# Questions tagged [fourier-series]

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### Fourier series representation of a full wave rectifier output

I am trying to compute the Fourier series representation of a full wave rectifier output. The equation of the signal is: $x_8(t) = | \cos (2 \pi f_o t)$ | I have tried to find the Fourier series ...
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### How to calculate fourier coefficients of sum of two discrete time with different fundamental periods

Assume that we have two discrete-time signals named x[n] with fundamental period 3 and fourier coefficients ak (k from 1 to 3), and y[n] with fundamental period 5 and fourier coefficients bk (k from 1 ...
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### Fourier series expansion of $x_1(t) = \sum _{-\infty}^{\infty} \Delta (t-2n)$

I want to evaluate the Fourier series expansion of $x_1(t) = \sum _{-\infty}^{\infty} \Delta (t-2n)$, where $\Delta (t)$ is a triangular function defined as: I have done the following ...
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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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### 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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### I want to invert my fourier transform components to waves again

Hi I am using R to analyze some data I basically did fft(data) and got a vector of complex numbers but from that now I want to remove certain harmonics from my actual wave but how do I convert one of ...
A function $u:[0,2\pi]\to\mathbb R$ sampled over $N$ equidistant points $\theta_j=(2\pi/N)j,\, j = 0, \dots, N-1,$ can be interpolated by a set of functions $\{u_{k_0}\}$ enumerated by integers $k_0\... 0answers 72 views ### How to find fundamental frequency of two signals? I am facing difficulty with finding fundamental frequency of signals I mean by fundamental frequency=(1/Time period) Correct me if I am wrong consider two continuous time signals with Time period ... 0answers 11 views ### 2D Fourier Synthesis (IDFT) not yielding expected result I am trying to recover a 2D signal using inverse DFT, to my understanding the IDFT outputs the coefficients of the fourier series of the original function up to the Nyquist frequency. So for example ... 0answers 47 views ### 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 ... 1answer 152 views ### 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 ... 0answers 136 views ### Range of function$ \frac{1}{n\pi}(1-\cos(n\pi))\sin(\frac{n\pi}{2})$and determination of Fourier coefficients I am computing the Fourier series expansion of the given signal$x(t)$. In that I am having difficulties in calculating range of function$ \frac{1}{n\pi}(1-\cos(n\pi))\sin(\frac{n\pi}{2})$(or) I am ... 0answers 71 views ### the DFT of a periodic signal represented by a fourier series If I have a signal represented by a Fourier series(like in the photo), which is sampled with$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 ... 0answers 35 views ### 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 ... 1answer 94 views ### Fourier Coefficients Consider the signal $$x(t)=\cos(2\pi t)$$ Since$x(t)$is periodic with a fundamental period of$1$, it is also periodic with a period of$N$, where$N$is any positive integer. What are the ... 1answer 109 views ### 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/...
Can someone please help me with this Fourier series question: Determine the Fourier series coefficients of $x(t)$ given as $x(t) = > \cos4t +\sin8t+3$?