# Questions tagged [fourier-series]

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### 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 ...
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### What is the exact meaning of the output of the Discrete Fourier Transform

I'm fairly new to the subject, but so far my understanding that this would be a transform you could use to go from a discrete set of data, say [1, 0, 1, 2] to a continuous sinusoidal function in the ...
331 views

### Inverse Discrete-Time Fourier Transform of $X(Ω)=jΩ$

I am trying to solve it by using the properties but I can’t seem to find the same solution as on my book.
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### Fourier Series of Aperiodic convolution of periodic functions

we were given the following classic exercise: Given two periodic signals $x(t), y(t)$ with fundamental period $T$ with Fourier series coefficients $c_m^x, c_m^y$ respectively, find the Fourier ...
509 views

### Consider an ideal low pass filter $H(\omega)$, and the input to this filter is the periodic square wave $x(t)$. Find the output $y(t)$

The solution to the problem is $$y(t) = 5 + \frac{20}{\pi} \sin(\pi t) + \frac{20}{3\pi} \sin(3 \pi t)$$ and to get that the solution says to find the Fourier series expansion of $x(t)$ and I am ...
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### Fourier series coefficient of signal when Time period is twice the fundamental period

My try: First of all I tried observing the symmetry but I did'nt find any.So I tried to calculate the fourier series coefficient of the signal like this First I differentiated the signal $x(t)$ so ...
2k views

### 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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### Efficient format for 2D signal?

I'm trying to solve the following problem. I got a "low frequency" input 2D signal over a square region. I'll collect a few samples, somewhere around 10-30 maybe, the exact sample count will be ...
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### Explanation of fundamental filtering's consequences on signal

Can anyone explain why exactly an "Overshooting" phenomena is observed when the fundamental harmonic is removed as seen on the figures? Is it technically right to call this "overshooting" at all ? If ...
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### Fourier transform

Fourier transform of a DC signal is an impulse at the origin. Now if the spectrum of a signal is the plot of the amplitudes of the respective frequencies of each harmonic, then the Fourier transform ...
241 views

### Fourier Series Coefficients

Question: The fourier series coefficients is given as: $$c_k= \begin{cases} 1 \qquad & k \ \text{ even} \\ 2 \qquad & k \ \text{ odd} \\ \end{cases}$$ the period of the signal is $T=4$, ...
4k views

### Fourier series - time shift and scaling

What will be the new Fourier series coefficients when we shift and scale a periodic signal? Scaling alone will only affect fundamental frequency. But how to calculate new coefficients of shifted and ...