Questions tagged [fourier-series]
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286
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The difference between DFT and DFS
In the literature, I've found that DFS and DFT are one and the same. If they are one and the same why to use two different names for them? If there is really a difference what is it and what is the ...
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Advantages of the Karplus algorithm for sound synthesis
For a personal project I am trying to make a software to synthesize plucked and hammered string instruments. This is a whole research topic and there are already some models and algorithms such as the ...
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1
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Fourier transform of a time discrete signal
I would like some help to better understand the Fourier transform of a discrete time signal. My doubts are:
The sampling of a signal can be seen as $x_s(t)=x(t) \cdot
\sum_{k=-\infty}^{+\infty} \...
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positivity of the spectrum of quasi-stationary signals
I am working on the "System identification : theory for the user" by Lennart Ljung (freely available here) and it is one of these books which contains exercises but no answers... My exercise ...
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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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Creating infinite continuous time series out of a finite discrete spectrum
I have a power spectrum $S(\omega)$: a $1 \times N$ real vector that matches frequencies from 0 to 125Hz. I would like to create a time series $S(t)$ $[-\infty<t<\infty]$ that matches this ...
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3
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Trying to understand how to get this basic Fourier Series
I'm sorry if this kind of question isn't allowed, but I'm starting to learn Fourier series and I'm still not entirely sure what's going on... in this specific case, I'm trying to find the Continuous ...
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Can we control the maximum norm of a continuous signal whose finitely many Fourier coefficients are fixed?
Let us denote $C_{2\pi}$ by the set of all $2\pi$-periodic continuous signals $x:\mathbb{R}\to \mathbb{R}$.
Fix $n\in \mathbb{N}$ and put
$$\Lambda_n=\{y\in C_{2\pi}: \mathcal{F}(y)[k]=0 ~\...
- 24.2k
2
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1
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Discrete Fourier series of an odd signal
Assuming the signal shown below :
I have found an expression for fourier series coeffecients as the following:
$$a_{k} = \frac{1}{5}+\frac{j}{5}\sin{\frac{2\pi}{5}k}$$
Which matches with what the ...
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Is my solution correct?
$\textbf{Question:}$
$y_a(t)$ is a rectangular waveform defined as:
$$\
y_a(t) =
\begin{cases}
2 &t \in [0,1/25)s\...
- 125
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Finding $A_k$ coefficients
I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as:
$x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the ...
- 18.8k
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Fourier coefficients of two discrete-time signals of different periods
I'm trying to understand the Fourier series coefficients of the sum of two discrete-time periodic signals.
Consider two discrete-time periodic signals $x[n]$ and $y[n]$. $x[n]$ has period $N$, its ...
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Finding the Fourier Coefficients
Up until now, I have dealt with finding Fourier Coefficients for functions: $f(t) > 0$
Which made it convenient calculating the Fourier Analysis Integral. However, I am now presented with ...
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What happens to sidebands when they enter "negative" frequencies?
I am working with PWM signals. These signals are generated by comparing a modulating (at frequency $f_m$), and a carrier (at frequency $f_c$), as shown in the following image:
In the resulting ...
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What is $z[n]$ , when $Z[k]=X[2k]H[2k]$ with $y[n] = x[n]∗h[n]$ and $Z[k] = X(\omega)H(\omega)$ at $\omega = \frac{4πkn}{N}$
How do I express $z[n]$ in terms of $y[n]$, with:
$$y[n] = x[n]∗h[n]$$
$x[n]$ and $h[n]$ being 16 length sequences.
$X(\omega)$ and $H(\omega)$ are DTFT of $x[n]$ and $h[n]$
$Z[k]$ is defined as
$$Z[k]...
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Bandwidth of cosine of bandlimited signal
I have a signal $x(t)$ with bandwidth $B_x$, and I am taking its cosine to create $y(t) = cos(x(t))$. After checking the spectrum with FFT, it seems that $y(t)$ is also bandlimited. But, is there a ...
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From Fourier (k space) to wavelet domain in MRI sensing
In compressed sensing MRI (cSENSE MRI) technology the idea seems to entail sampling from the Fourier domain (k space) in a way that, when transformed to the wavelet domain ("sparsification"), the ...
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How to generate a sound closer to a saxophone using sinusoids after Fourier Transform?
Generate a sound wave of saxophone frequency and compare it to the original sound clip and play both to listen to if there is a good match.
I am trying to generate a sound closer to a saxophone using ...
0
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1
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219
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How to reconstruct original signal using IFFT after cutting past Nyquist limit
I'm working on a pitch shifting program. Everything works up to the point where I try to do the IDFT. Because I cut the DFT array past the Nyquist limit, when I run the IDFT, I don't get the same ...
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Pitch successfully changes with Phase Vocoder, but there's an issue
I've been working on a phase vocoder program. The goal is to change the pitch of a recording of my voice. While doing research on how to change pitch, I came across this from a paper on phase vocoders ...
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1
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How to change fundamental frequency with DFT?
I'm working on a voice changer. My plan is to make it so that it can change your voice in various different ways, but right now I'm just trying to make it change your voice to "chipmunk voice&...
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1
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How to Find "pitch" from Fourier Series
The end goal of my project is to create an autotune program, But the problem I'm trying to solve right now concerns finding the pitch of someone singing a note. I have written some code that performs ...
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2
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Fourier transform of periodic functions
The Fourier transform is derived from the Fourier series by considering a non-periodic signal, thinking of it as a infinitely long periodic signal, putting it into the Fourier series and making this ...
