Questions tagged [fourier]

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1answer
88 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 ...
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1answer
85 views

Is fft2 in MATLAB unitary? Some differences happen

I meet a problem when implementing fft2 in MATLAB. The question is I try to simulate the realistic measurements $Y = |FCXF^H|^2$ - the intensity of Fourier domain of object $X$, where $F$ denotes ...
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1answer
60 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 ...
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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 $k/N$, ...
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2answers
269 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 $y_f(x_f)$ ...
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1answer
78 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 ...
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40 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-...
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2answers
88 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.
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1answer
95 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 ...
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0answers
37 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 ...
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2answers
91 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 $k=0,1,2.., N-1$ ...
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1answer
272 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 ...
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1answer
33 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-...
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1answer
55 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 ...
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10 views

What is the Effect of Multiplying a Function by the Unit Impulse Function in the Frequency Domain? [duplicate]

I know about the the shifting property of the impulse function in the time domain as can be seen in the picture. But what is the effect of multiplication of a function by the impulse function in the ...
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32 views

$2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal

please help me find the error in the following counter example. Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
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2answers
48 views

Where did the length of time’s period disappear in Periodic Fourier Series Discrete Time

In continuous time Periodic Fourier Series has smallest n as possible, since it is an integral and a length of the repeating time (period time) which is T0. In discrete time however we don’t have ...
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5answers
1k views

Fast & accurate convolution algorithm (like FFT) for high dynamic range?

It seems that FFT-based convolution suffers from limited floating-point resolution due to evaluating everything around the roots of unity, as you can see in the $10^{14}$-factor error in this Python ...
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3answers
533 views

Why do we get different imaginary parts of a zero centered Gaussian for the the same number of data points N?

Suppose we have a total number N= 2048 points in a data and we wish to have zero centered Gaussian. There are two possibilities that we use the x-axis as ...
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2answers
29 views

How can it be that there is a series of integrals in Fourier Series if it’s a projection on a continuous basis?

If the process of finding Fourier coefficient is finding the projection of a signal on a member from an orthonormal basis, basis which is continuous in frequency. How can it be that Fourier ...
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34 views

frequencies in frequency spectrum with no correlation together

I have a lack of understanding of the following questions: If I have a signal from a motor that is recorded with an accelerometer. And the rotating speed of the motor is 150Hz(rpm 9000 ), I can see in ...
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2answers
42 views

difference in spectrum

First I defined 5 signals with same length (40 samples) with different frequency and sampling frequencies, then I've put them together like [X1 X2...] and took it's fourier transform and the result is ...
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1answer
109 views

Fourier transform of t*rect(t)

In my previous post I asked for help for a Fourier transform of $$ t \text{rect} ( t- \frac{1}{2} ) $$ and I think I’ve understand the process. Now I’ve 2 another similar Fourier transform to do , I ...
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3answers
155 views

Fourier transform of a rect*half triangle

I have to calculate the analytic expression of Fourier transform $$ x(t) = t{\rm rect} ( t- \frac{1}{2} ).$$ First I made the graph of these two signals and I obtained the graph I posted. Now I ...
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1answer
494 views

Characteristic function of a random Gaussian variable

I have to find the characteristic function of a random Gaussian variable of $$ \sigma_z (w) = E e^{i w z } $$. This is the variable and I know , from the theory that the characteristic function of ...
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2answers
2k views

Frequency Analysis (DFT / FFT) of a Signal Without a Constant Sampling Frequency (Non Uniform Sampling in Time Domain)

I'm a stack exchange user for some time and now I'm registering to ask a simple question (I think!). I have a vibration signal with an amplitude and time (sampling frequency not constant) in a $...
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1answer
826 views

Effect of DC component on the whole signal - comparison between normalised and non normalised

I have a fourier analysis signal as in the picture attached, where red represents the FFT of movement of the hand of a stroke subject and the blue one is the movement of a healthy subject. I am doing ...
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1answer
36 views

Confusing regarding triangular wave vs square wave?

