Questions tagged [fourier-series]
The fourier-series tag has no usage guidance.
302
questions
1
vote
1
answer
90
views
I want to understand the fundamental difference/connection between DFS, DFT and DTFT
I'm an EE student and I seem to miss some basic concept of my Signals course.
We have learned about all the different Fourier methods available, but I don't seem to find a difference/understand it.
As ...
- 11
1
vote
1
answer
136
views
Don't we need both negative and positive discrete complex exponentials to make a real discrete time signal?
For a continuous time periodic signal , the Fourier spectrum has both negative and positive complex exponentials in equal numbers ,but I have seen for some discrete time periodic signals it is not the ...
0
votes
1
answer
33
views
why we don't get equal number of negative and positive complex exponentials for the DTFS of a discrete time periodic signal?
When we compute the Discrete time Fourier series of a discrete time periodic signal , why don't we get the same number of negative complex exponentials and positive complex exponentials ?
Even though ...
1
vote
2
answers
85
views
Fourier series - finding its period from frequency representations
I’ve been given the following signal:
$$X^F(\omega) = \sum_{n=-\infty}^{\infty} 2\pi a[n] \delta(\omega - \omega_0 n)$$
and I was asked to:
find it’s period
given $|X^F(\omega)| \ne 0$ only at $|\...
0
votes
1
answer
73
views
Why the Discrete time fourier series coefficients of a real discrete time periodic signal are not symmetric about y axis?
If the signal is something like cos(πn/3) , we get the two DTFS coefficients that are symmetric about y axis and the resulting frequency spectrum is an even function .
Now take the example given in ...
- 23
0
votes
1
answer
124
views
Is the magnitude spectrum of the Discrete Time Fourier Series of a Discrete Time periodic Signal , an even Function?
We know that the magnitude spectrum of a continuous time fourier series representation of a real periodic signal is an even function (i.e. symmetric about y axis). Does this hold true for discrete ...
- 23
-1
votes
1
answer
54
views
Result of complex exponential fourier series approximation and trignometric fourier series approximation are not exactly same in MATLAB?
I have a signal and i am trying to observe its approximations using complex exponential fourier series and trignometric fourier series but i am not getting exactly same result(graph of trignometirc ...
- 1,918
0
votes
1
answer
96
views
what will be the DC component of this function? [closed]
My answer is that the signal can be splitted into 2 regions, and cancel out the negative and positive areas under the integral, based on the definition
Needed some validation on this analysis
Thanks.....
- 13
2
votes
2
answers
177
views
What is the difference between the DFS (Discrete Fourier Series) and DTFS (Discrete-Time Fourier Series)
I'm looking at two different books written by Oppenheim. In Discrete-Time Signal Processing (source 1) he defines the DFS to be:
where, $W_N=e^{-j(2\pi/N)kn}$ , while in Signals and Systems (source 2)...
- 131
6
votes
2
answers
912
views
How to know if a continuous function can be represented by a finite sum of sinusoids?
I have a lack of mathematical knowledge, and notably in mathematical vocabulary, so maybe a similar question exists but with a different wording.
What I want to know, is actually how to know if a ...
- 63
1
vote
1
answer
266
views
Are complex exponentials real thing?
Is there any physical significance of complex exponentials.
I mean can we produce them like how we can produce sinusoidal signals using a signal generator?
OR are they just pure mathematical ...
- 23
0
votes
1
answer
373
views
Can someone explain me how the phase spectrum of trigonometric fourier series is related to phase spectrum of exponential fourier series of a signal?
Suppose we take a periodic signal and perform fourier analysis over it . Now we have two ways of representing the fourier series of this particular signal , one is trigonometric fourier series and ...
- 23
1
vote
1
answer
43
views
Relationship between IDFT and discrete Fourier series?
I want to know how IDFT
$$x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k\cdot e^{\frac{i 2 \pi}{N} k n}$$
is related to discrete Fourier series (Eq. 3)
$$x_{_N}(n) = \sum_{k=-N}^N C_k \cdot e^{\frac{i 2 \pi}{...
- 113
0
votes
0
answers
42
views
Separating 'heart sound' from 'lung sound'
I have audio files recorded from electronic stethoscope and in those files I want to filter out heart sounds and retain just the breathing sounds. How can I do this using just the signal processing ...
