# Questions tagged [fourier-transform]

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

1,375 questions
Filter by
Sorted by
Tagged with
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ?
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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....
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 ...
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 ...
25 views

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 ...
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?
87 views

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 ...
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 ...
983 views

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); ...
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 ...
17 views

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 ...
33 views

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 ...
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 ...