Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

Filter by
Sorted by
Tagged with
-2
votes
1answer
25 views

Hand implementation of Fourier transform have small peaks unseen in Python package

I've implemented the basic version of discrete Fourier Transform and I'm testing it using a pure sinusoid. However, small bumps show up in addition to the large peak. I tried Numpy.fft for this and I ...
0
votes
2answers
53 views

Fourier transform properties

I have to find the Fourier transform of $$ x(t)= \frac{1}{T}e^{-\frac{t-T}{T}}u(t-T) $$ First I applied traslation property , so $$ F[x(t-T)] = X(f) e^{-i 2 \pi f T} $$ after I applied time scaling ...
5
votes
3answers
735 views

Spectral Leakage in layman's terms

I'm trying to understand the concept of spectral leakage for the DFT, without going deep to the mathematical intricacies (it's for practical purposes). I've read from the book "Introduction to Digital ...
0
votes
1answer
39 views

Autocorrelation to diagnose faults

I'm attending a very practical course on signals and i have some doubts, i hope to receive answers in layman terms. 1) My prof said i can use the autocorrelation of the output of a process to ...
0
votes
2answers
45 views

Finite sequence input to DTFT

i'm studying the practical utility of Fourier transforms and i have some questions. I hope to receive answers in layman terms. 1) Does the DTFT take only infinite input sequences? 2) If i apply the ...
0
votes
1answer
30 views

Aliasing and DTFT of a real signal

We are analyzing a real signal with the DTFT. Since we are using a limited number of samples it's like we are transforming a finite signal. As I remember, the FT of a finite signal has an infinite ...
0
votes
2answers
334 views

Why Is the DFT of a Signal Symmetric About Its Central Bin?

When i take an N point DFT of a signal, it comes out to be conjugate symmetric about the point N/2 . Could someone please tell how to understand this intuitively or mathematically ?
0
votes
1answer
36 views

Fourier transform of a noisy signal

Let's suppose i have a sensor that measures the output of a process and this cause a not negligible noise that affects my signal. My goal is to analyze the process signal in order to find faults. How ...
1
vote
1answer
22 views

Linearity and time-shifting of $\mathcal{F}\{0.8^n\cos(0.1πn)u[n]\}$

To preface, this is not a homework related question but purely for self-study purposes. Hi there, I try to calculate $\mathcal{F}\{0.8^n\cos(0.1πn)u[n]\}$ by using the properties of Discrete time ...
7
votes
3answers
1k views

Sense of zeropadding in a time domain

I have the task related to Radon transform which contains a subtask which uses resampling by means of DFT. Let's consider the non-periodical discretized signal (Fig.1) (for example the string of ...
3
votes
1answer
39 views

ROC of the function in the problem 9.14 of Oppenheim's Signals and Systems textbook

I have solved the problem 9.14 in Oppenheim's Signals and Systems textbook, but my solution and the one in Slader is different. Problem is given above. And Slader solution is here. I have also ...
0
votes
1answer
105 views

Distortion in sound after multiplying frequency spectrum by constant

I make a simple sound equalizer that operates in frequency domain and lets user to adjust frequencies in sound by using 4 sliders. The first one responsible for 0 - 5kHz, the fourth one for 15-20kHz. ...
0
votes
1answer
32 views

inverse discrete FFT in python, multiple times?

I was wondering what really happens when taking the inverse discrete FFT on some set of numbers, for 3 times? Because looking at it, it looks like we're getting an output that is identically with the ...
3
votes
1answer
72 views

Fourier coefficients of 1/(1+it)

I have to find the Fourier coefficients of $$ \frac{1}{1+ t^{2}} $$ I tried with $$ \frac{1}{T}\int_{0}^{T} \frac{1}{1+it}e^{-i 2 \pi f_0 T } $$ but I should do at least two integrals by parts , so I ...
1
vote
1answer
61 views

Fourier coefficients of odd and even part of a signal

I have this signal and I have to find the Fourier coefficients of the odd and even part. First I found that $$ x_p(t) = \frac{1}{2} ( x(t) + x(-t) ) $$ and I made the graphic of this part and I ...
9
votes
3answers
2k views

Implementation of Wikipedia Equation for the DFT

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 ...
1
vote
2answers
765 views