1
vote
1
answer
83
views
Relationship between fourier transform and fourier series
Let
$$x(t) = A\sin(2 \pi f_0 t + \alpha)$$
its Fourier transform is given by $$ X(\omega) = \frac{A \pi}{i}(e^{ia}\delta(\omega-2\pi f_0) - e^{-ia}\delta(w+2\pi f_0)). $$
the Fourier series complex ...
- 125
0
votes
1
answer
280
views
Magnitude and phase spectrum of a periodic signal
Let the following T-periodic signal :
I found that
$$ x(t) = \frac{A \cdot t}{T} \qquad 0 \le t < T $$
and its Fourier series is :
$$ x(t) = \frac{A}{2} - \frac{A}{\pi} \sum_{n=1}^\infty \frac{\...
- 125
1
vote
1
answer
85
views
Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?
Suppose you have a function that can be described as $$f(s) = \sum_{n=0}^{\infty} a_n e^{f_n s}$$ where each $f_n$ is a complex number. I am looking for a transform $T$ to act on $f$ which produces a ...
- 121
1
vote
1
answer
102
views
Finding a discrete signal using some information about its Fourier coefficients
I'm struggling to solve the following question. I've solved it partially, but I can't get complete it.
We have the given information about a signal of the form ...
- 113
1
vote
1
answer
266
views
Complex exponential Fourier series coefficient of periodic convolution
Let the complex exponential Fourier series coefficients of two periodic signals $x_1(t)$ and $x_2(t)$ be $C_{1n}$ and $C_{2n}$, respectively, with $T_0$ being the fundamental time period of both the ...
- 113
3
votes
1
answer
298
views
Fourier transform of a time discrete signal
I would like some help to better understand the Fourier transform of a discrete time signal. My doubts are:
The sampling of a signal can be seen as $x_s(t)=x(t) \cdot
\sum_{k=-\infty}^{+\infty} \...
- 85
2
votes
1
answer
49
views
positivity of the spectrum of quasi-stationary signals
I am working on the "System identification : theory for the user" by Lennart Ljung (freely available here) and it is one of these books which contains exercises but no answers... My exercise ...
- 507
3
votes
3
answers
530
views
Trying to understand how to get this basic Fourier Series
I'm sorry if this kind of question isn't allowed, but I'm starting to learn Fourier series and I'm still not entirely sure what's going on... in this specific case, I'm trying to find the Continuous ...
- 43
1
vote
1
answer
52
views
Can we control the maximum norm of a continuous signal whose finitely many Fourier coefficients are fixed?
Let us denote $C_{2\pi}$ by the set of all $2\pi$-periodic continuous signals $x:\mathbb{R}\to \mathbb{R}$.
Fix $n\in \mathbb{N}$ and put
$$\Lambda_n=\{y\in C_{2\pi}: \mathcal{F}(y)[k]=0 ~\...
- 387
2
votes
1
answer
88
views
Discrete Fourier series of an odd signal
Assuming the signal shown below :
I have found an expression for fourier series coeffecients as the following:
$$a_{k} = \frac{1}{5}+\frac{j}{5}\sin{\frac{2\pi}{5}k}$$
Which matches with what the ...
- 123
1
vote
1
answer
93
views
Is my solution correct?
$\textbf{Question:}$
$y_a(t)$ is a rectangular waveform defined as:
$$\
y_a(t) =
\begin{cases}
2 &t \in [0,1/25)s\...
user64710
1
vote
0
answers
80
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
3
votes
1
answer
127
views
Fourier coefficients of two discrete-time signals of different periods
I'm trying to understand the Fourier series coefficients of the sum of two discrete-time periodic signals.
Consider two discrete-time periodic signals $x[n]$ and $y[n]$. $x[n]$ has period $N$, its ...
- 75
0
votes
0
answers
82
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 ...
3
votes
0
answers
187
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 ...
- 135
0
votes
1
answer
126
views
Bandwidth of cosine of bandlimited signal
I have a signal $x(t)$ with bandwidth $B_x$, and I am taking its cosine to create $y(t) = cos(x(t))$. After checking the spectrum with FFT, it seems that $y(t)$ is also bandlimited. But, is there a ...
