# Questions tagged [fourier-series]

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### How can understand periodicity of a Signal from frequency domain representation?

Is it possible to say a signal is periodic from its frequency domain representation? A periodic signal is sum of its sinus and cosinus. Frequency translation of sinus and cosinus functions are ...
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### Effects of interchanging sine terms with cosine terms

Suppose we have a real signal $x(t)$. Now, we know that $x(t)$ can be represented as a sum of sines and cosines. w be the angular frequency. If $a(\omega)$ be the coefficients of the cosine terms, ...
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### Why are wavelet transforms (Multi Resolution Analysis) used more in practice for compression rather than Fourier series?

I know that both Fourier and wavelet can be used for compression of signals. The Fourier series guarantees that it gets the closest approximation of the original signal in the least squared sense. ...
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### Unipolar Transmission Spectrum

I am currently trying to understand mathematically the amplitude shift keying modulation technique. My question is, say I wanted to compute the Fourier series of a basic pulse train, it is quite ...
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### 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 ...
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### fourier series fitting matlab

I am using cftool in Matlab to fit time series values to Fourier model with 8 terms: ...
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A signal $$x(t)=\left|\sin(2\pi(1000)t)\right|$$ ($\left|x\right|$ is the absolute value function) is fed to an ideal low-pass filter with cutoff frequency of $1500\,\mathrm{Hz}$ to produce an output $... 0 votes 1 answer 5k views ### Fourier-series odd vs even square wave? I really need to know the difference when doing a fourier seires between even and odd square waves. I've been trying to understand but I just get the same results and the same spectrums... Is the ... 2 votes 1 answer 60k views ### Why Fourier series and transform of a square wave are different? Here is a square-wave presented by Fourier series perspective: Above coefficients shows that a square-wave is composed of only its odd harmonics. But here below a square-wave is presented by ... • 327 3 votes 3 answers 3k views ### Periodicity of Fourier series's coefficients Why exactly continious Fourier-series's coefficients aren't periodic like coefficients of discrete Fourier series (DFS)?$e^{-j2\pi}$is periodic in both sequences. • 33 0 votes 2 answers 649 views ### Discreteness and periodicity in Fourier transform Why discreteness in time / frequency domain dictates periodicity in the other frequency / time domian? For example the DTFT is perodic in frequency? Why it doesn't contain all the frequencies? Why ... 3 votes 2 answers 733 views ### Fourier series expansion of$\exp[-j2kA\sin(\omega t)]\$

I've been going through this paper where we exploit the well known Fourier expansion of the model signal as shown in the image below. I've never come across this well known fourier expansion before. ...
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### Discrete Fourier Series - Time Index

I have been trying to understand Discrete Fourier Time Series (NOT Transform). It is defined as $$a_k = \sum_{n=0}^{N-1} x[n]e^{jk\frac{2\pi}{N}n}$$ where N is the Time period and an integer (by ...
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### How we can obtain the time-integration of a sine signal?

could we calculate the below integral by the Fourier series or the Fourier transform properties? $$\int_{-\infty}^t \sin(\omega_0\tau)d\tau=?$$
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### What is the time-integration property in the Fourier series analysis?

In the continuous Fourier series properties for a periodic continuous-time signal, we have time-integration property: $$\int_{-\infty}^t x(\alpha)d\alpha \leftrightarrow \frac{a_k}{jk\omega_0}$$ ...
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### Inverse fourier transform of Hermitian function, getting an imaginary part

in the cartoon below It shows that if we take the inverse Fourier transform of a Hermitian function, real part even and imaginary part is odd we should get a purely real function in the time domain. ...
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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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