Questions tagged [fourier-series]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
-2
votes
1answer
89 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 ...
0
votes
1answer
223 views

What is the exact meaning of the output of the Discrete Fourier Transform

I'm fairly new to the subject, but so far my understanding that this would be a transform you could use to go from a discrete set of data, say [1, 0, 1, 2] to a continuous sinusoidal function in the ...
0
votes
1answer
331 views

Inverse Discrete-Time Fourier Transform of $X(Ω)=jΩ$

I am trying to solve it by using the properties but I can’t seem to find the same solution as on my book.
0
votes
1answer
85 views

Fourier components of $\cos(2\pi f_1t)$

I have the signal $s(t) = \cos(2\pi f_1t)$ and I am looking for its components vs the Fourier basis, over the interval $[0, T]$. The formula for computing the coefficients is $$ s_n = \int_{t_0}^{t_1} ...
2
votes
1answer
506 views

Fourier coefficients of product of two periodic signals

question: If $x(t)$ and $y(t)$ are two periodic signals(both with period T) with Fourier coefficients $c_{n}$ and $d_{n}$ respectively then, Fourier coefficient of $z(t)=x(t)\cdot y(t)$ is: (a) $\...
3
votes
2answers
2k views

Finding the fundamental frequency of a periodic signal

Suppose we have the signal $$x(t) = e^{j\omega_1 t} + e^{j\omega_2 t} + e^{j\omega_3 t},$$ where all the frequencies are rationally related (that is, the ratio of any pair of frequencies is a rational ...
2
votes
1answer
56 views

Rationally related frequencies and the Fourier Series representation

Suppose that we have the signal $$x(t) = e^{j\omega t} + e^{j\frac{3}{2} \omega t},$$ and we want to find a Fourier Series representation for that signal. Is this possible? According to my ...
0
votes
1answer
44 views

Pulse wave question

Wikipedia, fount of all knowledge (Ha! LOL), gives a formula for a pulse wave here: The formula is: $$f(t)=\frac{\tau}{T}+\sum_{n=1}^{\infty}\frac{2}{n\pi}\sin\left(\frac{\pi n \tau}{T}\right)\cos\...
1
vote
2answers
232 views

Fourier Series of Aperiodic convolution of periodic functions

we were given the following classic exercise: Given two periodic signals $x(t), y(t)$ with fundamental period $T$ with Fourier series coefficients $c_m^x, c_m^y$ respectively, find the Fourier ...
1
vote
1answer
509 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 ...
1
vote
2answers
214 views

Fourier series coefficient of signal when Time period is twice the fundamental period

My try: First of all I tried observing the symmetry but I did'nt find any.So I tried to calculate the fourier series coefficient of the signal like this First I differentiated the signal $x(t)$ so ...
2
votes
1answer
2k views

How to do simple extrapolation with Fourier transformation?

I have 1024 sample points, and I would like to do really simple extrapolation using Fourier transformation. First I apply Fast fourier transformation on the data. My first intuition was that I just ...
1
vote
0answers
30 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 ...
0
votes
2answers
144 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 ...
0
votes
2answers
154 views

Fourier transform

Fourier transform of a DC signal is an impulse at the origin. Now if the spectrum of a signal is the plot of the amplitudes of the respective frequencies of each harmonic, then the Fourier transform ...
4
votes
1answer
241 views

Fourier Series Coefficients

Question: The fourier series coefficients is given as: $$c_k= \begin{cases} 1 \qquad & k \ \text{ even} \\ 2 \qquad & k \ \text{ odd} \\ \end{cases}$$ the period of the signal is $T=4$, ...
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 ...
1
vote
1answer
133 views

Dirichlet Conditions

What is meaning of a signal having a "finite number of maxima and minima during any single period of time"?
0
votes
1answer
431 views

Difference between frequency components and harmonic components - Fourier

What is the difference between frequency components and harmonic components? The first concern the continuous domain of frequency, while the second concern the discrete domain of frequency ($f_{k}=kf_{...
0
votes
2answers
104 views

Can I compute Fourier series without looping through all frequencies?