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3
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Slow Down Music Playing While Maintaining Frequency
Playing a piece of music audio at a slower speed would lower its pitch (frequency). Is there a tool and theory to slow down the song playing while keep the frequency the same? I suppose one can do ...
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Why does Hilbert filter distorts the shape of the signal?
If all the harmonics composing a the signal are shifted by the same amount, this would be the same as sampling later or earlier in time. I think.
Take a simple pulse train as an example.
If Fourier ...
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0
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Improving the intuition for the 2d fourier transform
As far as I understand, the 2d fourier transform is calculated as following:
...
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Can I reduce the complexity of multiplication with FFT if the input vector is repeating?
I have a Fourier matrix $F$ with size $N \times N$, such that $y = F \times x$, if I have the vector $x$ contains four identical parts, for example $x = [x_1, x_2,x_3,x_4]’$ and $x_1 = x_2 = x_3 = ...
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2
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Sampling of the DTFT causes the inverse transform to become periodic?
As you can see the above equation, DTFT is calculated from sample x[n] which is discrete sample of x(t).
But calculated X(w) is continuous, even though it is calculated from discrete value of x[n] as ...
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On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies
It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
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transform signal
Hello everyone I need help solving a Fourier transform for the given signal, I know it will be a frequency convolution for the first function it will be a window function and for the second function I ...
CommunityBot
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How do I plot a phase spectrum of rectangular pulse with Matlab?
As you can see, I made a code about rectangular pulse like this. And, I plotted complex-exponential-coefficient and Magnitude-Spectrum-of-Complex-Exponential-Form, Phase-Spectrum of-Complex-...
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Output of LTI (in time and frequency $\omega$ domain) : when input goes through LPF
I would like to raise a mathematical question :
Let's say we are been given :
$$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\
0 & \textrm{otherwise} ...
CommunityBot
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What's the difference between male and female voice? [duplicate]
If I record the voice of a man and a woman, what are the main differences I get in the various spectra and harmonics in Fourier analysis?
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Confusion understanding Fourier series line spectra?
I am reading book signals and systems Laboratory with MATLAB where I am studing chapter 5, Fourier series and i trying to understand magnitude spectrum and phase spectrum but i have certain confuisons ...
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Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals
If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away?
Suppose we are given the ...
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What is the Fourier convolution theorem range of application (example of Dirac comb times rectangular window)?
$\DeclareMathOperator{\sinc}{sinc}$
I have questions regarding the Fourier transform of the product of functions or distributions and the range of application of the convolution theorem.
Context
When ...
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Estimate the Discrete Fourier Transform / Series of a Signal with Missing Samples
Assuming we have a discrete signal $ { \left\{ x \left[ n \right] \right\}}_{n = 1}^{N} $.
Which has a Discrete Fourier Transform / Series.
Now, assume I'd like to estimate its Discrete Fourier ...
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2
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What is the reason of existence of Fourier transform? (Why we use Fourier transform?)
I'm currently trying to understand Fourier transform and I've got curious about why Fourier transform exists.
Let's suppose that we have a 10 seconds of non-periodic wave. For example:
As far as I ...
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Proving real and odd function has imaginary and odd Fourier Transform
Cheers, I am trying to prove that a real and odd function/signal has imaginary and odd Fourier Transform. Although it seems fairly easy, I can't find a way to achieve it, and searching online hasn't ...
- 85.7k
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A question on Fourier Series and the frequency of the sinusoids
On studying about Fourier series, I encountered 2 doubts:
How is it that a non-periodic function has a Fourier series?
When expressing a periodic function as summation of sinusoids, why is the ...
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Are there Fourier methods for VERY low frequency repeating signals?
Suppose I have a very low frequency pattern of sound. For example a 10 second music file. Then 10 seconds of silence. Then the same 10 second music file repeated again. The whole sequence repeats ...
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How to apply Butterworth high pass filter in the frequency domain?
I have a time series of measurements which I want to high pass with Butterworth filter.
Python scipy package has a built in function for Butterworth filter (signal.butter) and I know how to apply it ...
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Is there an analogy of the Fourier-decomposition in the Laplace space to decompose a signal to a few components?
I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components.
If it would be a sum of some sinusiod waves, it would be easy to ...
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Fourier Series of a piecewise function
I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
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Mistake or not - Fourier Series of x(2t+3)
I have a couple of resources I have from my university I had being checking and I found this:
Find Fourier Series coefficients of x(2t+3). x(t) is continuous and periodic by T.
I see this solution:
...
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How to do simple extrapolation with Fourier transformation?
I have 1024 sample points, and I would like to do really simple extrapolation using Fourier transformation. First I apply Fast fourier transformation on the data. My first intuition was that I just ...
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1
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The magnitude spectrum of a sharpening filter
I'm trying to derive an expression for the magnitude spectrum of the following sharpening filter.
$$
g(m,n) = \delta(m,n)+\lambda (\delta(m,n) - h(m,n))
$$
where $\lambda$ is some positive constant ...
CommunityBot
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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 ...
- 27.6k
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Fourier transform of time division
I know that Fourier transform of $t^n f(t)= i^n \frac{d}{d\omega^n} F(\omega)$.
But does this work when $n<0$?
Is there any direct relation to compute the Fourier transform of $\frac{f(t)}{t}$?
CommunityBot
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How to interpret Fourier transform?
I am very new to this topic.
I ran a Fourier transform with the scipy fft function.
I than plotted the return values:
I am assuming the x-axis means how many cycles there are in all the data and y-...
- 31.3k