# Questions tagged [fourier-series]

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### Fourier Transform: interpretation of continuous spectrum at specific frequencies

B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform: When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
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### Aliasing when interpolating with DFT?

I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me. I have created a noiseless signal as: ...
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### Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
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### Proof of First Difference Property for Fourier Series

I am having trouble with deriving a proof for the first difference property for the Fourier Series. Here is my attempt at the derivation: $$y[n] = x[n] - x[n-1]$$ Fourier Series Representation: ...
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### 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 ...
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### How do I obtain the fourier series coefficients for a signal obtained by multiplication of two signals of different frequency?

What i assume here is that LCM of time periods of the two taken signals exist that is signals periods are not like pi/2 and 1 but are rather like 1 and 2 (just an example) I am given fourier series ...
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### How to get Fourier coefficients to draw any shape using DFT?

I'm teaching myself about Fourier Series and the DFT and trying to draw a stylised $\pi$ symbol by fourier epicycles as detailed by Mathologer on youtube (from 18:39 onwards), and the excellent ...
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### integration property of fourier series

Please help me sort this issue out. The integration property in Fourier series is as follows: So, for proving the above property, i took this approach: This is where my doubt is. Some books and ...
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### Phase diagram of a rectangular pulse with Fourier Series - help understanding

I understand perfectly fine how to plot the magnitude of a Fourier series, but I'm having serious trouble understanding how to plot the phase spectrum. Below is a picture of a rectangular pulse. The ...
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### fftshift in MATLAB with even number of data points in double sided spectrum

I have a question with reference to this Table. With even N, the frequency axis extremes should be $\pm$Fs/2, where Fs is the sampling frequency. However in the array we have only one value ...
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### Is there a generalized method to get the input with the given output and the impulse response?

$y(t)=y(t+12), y(t) = x(t) \ast h(t)$ The continuous time signal output $y(t)$ is a periodic square wave, 50% duty cycle pulse. The impulse response is a box function.($A = 1, T = 2$) By using ...
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### 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 ...
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### inner product zero?

I am studying about Fourier series from book"Signals and Systems Laboratory with MATLAB" I came across topic "Orthogonality of Complex Exponential Signals" I am confused in case when m=k, will the ...
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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 Transforms, symmetry, real/imaginary

I was hoping to clarify if the following was correct: -a real function (neither even nor odd) in time exhibits conjugate symmetry in frequency, so the real part of the frequency response is even, and ...
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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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### 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 ...