I need to compute Fourier series of an audio stream. But DFT/FFT is slow. Are there any ways to compute Fourier series of a signal without using the Fourier transform to check if whether a frequency ...
0
votes
3answers
10k views

How to get the Fourier series using Python's $\tt fft$

I Would like to be able to reconstruct every individual sinusoid that makes up a Discrete signal. I Have the following signal: (I am working in Python) The signal is essentially an array with about ...
0
votes
1answer
68 views

Why doesn't a sudden loud noise sound high pitched?

The jumpiness or high change of a signal is due to the higher frequency components in the signal. So if I have a sound signal that increases suddenly in amplitude, why doesn't the signal sound very ...
0
votes
1answer
562 views

Fourier series approximation: DC component and fundamental frequency

In the linked image below, what is meant by plotting the DC component and fundamental frequency for a Fourier series approximation? For dot point 1 does it want me to graph just the DC component ...
0
votes
1answer
46 views

How can $a_n$ for the trigonometric Fourier series be $0$ for a non-odd square signal?

Can $a_n$ for the trigonometric Fourier series be $0$ for a non-odd wave? Since at the moment the square wave is not even nor odd. Square wave is given by: $$ s_2(t)=\begin{cases} -4, & 0\leq t\...
0
votes
1answer
130 views

Why can Fourier series be used on a non-repetitive function?

I was just wondering why Fourier series can be used on the function in the linked image. This is since I thought the function had to repeat itself to use Fourier series on it. Or is it saying a period ...
0
votes
2answers
128 views

Basic Fourier Series Not Understanding how to interpret n values [closed]

I have a question regarding $n$ in the Fourier series. If a question states "find the Fourier series for (any function) and find the values of an $b_n$ etc", say I'm finding it from the trig way when $...
4
votes
2answers
766 views

How can understand periodicity of a Signal from frequency domain representation?

Is it possible to say a signal is periodic from its frequency domain representation? A periodic signal is sum of its sinus and cosinus. Frequency translation of sinus and cosinus functions are ...
1
vote
4answers
603 views

Why are wavelet transforms (Multi Resolution Analysis) used more in practice for compression rather than Fourier series?

I know that both Fourier and wavelet can be used for compression of signals. The Fourier series guarantees that it gets the closest approximation of the original signal in the least squared sense. ...
0
votes
1answer
233 views

Unipolar Transmission Spectrum

I am currently trying to understand mathematically the amplitude shift keying modulation technique. My question is, say I wanted to compute the Fourier series of a basic pulse train, it is quite ...
0
votes
0answers
133 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 ...
1
vote
1answer
600 views

fourier series fitting matlab

I am using cftool in Matlab to fit time series values to Fourier model with 8 terms: ...
1
vote
1answer
600 views

RMS of absolute-valued sinusoid

A signal $x(t)=|\sin(2π(1000)t)|$ ($|x|$ is the absolute value function) is fed to an ideal low-pass filter with cutoff frequency of 1500Hz to produce an output $y(t)$, what is the RMS voltage of $y(t)...
0
votes
1answer
3k views

Fourier-series odd vs even square wave?

I really need to know the difference when doing a fourier seires between even and odd square waves. I've been trying to understand but I just get the same results and the same spectrums... Is the ...
-1
votes
1answer
24k views

Why Fourier series and transform of a square wave are different?

Here is a square-wave presented by Fourier series perspective: Above coefficients shows that a square-wave is composed of only its odd harmonics. But here below a square-wave is presented by ...
1
vote
3answers
2k views

Periodicity of Fourier series's coefficients

Why exactly continious Fourier-series's coefficients aren't periodic like coefficients of discrete Fourier series (DFS)? $e^{-j2\pi}$ is periodic in both sequences.
0
votes
2answers
397 views

Discreteness and periodicity in Fourier transform

Why discreteness in time / frequency domain dictates periodicity in the other frequency / time domian? For example the DTFT is perodic in frequency? Why it doesn't contain all the frequencies? Why ...
2
votes
2answers
362 views

Fourier series expansion of $\exp[-j2kA\sin(\omega t)]$

I've been going through this paper where we exploit the well known Fourier expansion of the model signal as shown in the image below. I've never come across this well known fourier expansion before. ...
1
vote
1answer
74 views

How we can obtain the time-integration of a sine signal?

could we calculate the below integral by the Fourier series or the Fourier transform properties? $$\int_{-\infty}^t \sin(\omega_0\tau)d\tau=?$$
2
votes
1answer
569 views

What is the time-integration property in the Fourier series analysis?

