Questions tagged [fourier-series]
The fourier-series tag has no usage guidance.
42
questions with no upvoted or accepted answers
3
votes
0
answers
76
views
What happens to sidebands when they enter "negative" frequencies?
I am working with PWM signals. These signals are generated by comparing a modulating (at frequency $f_m$), and a carrier (at frequency $f_c$), as shown in the following image:
In the resulting ...
- 125
3
votes
0
answers
94
views
Improving the intuition for the 2d fourier transform
As far as I understand, the 2d fourier transform is calculated as following:
...
- 131
2
votes
0
answers
1k
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 ...
- 381
2
votes
0
answers
65
views
Power contained in a signal
Given a signal $$x(t)=16\cos(20\pi t+\frac\pi 4)+6\cos(30\pi t+\frac\pi 6)+4\cos(40\pi t+\frac\pi 3)$$how can I calculate the power contained in a frequency interval, say 12Hz to 22Hz.
The total power ...
- 169
2
votes
1
answer
398
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 ...
user33568
1
vote
0
answers
61
views
Finding $A_k$ coefficients
I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as:
$x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the ...
- 53
1
vote
0
answers
55
views
Pitch successfully changes with Phase Vocoder, but there's an issue
I've been working on a phase vocoder program. The goal is to change the pitch of a recording of my voice. While doing research on how to change pitch, I came across this from a paper on phase vocoders ...
1
vote
0
answers
67
views
What is the Fourier convolution theorem range of application (example of Dirac comb times rectangular window)?
$\DeclareMathOperator{\sinc}{sinc}$
I have questions regarding the Fourier transform of the product of functions or distributions and the range of application of the convolution theorem.
Context
When ...
- 11
1
vote
0
answers
124
views
Finding original signal $x(t)$
For given 4 conditions, I have to find out what is $x(t)$ with period of 3, and I don't know if $x(t)$ is real or not.
For fourier coefficients $x_k$,
$$1.\ x_k=x_{k+2}$$
$$2.\ x_k=x_{-k}$$
$$3.\ \...
- 103
1
vote
0
answers
105
views
Forecasting that FFT result
I have the following FFT result charts. Searching for a way to forecast the future AMPLITUDE steps from the Time Domain Plot if possible, or the next maximum/minimum deviation based on some previous ...
- 11
1
vote
0
answers
89
views
How to calculate fourier coefficients of sum of two discrete time with different fundamental periods
Assume that we have two discrete-time signals named x[n] with fundamental period 3 and fourier coefficients ak (k from 1 to 3), and y[n] with fundamental period 5 and fourier coefficients bk (k from 1 ...
- 11
1
vote
0
answers
127
views
Fourier series expansion of $ x_1(t) = \sum _{-\infty}^{\infty} \Delta (t-2n) $
I want to evaluate the Fourier series expansion of $ x_1(t) = \sum _{-\infty}^{\infty} \Delta (t-2n) $, where $ \Delta (t) $ is a triangular function defined as:
I have done the following ...
- 381
1
vote
0
answers
111
views
Is there an analogy of the Fourier-decomposition in the Laplace space to decompose a signal to a few components?
I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components.
If it would be a sum of some sinusiod waves, it would be easy to ...
- 119
1
vote
0
answers
399
views
The Fourier Transform of a periodic function and it's series
Let $X(f)$ be the Fourier transform of $x(t)$:
$$ 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}...
- 111
1
vote
0
answers
32
views
Efficient format for 2D signal?
I'm trying to solve the following problem. I got a "low frequency" input 2D signal over a square region. I'll collect a few samples, somewhere around 10-30 maybe, the exact sample count will be ...
- 11
1
vote
0
answers
7k
views
The Fourier Series, Amplitude and Phase Plot of a Saw Tooth Waveform
I am trying to find the amplitude and phase plots of the saw tooth waveform pictured.I have already computed the Fourier series of the waveform but I don't know how to derive the amplitude and phase ...
- 306
1
vote
0
answers
156
views
A Laymans Fourier transform and harmonics explanation?
Please bear with me, I know some of you will scoff but I have looked on Wiki and in various literature (see below) and can't quite get a handle on a few things.
I am a general business programmer, ...
- 111
1
vote
1
answer
77
views
On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies
It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
- 11
0
votes
0
answers
25
views
Advantages of the Karplus algorithm for sound synthesis
For a personal project I am trying to make a software to synthesize plucked and hammered string instruments. This is a whole research topic and there are already some models and algorithms such as the ...
- 1
0
votes
0
answers
43
views
Creating infinite continuous time series out of a finite discrete spectrum
I have a power spectrum $S(\omega)$: a $1 \times N$ real vector that matches frequencies from 0 to 125Hz. I would like to create a time series $S(t)$ $[-\infty<t<\infty]$ that matches this ...
0
votes
0
answers
45
views
Finding the Fourier Coefficients
Up until now, I have dealt with finding Fourier Coefficients for functions: $f(t) > 0$
Which made it convenient calculating the Fourier Analysis Integral. However, I am now presented with ...
