# Questions tagged [fourier]

The tag has no usage guidance.

247 questions
Filter by
Sorted by
Tagged with
36 views

### Find CT Fourier transform of $\left[ \frac{ \sin(\pi ~ t) }{\pi ~t} \right] \left[ \frac{ \sin(2\pi ~ (t-1)) }{\pi ~(t-1)} \right]$using properties

Use properties of Fourier Transform to solve the question. The question is in the imgur link below. I got $f_t$ of $\frac {sin(pi \cdot t)} {pi \cdot t}$ as rectangular pulse with value $1$ from -pi ...
70 views

### Can different Discrete-Time-Fourier-Series(DTFS) coefficients have the same discrete sequence in the time domain?

Please, check the following discrete periodic sequence when the period $N=2$. $x[k]=\exp(j\frac{2\pi}{N}k), N=\text{period}$ $..., x= 1, x= -1, x= 1, x= -1, ... , N=2$ According to my ...
40 views

### Why is the continuous time Fourier series of DC signal an impulse?

In case of continuous time Fourier transform(CTFT), I can easily calculate the Fourier transform of DC signal by using Fourier duality or inverse CTFT. But I don't know how to calculate the continuous ...
14 views

### Amplitude Matching for Exponential Swept Sine

I am working in the area of aerospace vibration testing and we use swept sine tests on structures and measure the response using the accelerometers. I tried implementing the technique "...
158 views

### Why does DFT have only $N$ components?

Why does the DFT have only $N$ components in it? I can see that after N components the frequency component is periodic and repeats with the same values but that does not seem to explain why we can ...
43 views

### frequency domain to time domain with magnitude and phase

I have a signal magnitude and phase in frequency domain. I need to have it in time domain but I really have no idea how to do it. I heard something about mirroring the signal but I'm kinda new at this....
94 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 ...
35 views

### 2D Fourier Transform [closed]

Is it possible to get a 2D Fourier Transform by first taking 1D Fourier transform in first dimension and then performing another 1D Fourier Transform in the other dimension? If yes, can you explain
70 views

### Prove a property using shift theorem and duality

I'm reading Lectures on the Fourier Transform and Its Applications and I'm going to prove shift theorem for the inverse Fourier transform using duality. According to the mentioned source, the duality ...
20 views

### Fundamental frequency in DFT [duplicate]

I was looking into the fundamental frequency in DFT and I noticed many sources mention that the fundamental frequency is $1/N$, where $N$ is the number of samples. (When doing the DFT, we have $k/N$, ...
156 views

### Amplitude after Fourier transform

How to obtain the correct amplitude after the numerical Fourier transform of a signal? Example: consider an exponential decaying wave $y(x)=e^{-x}\sin(100\pi x)$ with Fourier transform $y_f(x_f)$ ...
34 views

### I need help in understanding “Nyquist Criterion” definition

I am researching the split-step parabolic equation and its split step solution as in: Ozgun, Ozlem & Apaydin, Gokhan & Kuzuoglu, Mustafa & Sevgi, Levent. (2011). PETOOL: MATLAB-based one-...
47 views

### Time scale and Fourier transform

Consider the Fourier transform $F(\omega)$ of the function $f(t)$. The magnitude of $F(\omega)$ depends on $\omega$ and thus also depends on the scale of the $t$-axis. For example, when $f_1(t)$ is a ...
39 views

### What's the relation between frequency band of $X(j\omega)$ and $\Phi_{xx}(j\omega)$?

in which: $x_{c}(t)$ is a continuous-time signal $X(j\Omega)$ is the Fourier Transform of $x_{c}(t)$ $\Phi_{xx}(j\Omega)$ is the Power Spectrum Density of $x_{c}(t)$ which defined as Fourier ...
44 views

### Frequency response and sampling theorem for triangular function

The triangular function is defined as follows: $h_l(x) = \begin{cases}1-|x|,&|x|<1;\\0&\text{otherwise}.\end{cases}$ According to ccrma.stanford.edu: "If the output of the interpolator ...
33 views

