Questions tagged [fourier-series]
The fourier-series tag has no usage guidance.
188
questions
0
votes
1answer
36 views
What kind of periodic signals cannot be represented with the Fourier Series?
Oppenheim et al. state in Signals and Systems that there exist periodic signals which cannot be represented with Fourier series. What signals are these?
Although Euler and Lagrange would have been ...
0
votes
1answer
51 views
How to do the Fourier Transform of bounded function?
I was trying to solve a Fourier transform of a function using the properties of Fourier transforms. The function is given as:
$\frac{At}{2}$ for $-2<t<2$ and $0$ for all other $t$. Doing the ...
0
votes
2answers
159 views
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 ...
13
votes
2answers
6k views
A good mathematical explanation of Gibbs phenomenon
I was explaining to someone how Fourier series work in context of constructing signals that are not everywhere differentiable, e.g. square waves, sawtooth waves, etc. When I mentioned the Gibbs ...
1
vote
1answer
657 views
RMS of absolute-valued sinusoid
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 $...
2
votes
2answers
65 views
Inverse Fourier transform Of a triangular impulse
I have to find the expression of this graphic and after find the inverse Fourier transform of it. First of all I found that the expression of the graphic is $$ X(f) = \frac{1}{2} tri (\frac{f+f_0}{B}) ...
0
votes
0answers
44 views
express pass band filter as sum of low pass filter
I have to find impulsive response of an ideal pass band filter, but I have a problem to express $$ H_{BP} (f) $$ as a sum of $$ H_{LP} (f) $$. I mean that $$ H_{BP} (f) = rect ( \frac{f-f_0}{B} ) + ...
0
votes
0answers
49 views
Energy of a sinc signal
My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me
$$ x(t)=\operatorname{sinc}(t) $$
and
$$ s(t)=x(t-T)$$
and I found that ...
0
votes
2answers
66 views
Fourier transform properties
I have to find the Fourier transform of $$ x(t)= \frac{1}{T}e^{-\frac{t-T}{T}}u(t-T) $$
First I applied traslation property , so $$ F[x(t-T)] = X(f) e^{-i 2 \pi f T} $$
after I applied time scaling ...
3
votes
1answer
76 views
Fourier coefficients of 1/(1+it)
I have to find the Fourier coefficients of $$ \frac{1}{1+ t^{2}} $$ I tried with $$ \frac{1}{T}\int_{0}^{T} \frac{1}{1+it}e^{-i 2 \pi f_0 T } $$ but I should do at least two integrals by parts , so I ...
1
vote
1answer
65 views
Fourier coefficients of odd and even part of a signal
I have this signal and I have to find the Fourier coefficients of the odd and even part. First I found that $$ x_p(t) = \frac{1}{2} ( x(t) + x(-t) ) $$ and I made the graphic of this part and I ...
4
votes
1answer
417 views
Estimate the Discrete Fourier Series of a Signal with Missing Samples
Assuming we have a discrete signal $ { \left\{ x \left[ n \right] \right\}}_{n = 1}^{N} $.
Which has a Discrete Fourier Series.
Now, assume I'd like to estimate its Discrete Fourier Series ...
0
votes
1answer
23 views
E of a signal using Rayleigh
I have to find The energy of a signal using Rayleigh th. the signal is $$ x(t) = A e^{-At } u(t) $$ assuming A>0
Using the classic definition of E , I found that it should be $$ \frac{A}{2} $$
Using ...
0
votes
2answers
119 views
Fourier coefficients of |A cos (x)|
I have to find Fourier coefficients of $x(t) = |A \cos (2 \pi f t )|$. The problem also give me $y(t) = |x(t)|$. To find Fourier coefficients I wrote
$$ \frac{1}{T_0} \int_{0}^{T_0} |A \cos (2 \pi f ...
-1
votes
1answer
17 views
Discrete signal - fourier transform coefficient period [closed]
if I have an example signal in the picture, how can i decide its period?
1
vote
1answer
566 views
Consider an ideal low pass filter $H(\omega)$, and the input to this filter is the periodic square wave $x(t)$. Find the output $y(t)$
The solution to the problem is $$y(t) = 5 + \frac{20}{\pi} \sin(\pi t) + \frac{20}{3\pi} \sin(3 \pi t) $$ and to get that the solution says to find the Fourier series expansion of $x(t)$ and I am ...
0
votes
1answer
142 views
Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals
If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away?
Suppose we are given the ...
1
vote
0answers
19 views
How to calculate fourier coefficients of sum of two discrete time with different fundamental periods
Assume that we have two discrete-time signals named x[n] with fundamental period 3 and fourier coefficients ak (k from 1 to 3), and y[n] with fundamental period 5 and fourier coefficients bk (k from 1 ...
0
votes
0answers
26 views
I want to invert my fourier transform components to waves again
Hi I am using R to analyze some data
I basically did fft(data) and got a vector of complex numbers but from that now I want to remove certain harmonics from my actual wave but how do I convert one of ...
0
votes
2answers
40 views
Complex signal sine reconstruction
Noob here, I read that any signal can be made by putting together sines and cosines, it always shows some kind of basic harmonic wave with constant amplitude such as square wave.
I understand that ...
