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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381 views

Need to learn wavelet, suggest steps and resources [closed]

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and Orthonormality – ...
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0answers
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Do not understand spectrogram of signal created from many sines with different frequencies

I get this spectrogram From the following code: ...
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1answer
52 views

Quite confused with Fourier Analysis results

So I'm meant to show how the DFT can find the frequencies, and respective amplitudes, associated to some data. And I have this data set from the curve $$ f(t) = 1 + 2\cos(2\pi t) + 4\cos(4\pi t) $$ ...
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130 views

Why do we need the power spectral density?

Since the power spectral density is just the squared of the fourier transform, why is it useful ? Can't I just replace every solution that requires the psd with the fourier transform ?
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98 views

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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110 views

Meaning of transform's area - Fourier

What is the graphic meaning of the transform's area? $$\int_{-\infty}^{+\infty}{X(f)df}$$ Where $X(f)$ is the continuous Fourier transform of the signal $x(t)$. Thank you very much.
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75 views

Is it mathematically possible to compute Fourier transform without comparing the signal?

If I'm correct, Fourier transform lets me know the magnitude and phase of any given frequency in a signal. I have a sampled signal and I want to compute its Fourier transform (any frequency) without ...
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1answer
144 views

Cepstrum analysis - Cut off frequencies displayed

My inquiry is regarding the so called cepstrum analysis. By conducting some experiments, i have real time data at my disposal. The acquisition rate is 1600Hz. I wanted to try cepstrum analysis just ...
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1answer
69 views

Calculating phase only component of a signal in MATLAB

I am working in the field of digital signal processing. Recently I read a paper that tells about phase only component of a Signal. It is given that the phase only component is calculated as $r_{phase}=...
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3answers
275 views

Derivation of PSD of sampled bandlimited random process

When a bandlimited random process whose PSD \begin{equation} S(\omega) = \begin{cases} \frac{N_0}{2} & -10B<\omega<10B\\[2ex] 0 & \text{otherwise.} \end{cases} \end{equation} is ...
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344 views

Discreteness and periodicity in Fourier transform

Why discreteness in time / frequency domain dictates periodicity in the other frequency / time domian? For example the DTFT is perodic in frequency? Why it doesn't contain all the frequencies? Why ...
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78 views

Trouble understanding discrete Fourier Transform

In the paper Calculation of a constant Q spectral transform - J.C.Brown it is mentioned The conventional linear frequency representation given by the discrete Fourier transform gives rise to a ...
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100 views

Exact formula for alias of Discrete Fourier transform for periodic sigals

Suppose that $f(t): \mathbb{R} \to \mathbb{C}$ is a $T$-periodic signal, with highest frequency $f_h$. Now suppose that our sampling rate frequency is lower than $f_h$, and is not any multiples of $1/...
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61 views

How is the decay of a signal exemplified in a Fourier Transform?

Is there any way to tell if a signal is decaying from its fourier transform?
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178 views

How to implement Cross Spectral Density [duplicate]

I am writing a program to compute the cross spectral density of an image, and a template image, which is the image I am trying to find in other image. Reading wiki1,wiki2,wiki3 from wikipedia, and ...
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194 views

Is it possible for a signal to be represented by *both* sinusoidal *and* rectangular/triangular Fourier transforms?

A signal might have both continuous and discrete parts (where the "discrete" parts are regions where a sinusoidal Fourier transform would be subject to unnecessary Gibbs Noise). So I would think that ...
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452 views

In Fourier transforms, can momentum space be analogized to frequency, and position space be analogized to wavelength?

We know that in quantum mechanics, momentum space is the fourier transform of position space (and vice versa) And also, in time-series analysis, that frequency (of cycles) is the fourier transform of ...
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2k views

Aliasing after downsampling [duplicate]

Let me start with time domain representation of the original signal \begin{equation} x_n=\sum_{k=0}^{2N-1}X_ke^{j\frac{2\pi nk}{2N}} \end{equation} where $2N$ is number of time/frequency samples ...
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What happens to the fourier transform of sample result of $30kHz$ sinusoidal signal when sampled with sample frequency $44.1KHz$?

As the title says,w hat happens to the fourier transform of the sample output of $30KHz$ when sampled with sample frequency $44.1KHz$? I do not get how alias can appear, because fourier transform of ...
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45 views

Is the following property true?

I was looking at a solution of a Fourier Transform question and following property was used, if: $$ x(t)\rightarrow X(jw) $$ then: $$ e^{jw_ot}x(t)\rightarrow X(j(w-w_0)) ...
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1answer
120 views

Confusion related to DFT in a paper [closed]

I was reading a paper related to privacy where they perform fourier transformation of a time series data and retain few coefficients of the FFT. Then they apply some noise to these coefficients. These ...
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1answer
204 views

Finite moving average filter

I am trying to solve this problem but I need a lot of help. Below are my answers for the separate parts, please check and tell me where I am wrong because I am weak on the fundamental concepts of this....
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1answer
46 views

Find $X_s(f)$ of a sampled continuous signal

I've been trying to find the transform of the following signal, but have not been successful, any help would be greatly appreciated: Find $X_s(f)$ of the following signal the "mathematical DAC" ...
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1answer
798 views

Fourier Transform for speech signal [closed]

I need some clue on how to apply the Fourier transform to a wideband discrete signal like speech in Matlab. What I want to do is to apply the MUSIC algorithm to the speech recorded by a set of ...
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1answer
218 views

How Fourier decomposition is performed?

The Fourier decomposition explains a time series entirely as a weighted sum of sinusoidal functions and with the Fourier series,it is possible to do it. But I have some doubts Suppose ,for any ...
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250 views

Is there any optimised algorithm to calculate 2D fourier transform

I m trying to implement my own code for finding the 2D fourier transform of an image in MATLAB using the formula for it, but it take toooo much time to come up with the answer, is there a defined fast ...
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2answers
105 views

Convolution & FT properties

I have been trying hardly to check if these equalities are true or false. However, I have not been able to conclude anything. Could you help me, please? $$y[2n]=h[n]\star x[2n] $$ $$\mathfrak{F}(x[-...
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567 views

How to calculate IDFT this signal? [closed]

$X(jw) = 1 + \frac {jw+3}{jw+4}$ what is the IDFT of this signal?