- 135
0
votes
0
answers
101
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
1
answer
563
views
How to reconstruct original signal using IFFT after cutting past Nyquist limit
I'm working on a pitch shifting program. Everything works up to the point where I try to do the IDFT. Because I cut the DFT array past the Nyquist limit, when I run the IDFT, I don't get the same ...
1
vote
0
answers
99
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 ...
0
votes
1
answer
366
views
How to change fundamental frequency with DFT?
I'm working on a voice changer. My plan is to make it so that it can change your voice in various different ways, but right now I'm just trying to make it change your voice to "chipmunk voice&...
2
votes
1
answer
636
views
How to Find "pitch" from Fourier Series
The end goal of my project is to create an autotune program, But the problem I'm trying to solve right now concerns finding the pitch of someone singing a note. I have written some code that performs ...
0
votes
2
answers
1k
views
Fourier transform of periodic functions
The Fourier transform is derived from the Fourier series by considering a non-periodic signal, thinking of it as a infinitely long periodic signal, putting it into the Fourier series and making this ...
3
votes
0
answers
243
views
Improving the intuition for the 2d fourier transform
As far as I understand, the 2d fourier transform is calculated as following:
...
- 131
1
vote
1
answer
125
views
Can I reduce the complexity of multiplication with FFT if the input vector is repeating?
I have a Fourier matrix $F$ with size $N \times N$, such that $y = F \times x$, if I have the vector $x$ contains four identical parts, for example $x = [x_1, x_2,x_3,x_4]’$ and $x_1 = x_2 = x_3 = ...
- 640
0
votes
2
answers
92
views
Sampling of the DTFT causes the inverse transform to become periodic?
As you can see the above equation, DTFT is calculated from sample x[n] which is discrete sample of x(t).
But calculated X(w) is continuous, even though it is calculated from discrete value of x[n] as ...
0
votes
0
answers
448
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
1
answer
204
views
What's the difference between male and female voice? [duplicate]
If I record the voice of a man and a woman, what are the main differences I get in the various spectra and harmonics in Fourier analysis?
- 15
0
votes
1
answer
438
views
Confusion understanding Fourier series line spectra?
I am reading book signals and systems Laboratory with MATLAB where I am studing chapter 5, Fourier series and i trying to understand magnitude spectrum and phase spectrum but i have certain confuisons ...
- 1,918
1
vote
0
answers
127
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
0
votes
3
answers
513
views
What is the reason of existence of Fourier transform? (Why we use Fourier transform?)
I'm currently trying to understand Fourier transform and I've got curious about why Fourier transform exists.
Let's suppose that we have a 10 seconds of non-periodic wave. For example:
As far as I ...
- 57
2
votes
2
answers
3k
views
Proving real and odd function has imaginary and odd Fourier Transform
Cheers, I am trying to prove that a real and odd function/signal has imaginary and odd Fourier Transform. Although it seems fairly easy, I can't find a way to achieve it, and searching online hasn't ...
0
votes
4
answers
583
views
Are there Fourier methods for VERY low frequency repeating signals?
Suppose I have a very low frequency pattern of sound. For example a 10 second music file. Then 10 seconds of silence. Then the same 10 second music file repeated again. The whole sequence repeats ...
- 101
1
vote
1
answer
2k
views
How to apply Butterworth high pass filter in the frequency domain?
I have a time series of measurements which I want to high pass with Butterworth filter.
Python scipy package has a built in function for Butterworth filter (signal.butter) and I know how to apply it ...
- 13
0
votes
1
answer
399
views
Fourier Series of a piecewise function
I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
- 1
1
vote
1
answer
157
views
How to interpret Fourier transform?
I am very new to this topic.
I ran a Fourier transform with the scipy fft function.
I than plotted the return values:
I am assuming the x-axis means how many cycles there are in all the data and y-...
- 115
2
votes
1
answer
401
views
Fourier transform of shifted periodic function
Assuming $x(t)$ is a periodic function of period $T$ and having the Fourier transform $X(\omega)$, it is required to calculate the Fourier transform of the signal $x(t)+x(t-T)$. Since x(t-T) is equal ...
