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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Derivation of Nyquist Frequency and Sampling Theorem [closed]

I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
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How to compute the Fourier Transform of this ramp-like signal?

I have the following signal: and this as the solution to the problem: $$\begin{align} X(j\omega) &= \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \\ &= \int_0^\tau \frac{E}{\tau}t\; e^{-j\...
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38 views

How do I obtain the fourier series coefficients for a signal obtained by multiplication of two signals of different frequency?

What i assume here is that LCM of time periods of the two taken signals exist that is signals periods are not like pi/2 and 1 but are rather like 1 and 2 (just an example) I am given fourier series ...
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49 views

Sampling of frequency response

Let's consider any physical quantity depending on the frequency. For example, the impedance of a certain electrical component: $Z(f)$. Now, imagine to measure it in a continuous interval of ...
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1answer
661 views

PDF of a sum of two RVs by convolution of their samples via fourier transform in Excel

I apologies if this is off topic for this site, but I am trying to figure out (and not having much luck) how to get an empirical distribution function of a sum of two random variables given two ...
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1answer
24k views

Why Fourier series and transform of a square wave are different?

Here is a square-wave presented by Fourier series perspective: Above coefficients shows that a square-wave is composed of only its odd harmonics. But here below a square-wave is presented by ...
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1answer
258 views

Fourier transform properties. Spectral density function [closed]

I have the following signal for which amplitude and phase spectrums have to be computed: This exercise also has a solution which begins by deriving the signal twice. Next, they say the spectral ...
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2answers
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Getting bpm of song with fft [duplicate]

I would like to get the bpm of a song analyzing the spectrum of the volume. Doing a fft what I get is a peak at the origin and of course that can't be the frequency corresponding to the bpm, so I do ...
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77 views

Spectral structure of sinusoidal model

Let us consider the following code: ...
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1answer
39 views

Effect of Nyquist frequency on Fourier transformed data

Upper plot is the original data's plot, and the bottom plot is Fourier transformed data. For the bottom plot, x-axis is the frequency and y-axis is the amplitude. I don't understand the weird behavior ...
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1answer
32 views

How to get descrete fourier tarnsfom [closed]

Could anyone explain me please how to produce descrete fourier transform of such signal? There are no anymore information besides the picture in this task.
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71 views

Properties of DTFT to Infer the Inverse DTFT of Altered Data [closed]

Given a signal $ x \left[ n \right] $ and its DTFT $ X \left( {e}^{j \omega} \right) $. Which property of the DTFT allows you to easily compute the inverse DTFT of $ \frac{4 X \left( {e}^{j \omega} \...
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322 views

How to calculate multiplication of two discrete series

Short version: How to multiply two discrete sequences? Long version: Convolution of two discrete sequences is weighted sum. For instance, convolution of two sequences: ...
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1answer
122 views

Plotting a sampled signals DTFT using its CTFT

So I know the connection between the DTFT and the CTFT is the following: Where the left-hand side is the discrete time fourier transform. I need to choose a sampling rate which won't cause any ...
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3answers
314 views

What is the physical meaning of Fourier Transform having only $\delta(\omega)$ functions?

While calculating the Fourier Transform of the signal $$x(t) = 1 + \cos(6 \pi t + \pi/8)$$ I found that its Fourier Transform is purely in terms of Dirac Delta $\delta(\omega)$, that is its transform ...
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Does anyone can help me with signal processing problem?

(c)A linear time-invariant system with impulse response $h(t)=e^{-\alpha t} u(t)$ is driven by the input $x(t)=e^{-\beta t} u(t)$ . It is assumed that $\alpha, \beta > 0$. (i) Using ...
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1answer
705 views

Given a discrete signal, how to get bandwidth and duration under MATLAB?

Is there any kind of built-in function or formula that I can use to conveniently compute the (effective) bandwidth and (effective) duration of a given digital signal with known sampling frequency?
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2answers
391 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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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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1answer
115 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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125 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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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
167 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
309 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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81 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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1answer
108 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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1answer
90 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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218 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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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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210 views

What Are the Suggested Resources for Extensive Knowledge About the Fourier Transform (DFT, FFT, etc…)? [closed]

I would like to improve my knowledge about Fourier Transform related subjects. What are the recommended resources in order to self study about it?
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How do I decide which frequencies are signal and which are noise?

I have an arbitrary recorded digial signal, on which I have run a Fourier transform. I'm not sure what conventions are on a case like this, but I have 1024 frequency bins. Second bin is the highest ...
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1answer
471 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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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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1answer
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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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1answer
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
271 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
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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
831 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
272 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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2answers
341 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
114 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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1answer
624 views

How to calculate IDFT this signal? [closed]

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