0
votes
0
answers
47
views
What is $z[n]$ , when $Z[k]=X[2k]H[2k]$ with $y[n] = x[n]∗h[n]$ and $Z[k] = X(\omega)H(\omega)$ at $\omega = \frac{4πkn}{N}$
How do I express $z[n]$ in terms of $y[n]$, with:
$$y[n] = x[n]∗h[n]$$
$x[n]$ and $h[n]$ being 16 length sequences.
$X(\omega)$ and $H(\omega)$ are DTFT of $x[n]$ and $h[n]$
$Z[k]$ is defined as
$$Z[k]...
0
votes
0
answers
47
views
How to generate a sound closer to a saxophone using sinusoids after Fourier Transform?
Generate a sound wave of saxophone frequency and compare it to the original sound clip and play both to listen to if there is a good match.
I am trying to generate a sound closer to a saxophone using ...
0
votes
0
answers
215
views
How do I plot a phase spectrum of rectangular pulse with Matlab?
As you can see, I made a code about rectangular pulse like this. And, I plotted complex-exponential-coefficient and Magnitude-Spectrum-of-Complex-Exponential-Form, Phase-Spectrum of-Complex-...
0
votes
0
answers
151
views
Approximation of Periodic Parabolic Function by Fourier Series!
I've just tried to approximate the periodic-parabolic signal by Fourier Series. I know, this sounds a bit strange. I am just trying to figure out relationship between Fourier Series and Taylor ...
- 71
0
votes
0
answers
21
views
Square pulse test of Upwind Finite Differences
I`m analyzing the numerical methods for the 1D convection equation for stability, consistency, and accuracy. I want to see How does this square pulse move in domain and time?
Here is my code
% ...
0
votes
0
answers
59
views
How to get coefficient of the discrete fourier Series from the fourier transform
Given $X(v)$ the Discrete Fourier transform of a discrete periodic signal $x(n)$, it's possible to arrive to the $c_k$ of the Fourier series $$x(n)=\sum_{k=0}^{n-1} c_k \exp(2\pi i k t) $$ directly?
0
votes
0
answers
169
views
Rectangular Pulse Train and Sinc Function
I wanted to ask that in frequency domain the rectangular pulse is a sinc function, so is this sinc function periodic or aperiodic?
Also if signals that are continuous in time domain then they are ...
0
votes
0
answers
142
views
Can different Discrete-Time-Fourier-Series(DTFS) coefficients have the same discrete sequence in the time domain?
Please, check the following discrete periodic sequence when the period $N=2$.
$x[k]=\exp(j\frac{2\pi}{N}k), N=\text{period}$
$..., x[0]= 1, x[1]= -1, x[2]= 1, x[3]= -1, ... , N=2$
According to my ...
- 19
0
votes
0
answers
28
views
Redundancy when using Nyquist rate for a time series
I sample temperature at one sample per second (the hardware I am using takes the temperature at this rate, so this is the max I can efficiently sample.) The Nyquist rate for this signal would be 2 ...
0
votes
0
answers
40
views
How to apply FT to real-life signal that labeled in seconds, not radians
In training examples we always do a transformation on signals which have t-scale in labeled in radians.
I understand that Pi is just a number, but I still have some troubles to understanding how to ...
- 57
0
votes
0
answers
43
views
frequencies in frequency spectrum with no correlation together
I have a lack of understanding of the following questions:
If I have a signal from a motor that is recorded with an accelerometer. And the rotating speed of the motor is 150Hz(rpm 9000 ), I can see in ...
- 141
0
votes
0
answers
107
views
express pass band filter as sum of low pass filter
I have to find impulsive response of an ideal pass band filter, but I have a problem to express $$ H_{BP} (f) $$ as a sum of $$ H_{LP} (f) $$. I mean that $$ H_{BP} (f) = rect ( \frac{f-f_0}{B} ) + ...
- 309
0
votes
0
answers
549
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 ...
- 309
0
votes
0
answers
181
views
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 ...
- 381
0
votes
0
answers
76
views
the DFT of a periodic signal represented by a fourier series
If I have a signal represented by a Fourier series(like in the photo), which is sampled with $T_s$:
$$x[n]=x(t=nT_s) = \sum_{m=-\infty}^{\infty}a[m]e^{j2\pi m(nT_s)/T_0} $$
How do I find its DFT? I ...
- 11
0
votes
0
answers
78
views
Approximating the fourier coefficients from a discrete time signal
Suppose I have a discrete time signal $x_t$ sampled with a frequency $f_s$. I know that if I take the discrete fourier transform of the signal and compute the power, I can easily (by visual ...
- 351
-1
votes
1
answer
96
views
transform signal
Hello everyone I need help solving a Fourier transform for the given signal, I know it will be a frequency convolution for the first function it will be a window function and for the second function I ...
-1
votes
1
answer
104
views
Output of LTI (in time and frequency $\omega$ domain) : when input goes through LPF
I would like to raise a mathematical question :
Let's say we are been given :
$$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\
0 & \textrm{otherwise} ...
- 147
-1
votes
1
answer
85
views
Why do we scale bins in FFT in this code?
Hi I am learning FFT I am confused about this bit of code:
what is the reason for scaling the sampling frequency and what is bin scale and why and when do we use it? thank you
...
-1
votes
1
answer
489
views
Fourier Coefficients
Consider the signal
$$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 ...
-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 $x(t) =
> \cos4t +\sin8t+3$?
- 11