Questions tagged [fourier-series]
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319 questions
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Why does the frequency spectrum "fill in" under an existing envelope when you increase the period to go from Fourier Series to Fourier Transform?
I am trying to understand this concept (and everything in Signals and Systems) intuitively. If we look at a typical square wave to box example of this, I understand that when instructors explain ...
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Fourier series coefficients for a discrete signal with fractional fundamental time period
Need to compute Fourier series coefficients for following discrete time signal;
$$x[n] = \cos(\tfrac{11\pi}{4}n - \tfrac{\pi}{3}) \tag 1$$
My approach
My plan is to use the exponential expansion for $...
- 199
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Checking periodicity for a continuous time periodic signal
I am working on finding Fourier Transform for a signal given by
$$ x(t) = \sum\limits_{n=-\infty}^{\infty} e^{\vert t-2n \vert} $$
I got a hint that this sign is periodic with period, $T = 2$.
But to ...
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Fourier coefficients of time-scaled signal
Given a periodic signal $x(t)$, with period $T =
\frac{2\pi}{\omega_0}$ so that $$ x(t+T) = x(t) \qquad \qquad
\forall t \in \mathbb{R} $$ $$ x(t) =
\sum\limits_{k=-\infty}^{\infty} c_k \, e^{...
- 199
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Converting all sine waves in a signal to sawtooth waves
I'm trying to write a program in Matlab that takes the frequency representation of a signal and replaces each sine wave component with a sawtooth wave component of equal frequency, amplitude and phase....
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309
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Time reversal flips the Fourier coefficients
Given a periodic signal $x(t)$, with period $T = \frac{2\pi}{\omega_0}$ so that
$$ x(t+T) = x(t) \qquad \qquad \forall t \in \mathbb{R} $$
$$ x(t) = \sum\limits_{k=-\infty}^{\infty} c_k \, e^{j k \...
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Harmonic analysis
There is a motor within a housing and I measured acceleration with accelerometer attaching on the housing, while it driving. The FFT result of the acceleration shows 2X is bigger than 1X. As a ...
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How can compression remove a “softer” sound if the microphone only records one waveform?
I was reading about audio lossy compression, and I came across an example saying that if a softer sound plays at the same time as a louder sound, the softer one can be removed.
But I’m a little ...
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Dimensionally consistent discrete and continuous Fourier Transforms
If a signal $x(t)$ is sampled $x[n] = x(n\Delta t)$, then the discrete Fourier transform $X[k]$ of $x[n]$ should approximate the continuous Fourier transform $X(f)$ of $x(t)$ up to linear rescaling.
[...
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Why does the reconstruction signal repeat and has artifacts near the switching points? [python assignment]
I have the discrete window signal $a\left[n\right]=\begin{cases}1 & \left|n\right|<100\\0 & 100\leq\left|n\right|\leq1000\end{cases}$ with the respective Fourier coefficients $a_k=\frac{\...
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What's causing this weird jump in these phase graphs of Fourier coefficients?
from an assignment in signal processing in Python. It's all done in Python (through Google Colab) with the libraries cmath, numpy, and matplotlib alone.
Signal a is a window signal where $a\left[n\...
- 141
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why am i getting the exact opposite of what my calculations show me?
from an assigment in python about mostly the connection between a signal and its Fourier coefficients, im asked to plot the wave that stems from $b_{k=10}$ in my case it's suposed to be $b_{10}\cdot e^...
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help with python HW about Fourier coefficients - shifting is being calculated wrongly?
can someone help me understand what I'm doing wrong here? (using python only with cmath, numpy and matplotlib)
I received a simple "window" signal (called a[n]) which I transformed into the ...
- 141
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Must band-limited signals have a finite Fourier series?
Let $x(t)$ be a periodic signal with period $T$ that is a band-limited signal and let
$$
x(t)=a_0+\sum_{k=1}^{M}a_k\cos\left(2\pi f_k t+\phi_k\right)
$$
be its Fourier series, where $f_k = k \, f_1 = \...
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What is the Fourier transform of a train of square waves? [duplicate]
I've read that the Fourier series is used for periodic functions, and that the Fourier transform is used for both periodic and aperiodic functions. Sines and cosines are periodic and their Fourier ...
