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Questions tagged [fourier-series]

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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 $|\...
Piratemetaldrinkingcrew's user avatar
0 votes
1 answer
59 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 ...
amoghfyi's user avatar
0 votes
1 answer
77 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 ...
amoghfyi's user avatar
-1 votes
1 answer
50 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 ...
DSP_CS's user avatar
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0 votes
1 answer
89 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.....
Wireshark's user avatar
2 votes
2 answers
119 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)...
eball's user avatar
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6 votes
2 answers
866 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 ...
endyx's user avatar
  • 63
1 vote
1 answer
210 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 ...
amoghfyi's user avatar
0 votes
1 answer
185 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 ...
amoghfyi's user avatar
0 votes
1 answer
33 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}{...
Ray Siplao's user avatar
0 votes
0 answers
40 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 ...
hamza nawaz's user avatar
1 vote
1 answer
72 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 ...
MOHAMED SALHI's user avatar
0 votes
1 answer
213 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{\...
MOHAMED SALHI's user avatar
1 vote
1 answer
83 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 ...
Sidharth Ghoshal's user avatar
1 vote
1 answer
99 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 ...
Danialz's user avatar
  • 113
1 vote
1 answer
217 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 ...
Kushagr Jaiswal's user avatar
0 votes
0 answers
26 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 ...
Agustín's user avatar
3 votes
1 answer
243 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} \...
Maghreb_1911's user avatar
2 votes
1 answer
46 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 ...
NokiYola's user avatar
  • 507
3 votes
3 answers
505 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 ...
Fern Mendiz's user avatar
1 vote
1 answer
50 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 ~\...
ABB's user avatar
  • 387
2 votes
1 answer
76 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 ...
Ait-Gacem Nabil's user avatar
1 vote
1 answer
92 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\...
user avatar
1 vote
0 answers
74 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 ...
Anna Smith's user avatar
3 votes
1 answer
124 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 ...
Miumiu's user avatar
  • 75
0 votes
0 answers
64 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 ...
JellyTree's user avatar
3 votes
0 answers
165 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 ...
Olayo's user avatar
  • 125
0 votes
1 answer
115 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 ...
Olayo's user avatar
  • 125
0 votes
0 answers
90 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 ...
Adrian Surani's user avatar
0 votes
1 answer
497 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 ...
BigChungus443's user avatar
1 vote
0 answers
85 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 ...
BigChungus443's user avatar
0 votes
1 answer
312 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&...
BigChungus443's user avatar
2 votes
1 answer
570 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 ...
BigChungus443's user avatar
0 votes
2 answers
966 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 ...
ozgun can's user avatar
3 votes
0 answers
222 views

Improving the intuition for the 2d fourier transform

As far as I understand, the 2d fourier transform is calculated as following: ...
dmmpie's user avatar
  • 131
1 vote
1 answer
116 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 = ...
Gze's user avatar
  • 640
0 votes
2 answers
84 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 ...
Nervous Hero's user avatar
0 votes
0 answers
382 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-...
user299980's user avatar
0 votes
1 answer
193 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?
Luca Leone's user avatar
0 votes
1 answer
407 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 ...
DSP_CS's user avatar
  • 1,870
1 vote
0 answers
118 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 ...
kapytaine's user avatar
0 votes
3 answers
457 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 ...
Doohyeon Won's user avatar
2 votes
2 answers
2k 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 ...
average_discrete_math_enjoyer's user avatar
0 votes
4 answers
454 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 ...
Daron's user avatar
  • 101
0 votes
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 ...
Judita's user avatar
  • 3
0 votes
1 answer
257 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 & \...
ian's user avatar
  • 1
1 vote
1 answer
151 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-...
Borut Flis's user avatar
2 votes
1 answer
343 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 ...
Mathpdegeek497's user avatar
0 votes
0 answers
215 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 ...
LunaLOVEGOOD's user avatar
1 vote
1 answer
709 views

Prove Convolution Property for DFT using duality

If $x_1[n]$ and $x_2[n]$ are finite length sequences of length $N$ $$\mathcal{DFT}(x_1[n] \circledast x_2[n]) = X_1[k]X_2[k]$$ where $X_1[k]$ and $X_2[k]$ are the DFTs of$x_1[n]$ and $x_2[n]$, ...
Orpheus's user avatar
  • 211

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