### How to downsample a fourier transformed signal?

I have a signal of length 100000 timestamps sampled at a frequency of 25kHz. First I apply a high pass filtering at (300Hz) and then do the Fast Fourier Transformation. Then the absolute values are ...
75 views

### Why the Nyquist frequency is 0.5 of Fs, why not 0.55 or 0.65?, brief explanation [duplicate]

This my elaboration of the aliasing issue: a continuous signal can be represented by factors of : $e^{(i2{\pi}ft)}$ if we sample this signal then I will get: $e^{(i2{\pi}fk/N)}$ where $k=0,1,2.., N-1$ ...
40 views

### Receiver function, frecuency domain deconvolution not giving logic results

I'm working on some code for receiver function method in seismology. For anyone one not into the topic, it's just a deconvolution of two time series (seismograms). This can be done in the time domain ...
68 views

### Question on N point DTFT - Fourier transform

I have been trying to use the logic that both X and Y should have same Z transform, but according to the definition, Y is not anti causal.
69 views

### Conjugate symmetry of the DFT of real-valued sequences

I have read about Fourier transformation that real signals are "mirrored" in the real and negative halves of the Fourier transform because of the nature of the Fourier transform. For ...
30 views

### Understanding index transformation in derivation of Fourier transform for sampling rate reduction

Was going over some notes regarding deriving fourier transform equation for Sampling Rate Reduction. Reference to Notes from below link https://ocw.mit.edu/courses/electrical-engineering-and-computer-...
45 views

### Fourier transform of an integrator filter

I have to find the Fourier transform , and $y(t)$ of an $x(t) = e^{- \frac {t}{T} } u(t)$ that passes into a integrator filter. I know that $Y(f) = X(f) H(f)$ so I first calculate the Fourier ...
249 views

66 views

### How to understand the sum of all “fourier frequencies”?

I got the data of an acceleration sensor to analyze. It consists of special terms of 30 Hz, 60 Hz and 120 Hz. In the following you can see in the first plot the 60 Hz data and in the second one the ...
60 views

### How do I deconstruct a signal with fast fourier transformation in Python?

I want to use the fast Fourier transformation in python to deconstruct a periodic signal into its harmonic periodicities. Since the FFT of the original signal is the same as adding the FFT of the ...
67 views

### What kind of periodic signals cannot be represented with the Fourier Series?

Oppenheim et al. state in Signals and Systems that there exist periodic signals which cannot be represented with Fourier series. What signals are these? Although Euler and Lagrange would have been ...
13 views

### USRP N210 and FFT

I am getting IQ data from my usrp N210. It has been written in a file as a complex number and I can analyze it with matlab. The IQ data actually resembles the power of my processor. The sampling ...
172 views

### How to do the Fourier Transform of bounded function?

I was trying to solve a Fourier transform of a function using the properties of Fourier transforms. The function is given as: $\frac{At}{2}$ for $-2<t<2$ and $0$ for all other $t$. Doing the ...
58 views

### Math.Net and alglib returning different FFT outputs by default

I am developing an application in C# with spectrogram drawing functionality. For my fist try, I used MathNet.Numerics, and now I am continuing to develop with alglib. When I changed from one to the ...
83 views

### y(t) a of an integrator circuit

I have a signal $$x(t)= \frac{1}{T} e^{-\frac{t}{T}} u(t) - \frac{1}{T} e^{\frac{t}{T}} u(-t)$$ and I know that it transits in a integrator circuit and I have to find y(t) in time and frequency ...
14 views

### average value of modulated signal with Fourier Analysis

I am using an instrument that uses a modulated heating program. The instrument returns an average heat flow signal calculated from the modulated heat flow. I would like to understand how this average ...
102 views

### Inverse Fourier transform Of a triangular impulse

I have to find the expression of this graphic and after find the inverse Fourier transform of it. First of all I found that the expression of the graphic is  X(f) = \frac{1}{2} tri (\frac{f+f_0}{B}) ...
Given a signal $\mathbf{z} \in \mathbb{C}^n$ and its Discrete Fourier transform $\hat{\mathbf{z} }$, does $||\mathbf{z}|| = ||\hat{\mathbf{z} }||$ hold? The question is given to me like this with ...