I am reading signal processing first by Mcclellan. In chapter 3, I came across the term "discontinous" as shown underlined in attached photo. Apparently "discontinuous" means having a gap/break but ...
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1answer
95 views

What is issue in square wave reconstruction?

As shown in attached photo: What is the reason that the approximate square wave $$x_N (t)$$ at right side is not like the original $$x(t)$$ at left side .? Is the only reason is that number of ...
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2answers
51 views

Confusion regarding sinusoidal synthesis formula,

I am reading signal processing first by McClellan As shown in attached snapshot, we have formula of sinusoidal synthesis I am confused ,why in expression of x(t), there is a '2' in first line ...
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3answers
111 views

Complex exp. Fourier series, finding $x(t)$ when $X(j\omega)$ is given as magnitude and phase plot

I'm watching Neso Academy series on Signals and Systems, and in one of the videos the problem is to find $x(t)$ when magnitude and phase plot are given. The plot looks like this: When he finishes ...
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2answers
495 views

Convolution of an Image with a Kernel That Is a Product of Two Functions

Suppose that $G(i,j)$ is a Gaussian decay function on the distance between points $i$ and $j$ of an image. In addition, $D(i,j)$ is the difference between the VALUES of the image at those points. Now,...
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0answers
38 views

Short Time Discrete Fourier Transform to detect time dependent changes in a frequency of interest & Filter

I am working in matlab to compute the fourier relative phase of two signals as per https://sci-hub.tw/10.1123/jab.2017-0250 I have identified the fundamental frequency ($f_1$) for the signals (1.7 Hz)...
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1answer
93 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 ...
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0answers
67 views

Solving nonlinear Fourier relation

I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$: $S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$ with $n&...
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1answer
92 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 ...
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1answer
109 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 ...
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1answer
321 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 ...
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1answer
193 views

Using the given identities, find the inverse DTFT

Using the given identities, $$ a^nu[n] \Longleftrightarrow \frac{1}{(1-ae^{-jw})}$$ and $$\delta[n-k]\Longleftrightarrow e^{-jwk}$$ Find the inverse DTFT of, $$ H(e^{jw}) = B\cdot\frac{e^{-jw}}{(...
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1answer
1k views

frequency spectrum of the conjugate of $x(t)$

Is the frequency spectrum of $x^*(t)$ the same as the one of $x(t)$. I'm telling this because I found that $$X^\ast(f) = (X(-f))^\ast$$ So to find $X^\ast(f)$, intuitively i would just flip $X(f)$ ...
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1answer
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 ...
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1answer
521 views

Filtering Passband Signals using Complex Baseband Filtering

So I'm given a pass band filter with specific transfer function $H_p(f)$, I want to implement this via baseband processing. I already know how to take the input signal $u(t)$ and process it such ...
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2answers
281 views

Regarding Bode plots; $H(s)$ and $H(j\omega)$

In circuit analysis, I understand the use of Laplace Transforms to obtain the impedance of a linear RLC circuit, ie transforming from the time domain to the frequency domain. In most texts I have seen ...
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2answers
192 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}) ...
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1answer
101 views

Discrete Fourier Transform in Signal Processing - Interpreting graphs of transformed signals

Given above are the real parts of the signals I to IV. Which of the following statements are correct? (i): Signal III is the result of the discrete Fourier transform of signal I. The associated ...
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1answer
30 views

Discrete Fourier transform - Norms of complex input signals and their transformation

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 ...
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58 views

express pass band filter as sum of low pass filter

I have to find impulsive response of an ideal pass band filter, but I have a problem to express $$ H_{BP} (f) $$ as a sum of $$ H_{LP} (f) $$. I mean that $$ H_{BP} (f) = rect ( \frac{f-f_0}{B} ) + ...
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123 views

Energy of a sinc signal

My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me $$ x(t)=\operatorname{sinc}(t) $$ and $$ s(t)=x(t-T)$$ and I found that ...
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2answers
75 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 ...
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1answer
226 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 ...