1
vote
1answer
89 views
Understanding Fourier Transforms in abstract math terms
I am having a hard time implementing a method that computes Fourier transform coefficients for the complex form using the trapezoid rule.
I have floated questions in the math and stackoverflow ...
1
vote
1answer
43 views
Fourier Series representation of a signal
Use the defining equation for the Fourier Series coefficients to evaluate the Fourier Series representation of the following signal:
$$x(t)=\sum_{m=-\infty}^{+\infty}=(\delta(t-m/3)+\delta(t-2m/3))$$...
0
votes
0answers
20 views
Which frequency bins give the best interpolation for the derivative of a function?
A function $u:[0,2\pi]\to\mathbb R$ sampled over $N$ equidistant points $\theta_j=(2\pi/N)j,\, j = 0, \dots, N-1,$ can be interpolated by a set of functions $\{u_{k_0}\}$ enumerated by integers $k_0\...
1
vote
0answers
34 views
Fourier series expansion of $ x_1(t) = \sum _{-\infty}^{\infty} \Delta (t-2n) $
I want to evaluate the Fourier series expansion of $ x_1(t) = \sum _{-\infty}^{\infty} \Delta (t-2n) $, where $ \Delta (t) $ is a triangular function defined as:
I have done the following ...
2
votes
0answers
59 views
Fourier series representation of a full wave rectifier output
I am trying to compute the Fourier series representation of a full wave rectifier output.
The equation of the signal is:
$ x_8(t) = | \cos (2 \pi f_o t) $ |
I have tried to find the Fourier series ...
0
votes
2answers
101 views
Fourier Transform: interpretation of continuous spectrum at specific frequencies
B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform:
When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
0
votes
2answers
217 views
Aliasing when interpolating with DFT?
I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me.
I have created a noiseless signal as:
...
4
votes
4answers
823 views
Is Fourier series a sampled version of Fourier transform?
I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
1
vote
1answer
107 views
Proof of First Difference Property for Fourier Series
I am having trouble with deriving a proof for the first difference property for the Fourier Series.
Here is my attempt at the derivation:
$$
y[n] = x[n] - x[n-1]
$$
Fourier Series Representation:
...
5
votes
4answers
3k views
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 ...
0
votes
0answers
66 views
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 ...
-1
votes
1answer
40 views
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 ...
4
votes
3answers
6k views
How to Remove the Periodic Oscillations from a Signal
The task that I have is to remove the annual and semiannual oscillation from a set of temperature measurements, taken over several years, by means of least squares method.
I found the method ...
1
vote
3answers
453 views
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 ...
0
votes
3answers
202 views
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 ...
1
vote
1answer
117 views
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 ...
0
votes
1answer
64 views
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 ...
6
votes
2answers
2k views
Intuition behind the scaling property of Fourier Transforms
The Fourier transform of $f(ax)$ is $\frac{1}{|a|}F(\frac{u}{|a|})$. So the frequencies are scaled horizontally but the magnitudes are also scaled when the graph of $f$ is scaled horizontally.
On the ...
0
votes
0answers
11 views
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 ...
1
vote
2answers
48 views
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 ...
4
votes
1answer
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 ...
0
votes
2answers
146 views
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 ...
1
vote
0answers
51 views
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 ...
1
vote
0answers
236 views
The Fourier Transform of a periodic function and it's series
Let $X(f)$ be the Fourier transform of $x(t)$:
$$ X(f) \triangleq \mathscr{F}\Big\{ x(t) \Big\} = \int\limits_{-\infty}^{\infty} x(t)\,e^{-j 2 \pi f t} \ \mathrm{d}t $$
$$ x(t) \triangleq \mathscr{F}...
0
votes
0answers
73 views
How to find Fourier series coeffecients of convolution of two periodic continuous functions with different time periods?
Above given is my solution Plz check if it is correct and I got struck at last step .Plz help
3
votes
2answers
105 views
Why do waveforms that are symmetrical above and below their horizontal centerlines contain no even-numbered harmonics?
All About Circuits site states that waveforms that are symmetrical above and below their horizontal centerlines contain no even-numbered harmonics. Can somebody explain this mathematically, or point ...
1
vote
1answer
22 views
Sampling Frequency and Spectral Regrowth
Sampling a cosine wave of 10 Hz at Fs = 64 and number of samples Ns = 256
I setup my time vector for the cosine wave as n=(0:Ns-1)*(1/Fs)
If I change the sampling frequency from 64 to 64.0005 I get ...
1
vote
1answer
793 views
How can I improve my fit of cosines to periodic data using Python?
I have a space-separated csv file containing a measurement. First column is the time of measurement, second column is the corresponding measured value, third column ...
1
vote
2answers
212 views
A question on Fourier Series and the frequency of the sinusoids
On studying about Fourier series, I encountered 2 doubts:
How is it that a non-periodic function has a Fourier series?
When expressing a periodic function as summation of sinusoids, why is the ...
1
vote
4answers
1k views
Formulas of the Fourier transform family
It has annoyed me that there doesn't seem to be a source online where the complete complex Fourier transform family is presented with every variable defined. The lack of definitions can be a nuisance ...
robert bristow-johnson
13k3 gold badges20 silver badges54 bronze badges