In the continuous Fourier series properties for a periodic continuous-time signal, we have time-integration property: $$ \int_{-\infty}^t x(\alpha)d\alpha \leftrightarrow \frac{a_k}{jk\omega_0} $$ ...
0
votes
1answer
666 views

Inverse fourier transform of Hermitian function, getting an imaginary part

in the cartoon below It shows that if we take the inverse Fourier transform of a Hermitian function, real part even and imaginary part is odd we should get a purely real function in the time domain. ...
10
votes
3answers
2k views

Slow Down Music Playing While Maintaining Frequency

Playing a piece of music audio at a slower speed would lower its pitch (frequency). Is there a tool and theory to slow down the song playing while keep the frequency the same? I suppose one can do ...
2
votes
2answers
1k views

Why are Fourier analysis and transform only applicable for LTI systems?

Why are Fourier analysis and transform only applicable for LTI systems? What if the system is not LTI, won't Fourier analysis or transform be possible?
1
vote
1answer
219 views

Signal equation using signal waveform and Fourier series?

Part A: Obtain signal waveform from mathematical equation of the signal Let a sinusoidal periodical signal is represented by an equation $$y=f(t)=10+10\cos\left(\frac{2\pi f_1t}{T} +\frac{\pi}{6}\...
0
votes
1answer
621 views

Deriving the DFT magnitude of $A\cos(2\pi nk/N)$

Given that $$x(n) = A\cos(2\pi nk/N),$$ the $N$-point DFT of $x(n)$ can be expressed as follows—the derivation can be found in here: $$X(m) = \color{red}{\frac{A}{2}\sum_{n=1}^{N-1}e^{-j2\pi n(m-k)/N}}...
1
vote
1answer
62 views

Where does $\frac{N}{2}$ came from in approximating an N-point DFT?

I've came across the author saying that ... for a real cosine input having k cycles in the N-point input time sequence, the amplitude response of an N-point DFT bin in terms of the bin index m is ...
0
votes
1answer
252 views

Signal's Fundamental Frequency is different from Plotted Signal

I've been attempting to plot the following function using MATLAB: $$ x(k)=\sum_{n=11}^{50} \sqrt{n} \sin (2n\pi k) +\sum_{n=1}^{40}\sqrt[3]{n} \sin (3n\pi k) $$ Note that $k$ is a continuous variable....
1
vote
1answer
344 views

square wave frequency representation

New to this signals stuff and i'm confused about the frequency representation of the square wave. Correct me if i'm wrong, a periodic square wave is composed of odd harmonics sine waves which are ...
0
votes
1answer
113 views

Relation between Fourier Series & Fourier transform [duplicate]

So i was just revising some basic DSP concepts. Just wanted to verify this fact. Fourier series represents a periodic signal $\hat{x}(t)$ with period P as a countably infinite sum of sinusoids of ...
0
votes
1answer
305 views

How do I calculate the eigenvalues of a covariance matrix which contains harmonic functions

I have read that $ce^{-\frac{\phi_i-\phi_j}{\rho}}$ is a harmonic function of the form $e^{-in\phi_i}$, and therefore it's eigenvalues are one of the Fourier components of $(|\phi_i-\phi_j|)$. My ...
1
vote
1answer
588 views

Relation between sawtooth Fourier coefficients and its DFT

I'm having some trouble with understanding the DFT of a sawtooth single period signal and its relation with sawtooth Fourier coefficients. Let's say I have a signal $$ s(t) = \frac{At}{T} - \frac{A}{...