Questions tagged [fourier-series]
The fourier-series tag has no usage guidance.
286
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Where does $\frac{N}{2}$ came from in approximating an N-point DFT?
I've came across the author saying that
... for a real cosine input having k cycles in the N-point input time sequence, the amplitude response of an N-point DFT bin in terms of the bin index m is ...
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Signal's Fundamental Frequency is different from Plotted Signal
I've been attempting to plot the following function using MATLAB:
$$
x(k)=\sum_{n=11}^{50} \sqrt{n} \sin (2n\pi k) +\sum_{n=1}^{40}\sqrt[3]{n} \sin (3n\pi k)
$$
Note that $k$ is a continuous variable....
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square wave frequency representation
New to this signals stuff and i'm confused about the frequency representation of the square wave. Correct me if i'm wrong, a periodic square wave is composed of odd harmonics sine waves which are ...
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Relation between Fourier Series & Fourier transform [duplicate]
So i was just revising some basic DSP concepts. Just wanted to verify this fact.
Fourier series represents a periodic signal $\hat{x}(t)$ with period P as a countably infinite sum of sinusoids of ...
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How do I calculate the eigenvalues of a covariance matrix which contains harmonic functions
I have read that $ce^{-\frac{\phi_i-\phi_j}{\rho}}$ is a harmonic function of the form $e^{-in\phi_i}$, and therefore it's eigenvalues are one of the Fourier components of $(|\phi_i-\phi_j|)$.
My ...
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Relation between sawtooth Fourier coefficients and its DFT
I'm having some trouble with understanding the DFT of a sawtooth single period signal and its relation with sawtooth Fourier coefficients.
Let's say I have a signal
$$
s(t) = \frac{At}{T} - \frac{A}{...
- 166
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How to find Fourier Series Coefficients
I saw many solved examples about this topic but again I coudn't come up with any solutions about this question. How can I find the Fourier Series coefficients of the following signal ?
$x(t)=2 \cos(3\...
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2
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FFT of SIN waves with different phase delays
I have come across a peculiarity of FFTs which has got me somewhat baffled.
I've simply summed up 101 sine waves and taken the FFT using this matlab script :
...
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4
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Formulas of the Fourier transform family
It has annoyed me that there doesn't seem to be a source online where the complete complex Fourier transform family is presented with every variable defined. The lack of definitions can be a nuisance ...
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Calculating original signal from Discerete Fourier Transform
I am trying to calculate the original equation using a DFT. I start with a equation, generate values from this equation and then get the dft of these values. The aim is to generate the original ...
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Convolution in frequency domain
Simple math question. The convolution theorem states that multiplication in time domain is equal to convolution in frequency domain and vice versa. There is a condition that the signal has to be ...
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About Fourier transform of periodic signal
In Fourier transform for periodic signal, I checked different books and I found a different explanation in each book. Let's take the explanation in Signals and Systems by Rajeshwari & Rao:
The ...
- 383
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2
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815
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Finding Fourier Series Coefficients
I'm just beginning to learn about Fourier series and I'm trying to figure out how to find the Fourier series coefficients for $$x(t) = e^{j100\pi t}$$
I know that $$x(t) = \sum_{-\infty}^{\infty} a_{...
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Derive Frequency Representation of Impulse Train Function
I want to walk through the derivation of the frequency representation of an impulse train.
The definition of the impulse train function with period $T$ and the frequency representation with sampling ...
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Fourier Transform/Series DFT/DFS textbook problem (simple?)
Suppose $x_c(t)$ is a periodic continuous time signal with period 1 ms and for which the Fourier series is
\begin{align*}
x_c(t) &= \sum\limits_{k=-9}^9 a_k e^{j(2000 \pi k t)} \\
\end{align*}
...
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Relation between a Fourier series harmonic component and its power
My question is about the meaning of power spectrum derived from the Fourier series coefficients.