How to Match 2 Signals which Are a Shifted and Scaled Version of Each Other

I have 2 signals S1 and S2 that contain the same information, but S2 is shifted and scaled compared to S1 by an unknown amount (but small; eg shift would be of the order of 1-10 samples). What is the ...
0
votes
1answer
30 views

Different representations of frequency space of 2D image FFT

I'm learning images processing using FFT. In my test example provided below the input pixel values are clamped 0-1 (0-255), but I do eventually want to process floating point heightfield pixel values....
2
votes
2answers
59 views

Response of an ideal integrator to a cosine wave

It sounds like a very elementary question on system theory but I got quite confused about it, so hopefully you guys can enlighten me. I'm considering an ideal analog integrator, i.e., a system with ...
33
votes
7answers
5k views

What is the most lucid, intuitive explanation for the various FTs - CFT, DFT, DTFT and the Fourier Series?

Even after having studied these for quite sometime, I tend to forget [if I'm out of touch for a while] how they are related to each other and what each stands for [since they have such similar ...
0
votes
1answer
25 views

Fourier transform of $\sum_{n=-\infty}^\infty(-1)^n\delta(t-nT_0)$

Given $x(t)$ and $h(t)=\sum_{n=-\infty}^\infty(-1)^n\delta(t-nT_0)$, I have to compute $Y(f)$, where $y(t)=x(t)h(t)$. I have thought about using that, in this case, $Y(f)=X(f)*H(f)$. I know that $\...
0
votes
1answer
12 views

Frequency response of each component of a system given its global response

Given the following block diagram, find the frequency responses $H1(f)$ and $H2(f)$. The frequency response of the whole system has to be $H(f)=(\alpha_0+\alpha_1e^{-j2\pi T_1f}+\alpha_2e^{-j2\pi T_2f}...
0
votes
1answer
22 views

E of a signal using Rayleigh

I have to find The energy of a signal using Rayleigh th. the signal is $$ x(t) = A e^{-At } u(t) $$ assuming A>0 Using the classic definition of E , I found that it should be $$ \frac{A}{2} $$ Using ...
0
votes
1answer
56 views

Anyone explain to me this video?

I was watching a video in time 24:48 I would like to know where you got the value .9 (1.14z + .941) and 1.0232 + .757 Does anyone explain how he got those numbers?
2
votes
1answer
87 views

Frequency response of a system given its block diagram

Given the following block diagram, I am asked to find the frequency response $H(f)$ of the system. This is what I have done: The output of the first block is $j2\pi fX(f)$, and after going through $...
1
vote
1answer
2k views

Shift in Time Domain After DFT Based Convolution

To my understanding, multiplying a signal in the frequency-domain is equal to a convolution in the time-domain. I wrote a small python program, but i always end up with a shift in the time domain. ...
0
votes
4answers
85 views

Phase difference measurement of a signal sampled with two different sampling frequencies

I am working on phase interferometry for locating a transmitter. The direction of arrival of an incident wave can be estimated from the phase difference caused by the antenna separation as shown ...
0
votes
0answers
21 views

Fourier Transform of an acceleration signal containing engine orders

I am trying to understand how to evaluate this equation in the context of acceleration data which contain engine orders $a^{f_{e}^{crit}}(f)=\sum_{o}^{K}A^{o,f_{e}^{crit}}\mathscr{F}(cos(2\pi \cdot ...
0
votes
1answer
27 views

Fourier transformed acceleration from Fourier Transform of velocity and position using Omega arithmetic

Let's say the position of an object is given by simple sine function. By elementary calculus, I can calculate the acceleration in the time domain and find its Fourier transform. I can also calculate ...
4
votes
4answers
700 views

The Number of Sine and Cosine Waves in an $ N $ Point DFT

This is bound to be an embarrassingly simple question, but here it goes... I was reading the chapter on discrete Fourier transforms (DFT) of this really didactic online book, The Scientist and ...
3
votes
1answer
983 views

Calculate the Inverse DTFT of the DTFT Derivative in Terms of $ x \left[ n \right] $

Consider the signal $ x \left[ n \right] $ and its DTFT transform $ X \left( {e}^{j \omega} \right) $. Assume $ X \left( {e}^{j \omega} \right) $ is differentiable. What is the Inverse DTFT of: $$ j ...
1
vote
1answer
39 views

Why is DTFT of $e^{jn\omega_0}$ an impulse train?

update : After asking the question, I figured out that DTFT result is an impulse train. Now my question evolved to, how it is derived in this way? Using the DTFT formula seems not to be working, ...
1
vote
1answer
39 views

Why does the frequency window affect the inverse fourier transform oscillation frequency?

