# Questions tagged [fourier-series]

The tag has no usage guidance.

286 questions
Filter by
Sorted by
Tagged with
1 vote
93 views

### 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 ...
298 views

### Signal's Fundamental Frequency is different from Plotted Signal

I've been attempting to plot the following function using MATLAB: $$x(k)=\sum_{n=11}^{50} \sqrt{n} \sin (2n\pi k) +\sum_{n=1}^{40}\sqrt{n} \sin (3n\pi k)$$ Note that $k$ is a continuous variable....
1 vote
643 views

### 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 ...
180 views

### 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 ...
411 views

### 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 ...
966 views

11k views

### 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 ...
452 views

### 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*} ...
3k views

7k views

### 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(\...
4k views

### 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 ...
175 views

### 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 ...
1 vote
134 views

### 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 ...
107 views

257 views

### 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 ...
1 vote
132 views

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 $1/... 2 votes 3 answers 343 views ### Can I study continuous time Fourier Transform and treat the rest as special cases Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to Lapace transform, Z transform, DTFT, DFT, Fourier sequence ... 4 votes 1 answer 182 views ### Signal Processing using Fourier Transform How can I derive the fourier transform of ... 3 votes 2 answers 2k views ### A clarinet has no even harmonics. What would produce no odd harmonics? According to this link, the waveforms of clarinets do not have even-numbered components in their harmonic series: A closed cylindrical air column will produce resonant standing waves at a ... -1 votes 1 answer 191 views ### Fourier series qn determine the fourier series coefficients Can someone please help me with this Fourier series question: Determine the Fourier series coefficients of$x(t)$given as$x(t) = > \cos4t +\sin8t+3$? 0 votes 1 answer 1k views ### Why does Fourier Series have$\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)...
thanks for taking the time to help with this problem! I have to prove the time-scaling property: $$x_{(m)}[n] = \begin{cases} x[n/m], & n=0,\pm m, \pm 2m,...\\ 0, & otherwise \end{cases}$$ ...