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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Fourier transform of an integrator filter

I have to find the Fourier transform , and $y(t)$ of an $ x(t) = e^{- \frac {t}{T} } u(t) $ that passes into a integrator filter. I know that $ Y(f) = X(f) H(f) $ so I first calculate the Fourier ...
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Does it make sense to apply convolution in the frequency dimension of a fourier transformed signal?

What I have is more likely a theoretical question. Since I am not from a signal processing background it is hard for me to grasp the issue in using convolution in the frequency dimension of a Fourier ...
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Duality Property for DFT

I was watching a youtube video for the duality property for continuous time Fourier transforms, which shows that if Fourier transform of $x(t)$ is $X(\omega)$ then Fourier transform of $X(t)$ is $2\pi ...
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Fourier Transform of a PSD and response of a PSD input

Does a Fourier Transform of a white noise exist? If so, what is its general form? It is possible to compute the fourier transform of a Power Spectral Density? My problem in detail. I have to compute ...
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How to interpret the window size and FFT size while performing FFT? [closed]

I have a discrete signal of length 98,000 samples and I am supposed to a FFT of the discrete signal with certain window size and FFT size. Can someone help me explain what is meant by the window and ...
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Proof of fourier transformation of multiplication of two signals

I've been trying to find a proof of the following, but still I m unable to proof it, can someone help me? $$ ℱ[x(t)g(t)] = \frac{1}{2\pi} [X(\omega)*G(\omega)] $$
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Understanding zero-phase filters

I'm reading the book "Digital Image Processing" by Gonzalez and Woods and I'm wondering how their definition of zero-phase-shift filter is equivalent to the one given here. "Digital Image Processing" ...
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1answer
93 views

DFT symmetry vs DFT duality in Richard Lyons' “Understanding DSP”

I am reading Richard lyons, understanding dsp, chap 3. Article 3.2 is about property of dft symmetry but any where in this chapter, i am unable to find discussion about dft duality property I want ...
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Find a LTI system such that $\mathcal{T}\{\frac{\sin t}{t}\} = \frac{\sin 2t}{t}$

Let $$x(t) = \frac{\sin t}{t} \qquad\text{and}\qquad y(t) = \frac{\sin 2t}{t}$$ Is it possible to find a LTI system such that $\mathcal{T}\{x(t)\} = y(t)$? If not, what's the reason for ...
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Zero-padding or Interpolation in 3D FFT

I'm trying to perform a FFT of a 3D regular grid and then compute the bin average (in spherical shell bins) of the Fourier transformed grid. The problem is that the resulted vector is very noisy as I'...
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Calculating Transfer function numerator and denominator from the rationalfit model

I have a frequency response data called 'AC_data' which is a vector of complex numbers (real and imaginary part) at different frequency points. I have calculated a rationalfit model for the AC_data ...
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Impulse response of a time scaling system

Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system? \begin{array}{l} X( \omega ) \ =\ \int ^{\infty }_{-\...
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What is the DFT of a binomial filter?

I hope this question is not too simple, I just started learning digital image processing. The 1D binomial filter of size 2 is defined by $B_2 = \frac{1}{4}\begin{bmatrix}1 & 2 & 1\end{bmatrix}$...
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Fourier transform of unit step

I was reading pdf by caltech and in one of its section, Fourier transform of Unit step signal is calculated but I am confused, how this can be possible if region of convergence for Laplace transform ($...
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Why can we have non-integer frequency bins in FFT?

I am studying DFT/FFT and I'm very confused about one thing. I read online that the frequencies we can sample with DFT must be integer (Why does the frequency in the DFT have to be an integer?). Later ...
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1answer
76 views

Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$

Find the Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$ I thought of making it to be a sinc, but at the bottom there is $n+3$ and if I replace $n+3$ then I don’t know how ...
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finding FL and FH from continuous time signal

I have a continuous signal $x_{a}$ which is defined as $X_{a}(F)=0$ for $|F|>B$. Now if I multiplied the continuous signal $x_{a}$ by $cos6\pi Bt$. Then the fourier transform of the signal can be ...
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Confusion regarding DFT calculation?

