some approaches I could use to turn the ...
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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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Why edge sharpening produces high frequency?

I have a low-resolution image in which the high frequencies are missing. When I apply an edge sharpening filter some of the missed high frequency is recovered. I am wondering why this edge sharpening ...