Fourier series is shown below:
$$f(t)=a_0+\sum_{n=1}^{\infty}a_n\sin(\omega_n t)+\sum_{n=1}^{\infty}...
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Why Fourier series if Fourier transform can be calculated for both periodic and aperiodic?
While learning about Fourier Transform after Fourier Series, That we can calculate Fourier transform of periodic signals too. If we can take the Fourier transform of periodic signal too then my ...
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Determining Fourier Series coefficient for Discrete time
I am trying to solve the proof for determining the Fourier series representation of a periodic signal.
I understand fourier series equation for Discrete time which is $$x[n] = \sum^{}_{k=<N>} ...
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Proof of properties of Fourier series in CT
I feel problem in understanding the proof of Fourier series properties
Time scaling
\begin{align}
b_k &= \frac{1}{T}\int_{T}x(t)e^{jk\omega_0t}dt\\
& = \frac{a}{T}\int_{T/a}x(at)e^{jk(\...
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magnitude and phase Fourier coefficients
While solving Fourier series coefficients in example, i found couple of things which confuse me.
How the minus sign changes to plus sign $a_1= 1-\frac{1}{2j} = 1+\frac{1}{2}j$?
After plotting the ...
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1
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175
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Mathematical model of a signal in Compressive Sampling
Currently I am reading a paper on Compressive Sampling, and trying to understand each and every parts of it. When I came across the mathematical model of the signal in paper, I got confused. I have ...
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Proof for determining Fourier coefficients
While determining Fourier coefficients we have this equation
$$\int^{T}_{0} x(t) e^{-jn\omega_0t} dt = \sum^{+\infty}_{k\ =\ -\infty} a_k [\int^{T}_{0} e^{j(k-n)\omega_0t}dt]$$
I want to ask that how ...
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Value of $A_k$ in Fourier series
Fourier series in continuous time domain while representing $a_k$ in rectangular form $$ a_k = B_k + jC_k$$
But when using the value of $a_k$ in the main equation: $$ x(t) = a_0 + 2\sum^{+\infty}_{k\...
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107
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Fourier Series Proof
I want to ask Question about the Fourier series in continuous time domain while reading a book signals and systems Alan Oppenheim. I have confusion in understanding the statement on page 189 of its ...
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68
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Fourier series in continous time domain
I want to ask Question about the Fourier series in continuous time domain.
I am following signal and systems 2nd Edition by Alan Oppenheim.
I have confusion in understanding the statement that
...
- 383
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76
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the DFT of a periodic signal represented by a fourier series
If I have a signal represented by a Fourier series(like in the photo), which is sampled with $T_s$:
$$x[n]=x(t=nT_s) = \sum_{m=-\infty}^{\infty}a[m]e^{j2\pi m(nT_s)/T_0} $$
How do I find its DFT? I ...
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When is the Fourier transform of a signal periodic?
I mean not the time-domain signal being periodic, but the Fourier transform being periodic.
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785
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Bartlett's and Welch's Method for PSD
Lets say. I have an image of 100 samples, and I want to find the presence of smaller image of 24 sample using cross-correlation in the fourier domain. I use Bartlett's and Welch's method for PSD, ...
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483
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Finding Correlation response in fourier domain
Lets say I have a system that is trying to find a small image (assume all images are grayscale) within in an image by using correlation. So this system has the baseline image, and I input 5 different ...
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1
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120
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Fourier series calculation [closed]
I have tried to solve, but do not know if the answer is correct or not.
A person has a periodic voltage input to a circuit. The input repeats itself every 0.02 seconds i.e. the fundamental period is ...
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1
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330
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How to simplify the Fourier Series Using an Approximation?
I have a signal, $f(t)$. I know a function that can be used to generate this signal, such that I can determine its Fourier series. I want to express this Fourier series in simpler terms so that the ...
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What is difference between outputs of Fourier transform and Fourier series of a periodic square waveform?
We can use Fourier transform of an aperiodic signal and Fourier series of periodic signal. But we can use Fourier transform formula for periodic function also.