I am studying Richard lyon chap3 , article "Understanding the DFT equation " But i am bit confused how x(n) is calculated specially x(0) and x(1) because apparently x(n) is calculated by plugging ...
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58 views

Pitch shifting with bins creating large feedback

I am attempting to create a pitch correction algorithm. I started by performing a test. The test goes as such: Get WAV file Split it into bins of size n (512 in my case) Shift each bin by 2 semitones ...
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How to identify the frequencies of periodic peak signals in a noisy time series?

Suppose to have two time series with peak signals at different frequencies, like these two: ...
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38 views

Construct IFFT from only the major frequencies of an input signal?

I have data which when plotted looks like the green line in the below image. The data is from the walking-motion of a reinforcement-learning-model in a simulation and therefore the values do not ...
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2answers
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DFT without knowing the exact value of sampling rate?

I have a sequence of (real) numbers that represent the magnitude of a certain natural event. I know that the samples are equispaced in time, but not the exact value of the spacings. So does that mean ...
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Positive and negative frequencies in DFT due to frequency folding, or due to negatively indexed frequencies?

When I look for the cause of the mirroring of frequencies in DFT output, I get two types of explanations: The first one which says the frequencies are mirrored because of the complex exponential ...
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Cepstrum of white gaussian noise

What are the statistics of the cepstrum of gaussian white noise? \begin{align}\newcommand{\Nfft}{ {N_{\mathrm{FFT}} }}\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT} x_i &\sim \...
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64 point FFT Hamming window interpolated to 720-point sequences

Can someone here explain the meaning of, 64 point FFT Hamming window interpolated to 720-point sequences and its inverse? 720 point is from 0 to $2 \pi$ or (0 to 720 degree). I get the 64 point ...
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GSP as an extenstion of DSP

I am a PhD. in pure mathematics. Could you please illustrate the following statement: the eigenvectors of a graph Laplacian behave similarly to a Fourier basis, motivating the development of graph-...
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GSP as an extenstion of DSP

I am a PhD. in pure mathematics. Could you please illustrate the following statement: the eigenvectors of a graph Laplacian behave similarly to a Fourier basis, motivating the development of graph-...
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87 views

Is rotation of a Fourier transform the same thing as Fourier transform of a rotation?

I'm working on an image processing problem and wondering if DFT(rotation(image)) == rotation(DFT(image)) (1). My final goal is to apply rotations in the Fourier domain then do an inverse Fourier ...
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$2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal

please help me find the error in the following counter example. Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
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52 views

Calculating DCT in reversed vector

I'm doing an exercise in which I need to show that the DCT of $\tilde{x} = (x_{N-1}, x_{N-2}, ..., x_1, x_0) $, with $\tilde x_m = x_{N-m-1}$, is equal to $ \tilde{X}_k = (-1)^{k}X_{k}$, but I have ...
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Anti-Aliasing and the Fourier Transform, Gonzalez Digital Image Processing

In Gonzalez book Digital Image Processing, section 4.34 (third edition), he writes: Unfortunately, except for some special cases mentioned blow, aliasing is always present in sampled signals because, ...
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time scaling and shifting of cosine in Fourier transform

I've met some problems when calculating the Fourier transform of $\cos(at+b)$. I want to use the shifting and scaling properties to solve this problem. First, when I look up in the book and some ...
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Scipy.signal noise with rfft compared to fft

I'm trying to get the fourier transform of a signal with real values, however the results I get with rfft are noiser than those with fft. I wrote the following code: ...
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4answers
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Negative frequency in the Fourier Transform [duplicate]

Why use this instead of a positive frequency? I asked on the math forum but it just wasn't helpful. I understand the idea of a negative frequency is important in general since many real signals like ...
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53 views

STFT of ISTFT in the Griffin Lim Algorithm

The Griffin-Lim algorithm for phase recovery (based on the magnitude of an STFT) involves a step that is: STFT(Inverse STFT(...)). This seems to be the key iteration in the algorithm. This Quora ...
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How will magnitude and phase spectrum of an imaginary function would look like? Like if $x(t)=j \text{rect(t)}$. Is phase spectrum even or odd?

