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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Fast Fourier Transform and Clustering of Time Series

I'm making a project connected with identifying dynamic of sales. That's how the piece of my database looks like: There are free columns: Product - present the group of product Week - time since ...
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Why does the inverse fourier transform of a lowpass filter have complex components in matlab?

I am quite confused whether the following numerical differences i find are just severe round off errors made by matlab, or something i am doing wrong. The following happened when trying to see what a ...
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Determining Valid DTFT's

Are the following frequency domain signals valid DTFT's (Discrete Time Fourier Transforms)? Answer yes or no, and justify your answer. a) $X(\omega) = \omega + \pi$ b) $X(\omega) = i + \pi$ c) $X(\...
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discrete fourier transform in Matlab - theoretical confusion

I have a periodic term $V(x) = \sum_K \exp(iKx) V_K$ where $K =2\pi n/a$ where $a$ is the periodicity of the term and $n =0,1,2,3....$ Now I want to find the Fourier coefficient $V_K$ corresponding ...
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Suggestions for FFT based tools to analyze music - Preferably MATLAB/free software packages [closed]

I am interested in analyzing full length songs for general features of the track which are not otherwise apparent. For e.g., I want to look at various parts of the song with time-frequency plots/...
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Estimating and Improving the accuracy of fourier transform in the low frequency sector

I have a time series file which starts with 1 and then quickly tends to oscillating about 0.001. The time series has a resolution of 0.01s and has 10^6 sequential points starting from t=0. The goal is ...
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134 views

Fourier Transform & Convolution to get response - confused

in the past couple of years I've always been using Laplace transform for system responses, but today tried to do it with Fourier transform and failed. What am I doing wrong? If we have a signal $x(t) ...
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370 views

How is it possible to find the Fourier transform of unit impulse function?

Since Fourier transforms are applicable to only periodic functions, and unit impulse function{..0,0,1,0,0..} doesn't seem periodic, is this possible? Is it like we are considering unit impulse ...
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Covolution of DTFT [duplicate]

Possible Duplicate: Convolution and DTFT $x_1(n)=x_2(n)=1$ where $0 ≤ n ≤ N-1$ 1)The linear convolution of the signal gives a triangle how you write it in mathematical form? The DTFT of the ...
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42 views

The impact on the frequency of adding zero samples and non zero samples

Can someone give me a brief explanation of what is going on in here? I struggle to understand the full differences between the impact on the frequency of added zero samples and adding samples which ...
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750 views

How to understand FFT results of scipy.fftpack?

I calculated FFT for a speech wav-file using scipy.fftpack. How do I read (understand) the return of FFT? I have read that it supposed to be like so: y[0] is 0Hz loudness, y[1] is 1Hz loundess, ... y[...
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Problem designing a specific filter

I have the next problem. $H_{c1}(j\omega )$ is the ideal antialising filter and $H_{c2}(j\omega )$ is a real one. I'm asked to design $H(e^{j\Omega })$ so that $y[n]$ in the second diagram (the one ...
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175 views

Simulation of a pressure field developed by a song

Greetings! What I am doing: In short, I want to write a program that is fed a song as a wav file, and spits out an animated contour plot indicating the relative pressure/loudness/quantity indicating ...
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1answer
240 views

UWB radar to find heartbeat

I have a UWB radar that Im playing with. The problem is that my algorithms at the moment can clearly, reliably and validly pick up 1-2mm movements of a pendulum i've set up. However, when I use it on ...
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180 views

Basic Confusion About the DFT and Convolution

I am learning DSP (with Digital Images) and I have some elementary confusion about the convolution between two discrete periodic signals. Specifically, I have learnt that when filtering an image, we ...
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176 views

why $-$ sign in DTFT pair for constant

In discrete time Fourier transform, The DTFT of constant 1 is $$\sum_{l=-\infty}^{+\infty} \delta(\omega-2\pi l) $$. I have confusion that why there is $-$ sign, why it can't be $$\sum_{l=-\infty}^{+\...
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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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1answer
95 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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97 views

How to plot thermal noise in the “time domain”?

$P = 4kT$ (where $k$ = Boltzmann’s constant, and $T$ = temperature of the instrument ($K$)) And the mean voltage is thus, of course, $V^2/R = 4kT$ And the voltage is distributed as a Gaussian around ...
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1answer
108 views

How do I generate a smaller DFT result?

I have a very large input that I'm Fourier-transforming. Currently, I transform the entire signal and then downsample the result. Although the transform of the large input is expensive, my results ...
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2answers
74 views

Best approach for discarding the ends of convolution in FT

In a recent discussion Linear vs. Circular Convolution on avoiding circular convolution by FFT, it was shown that the FFT length for convolution purposes set should be = (data set 1)+ (data set 2) -1. ...
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72 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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901 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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267 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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80 views

Spectral structure of sinusoidal model

Let us consider the following code: ...
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2answers
128 views

How to get Spectrogram after fft in matlab?

I have many EEG signals which record at 100 Hz. I use FFT on them with fft Matlab toolbox. Now I wanted to get a Spectrogram. As I searched and read a lot, I figure that I should window my signal and ...
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1answer
47 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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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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686 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
252 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
433 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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91 views

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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808 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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417 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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On accurately computing continuous Fourier transfoms using FFT

Suppose I am given a bounded function $f$ with support on an interval $[0,A]$ and I want to compute the continuous Fourier transform $$\hat{f}(\omega_k) = \int_0^A f(t) e^{-i \omega_k t}\,dt, \quad k =...
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29 views

Why do we scale bins in FFT in this code?

Hi I am learning FFT I am confused about this bit of code: what is the reason for scaling the sampling frequency and what is bin scale and why and when do we use it? thank you ...
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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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140 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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173 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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80 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
209 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
73 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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359 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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88 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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110 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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113 views

Fourier series qn determine the fourier series coefficients

Can someone please help me with this Fourier series question: Determine the Fourier series coefficients of $x(t)$ given as $x(t) = > \cos4t +\sin8t+3$?
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141 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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263 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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195 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 ...