Now, let us consider a periodic square ...
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How Fourier decomposition is performed?
The Fourier decomposition explains a time series entirely as a weighted sum of sinusoidal functions and with the Fourier series,it is possible to do it.
But I have some doubts
Suppose ,for any signal ...
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2
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210
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Why does this Fourier series give lower amplitude for max value of signal?
I want to approximate below signal using Fourier series on Matlab.
My code is below
...
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78
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Approximating the fourier coefficients from a discrete time signal
Suppose I have a discrete time signal $x_t$ sampled with a frequency $f_s$. I know that if I take the discrete fourier transform of the signal and compute the power, I can easily (by visual ...
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Signal decompositon
I am not a good in writing algorithm but please follow below steps
1.There are 4 1D sinusoidal periodic signals.3 of them are given by
\begin{cases}
x(t)=4\sin(10\pi t) \\
y(t)=8\cos(20\pi t) \\
...
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1
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Change of discrete summation to definite integral
The Exponential Fourier Series for a signal is written as,
$$x(t) = \sum_{n=-\infty}^{\infty} X_n e^{jnw_0t}\tag{1}$$
and, Fourier Coefficient, $X_n$, is written as,
$$X_n = \frac{1}{T} \int_{t_0}^{...
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257
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how to create synthetic $1/f$ noise? [duplicate]
I am writing an app to work with synthetic time series data from a physics experiment. In our experiments we always have $1/f$ noise in our time series, but I haven't been able to find code/packages ...
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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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343
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Can I study continuous time Fourier Transform and treat the rest as special cases
Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to
Lapace transform,
Z transform,
DTFT,
DFT,
Fourier sequence ...
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Signal Processing using Fourier Transform
How can I derive the fourier transform of
...
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A clarinet has no even harmonics. What would produce no odd harmonics?
According to this link, the waveforms of clarinets do not have even-numbered components in their harmonic series:
A closed cylindrical air column will produce resonant standing waves at a ...
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1
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191
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Fourier series qn determine the fourier series coefficients
Can someone please help me with this Fourier series question:
Determine the Fourier series coefficients of $x(t)$ given as $x(t) =
> \cos4t +\sin8t+3$?
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Why does Fourier Series have $\sin$ and $\cos$ Components
While we look at Fourier Series there are both $\sin$ and $\cos$ components.But I think $\sin$ component is ony needed to describe wave.why there is also an $\cos$ component in Fourier Series?
$S_n(x)...
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Deriving time-scaling property for Fourier Series
thanks for taking the time to help with this problem!
I have to prove the time-scaling property:
$$
x_{(m)}[n] =
\begin{cases}
x[n/m], & n=0,\pm m, \pm 2m,...\\
0, & otherwise
\end{cases}
$$
...
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DSP interview question: use of the identity in development of a significant transform
I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform?
How the simple identity
$$xy=\frac{1}{2}x^2 + ...
user11535
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Fourier synthesis
I know what I am attempting is not easy but I have a spectrum with peaks at 10Hz 20Hz and 30Hz. I also have various amplitudes at these peaks. I want to recreate my original signal. I initially ...
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Determine spectrum amplitudes for half-wave rectified sine
I am trying to learn how to solve a bunch of digital signal problems and I have trouble understanding the solutions provided by this book I'm using. Basically, this problem asks me to determine ...
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Estimate the Discrete Fourier Transform / Series of a Signal with Missing Samples
Assuming we have a discrete signal $ { \left\{ x \left[ n \right] \right\}}_{n = 1}^{N} $.
Which has a Discrete Fourier Transform / Series.
Now, assume I'd like to estimate its Discrete Fourier ...
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Power contained in a signal
Given a signal $$x(t)=16\cos(20\pi t+\frac\pi 4)+6\cos(30\pi t+\frac\pi 6)+4\cos(40\pi t+\frac\pi 3)$$how can I calculate the power contained in a frequency interval, say 12Hz to 22Hz.
The total power ...
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