I am confused between when a phase spectrum is odd and when it is an even function of $\omega$(angular frequency, Fourier transform variable).
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Finding the frequency response $H(\omega)$ of a shifted sinc function

Given $$h[n]=\frac{\sin\left(\frac{\pi}{3}n-\frac{\pi}{3}\right)}{\pi n-\pi}\text,$$ use the table to find the frequency response $H(\omega)$. I don't have any clue that how to deal with the ...
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Rule of thumb / Best practice for Audio (voice) data normalization for use in Classification

TRIVIAL QUESTION: I am currently working with some audio data of speech utterances. I am attempting to perform classification on the data based on the phonemes. This means that I manually label the ...
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How to apply FT to real-life signal that labeled in seconds, not radians

In training examples we always do a transformation on signals which have t-scale in labeled in radians. I understand that Pi is just a number, but I still have some troubles to understanding how to ...
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Significance of steps involved in flipping process of an image?

The above image on the right was obtained by following steps Multiplying the image on the left by $(-1) ^ {(x+y)}$ Computing the DFT Taking the complex conjugate of the transform Computing the ...
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Why do we get different imaginary parts of a zero centered Gaussian for the the same number of data points N?

Suppose we have a total number N= 2048 points in a data and we wish to have zero centered Gaussian. There are two possibilities that we use the x-axis as ...
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Time domain to frequency domain conversion of audio signals to extract 1/3 octave frequencies

I am writing first time in this forum and I am not expert in programming and FFT. We have developed an android app (Noise Tracker) for noise measurement using smartphones. It displays noise levels in ...
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1answer
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Why is my fundamental frequency at the 15th harmonic order

I am trying to implement a code in MATLAB to show harmonic content and order in Matlab. my fundamental is supposed to be at harmonic order 1, however the ouput plot I am getting is wrong and I am ...
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Resources to understand DSP visually in 2020

I know you have been asked several times but the questions are old, and I would like to know if there are new intuitive web pages of applets or interactive DSP animations (Filters, FFT, Wavelets)
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FFT one-sided and Parseval theorem

I'm trying to get Parseval theorem working on a one-sided FFT. So far I have this code (matlab): ...
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Simplifying frequency response equation

I am trying to to find a magnitude and phase response of a FIR filter as in problem 5.18 Digital Signal Processing 4th Edition by John Proakis. I got the frequency response as: $$ H(\omega ) = 1 - e^{...
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non-consistent normalization problem in fft

I have a csv file of data sampled with Ts=1ns which looks like this: This signal is a step response of some system which responds to a step of value 1. I'm trying to get the impedance profile of the ...
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Validity of differentiation property of Fourier transform

we know the differentiation property of Fourier transform says that, if $$x(t)\longleftrightarrow X(j\omega)$$ then $$\dfrac{d}{dt}x(t)\longleftrightarrow j\omega X(j\omega)$$ We know that we can use ...
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Are there any difference between the FFT magnitude of a signal and average FFT magnitudes of the signal broken into multiple frames?

Suppose I calculate the FFT of a 5 seconds sound wave. If I'm only interested in the FFT magnitudes across frequencies, I should obtain the same result if I segmented the sound wave into five 1-second ...
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Where did the k of $a_k$ disappear from Fourier Reverse Transform if $\omega=\omega_0k$?

Where did the $k$ of $a_k$ disappear from Fourier Reverse Transform if $\omega=\omega_0k$? We turn $\omega0$ to be $d\omega$, but $\omega=\omega_0k$, so shouldn’t there be a $k$ in the reverse ...

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