I have an oscillating pulse in the frequency domain that I would like to inverse Fourier transform. My signal looks like: Which was coded in MATLAB using the following code: ...
0
votes
1answer
101 views

Matlab FFT not producing symmetric spectrum

I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset. ...
0
votes
0answers
58 views

How to design FFT for 2000 points?

How should I design FFT with fixed samples - always 2000, sampling frequency is also 2000, memory is external, there is no need to get sorted array. As far I know it may go like factoring 2000 into $2^...
1
vote
3answers
223 views

Sawtooth wave Fourier coefficients

I have to calculate the Fourier coefficients of this signal. I found that signal equation is $$ y = \frac {A(2t-T)}{T} $$ To find Fourier coefficients I wrote $$ x_k = \frac{2A}{T} \int_{0}^{T/2} \...
2
votes
2answers
1k views

Shifting in DFT (FFT)

Input image Listing-1 i = imread('Untitled.png'); i = rgb2gray(i); F = fft2(i); %%%F = fftshift(F); F = abs(F); F = log(F+1); F = mat2gray(F); imshow(F); ...
0
votes
1answer
23 views

What is the unit for power spectrum of acceleration signals in log scale

I have a signal recorded by an accelerometer in m/s^2. It is basically accelerations over a period of time. I have calculated the power spectrum of the signal over in a certain frequency band and then ...
0
votes
1answer
17 views

DFT practice question

This is probably basic but as I am new to the field it confuses me a bit. While looking at some solutions provided to a problem in the final step following happens: $$ \frac{1}{10}\sum_{l=-\infty}^{\...
0
votes
1answer
16 views

Relationship between real and imaginary part of a real-valued and causal system

I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by $$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
2
votes
1answer
24 views

Proof that module of FT of 2 independent signals is sum of modules

I found on these posts (PSD subtraction and PSD of a sum of two stationary real signals) what I expected : that, just like the variance of the sum of 2 independent signals is the sum of the variances ...
1
vote
1answer
33 views

The expectation in power spectral density

I'm a bit confused with the definition of the power spectral density (PSD). From Wiki https://en.wikipedia.org/wiki/Spectral_density , I found the definition is: $$ S_{xx}(\omega) = \lim_{T\...
1
vote
1answer
224 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. ...
0
votes
2answers
116 views

Fourier coefficients of |A cos (x)|

I have to find Fourier coefficients of $x(t) = |A \cos (2 \pi f t )|$. The problem also give me $y(t) = |x(t)|$. To find Fourier coefficients I wrote $$ \frac{1}{T_0} \int_{0}^{T_0} |A \cos (2 \pi f ...
0
votes
1answer
55 views

Fourier Transform of the full Morlet wavelet

In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below: Fourier Transform of Morlet wavelet Function? However, it was the approximated Morlet wavelet not written with the ...
0
votes
1answer
497 views

Relation between two k-spaces phase-frequency and spatial frequencies in

When I see MRI explained, two types of 2D k-space images seem to be described as if they were the same. Axes are the two spatial frequencies. This images is directly fourier-transformed into the ...
0
votes
2answers
1k views

Convolution in Spatial Domain Is Multiplication in Frequency Domain

I have to prove convolution in spatial domain is equivalent to multiplication in frequency domain using two matrices. $$ x(m, n) = \begin{bmatrix} 1 && 2 \\ 3 && 4 \end{bmatrix} $$ $...
1
vote
5answers
74 views

Interpreting the amplitude of signals in fourier transform

I totally understand the concept of fourier transform, but one thing thats bothering me is the amplitude that we plot in the frequency domain. What does that amplitude of each frequency signifies? Is ...
1
vote
2answers
170 views

Problem identifying the analytic expression of such determined signal

I came across this problem I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal. The teacher suggests that I should consider ...
8
votes
2answers
5k views

Using the Inverse Filter to Correct a Spatially Convolved Image (Deconvolution)

As part of a homework assignment, we are implementing the Inverse Filter. Degrade an image then recover with an Inverse Filter. I convolve the image in the spatial domain with a 5x5 box filter. I FFT ...