Questions tagged [fourier-series]

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194 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 ...
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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 ...
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0answers
29 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 ...
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2answers
141 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 ...
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2answers
147 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 ...
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1answer
235 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 $T=4$, ...
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1answer
3k 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 ...
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1answer
122 views

Dirichlet Conditions

What is meaning of a signal having a "finite number of maxima and minima during any single period of time"?
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1answer
410 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_{...
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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 ...
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3answers
8k 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 ...
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1answer
67 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 ...
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1answer
533 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 ...
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1answer
44 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\...
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1answer
116 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 ...
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2answers
106 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 $...
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2answers
703 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 ...
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4answers
543 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. ...
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1answer
210 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 ...
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0answers
123 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 ...
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1answer
520 views

fourier series fitting matlab

I am using cftool in Matlab to fit time series values to Fourier model with 8 terms: ...
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1answer
507 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)...
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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 ...
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1answer
18k 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 ...
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3answers
1k 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.
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2answers
357 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 ...
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2answers
304 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. ...
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1answer
66 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? $$\int_{-\infty}^t \sin(\omega_0\tau)d\tau=?$$
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1answer
480 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: $$ \int_{-\infty}^t x(\alpha)d\alpha \leftrightarrow \frac{a_k}{jk\omega_0} $$ ...
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1answer
569 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. ...
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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 ...
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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?
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1answer
217 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}\...
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1answer
494 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}}...
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1answer
61 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 ...
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1answer
249 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....
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1answer
308 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 ...
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1answer
109 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 ...
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1answer
290 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 ...
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1answer
526 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}{...
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2answers
817 views

How to find Fourier Series Coefficients

I saw many solved examples about this topic but again I coudn't come up with any solutions about this question. How can I find the Fourier Series coefficients of the following signal ? $x(t)=2 \cos(3\...
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2answers
633 views

FFT of SIN waves with different phase delays

I have come across a peculiarity of FFTs which has got me somewhat baffled. I've simply summed up 101 sine waves and taken the FFT using this matlab script : ...
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4answers
883 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 ...
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1answer
110 views

Calculating original signal from Discerete Fourier Transform

I am trying to calculate the original equation using a DFT. I start with a equation, generate values from this equation and then get the dft of these values. The aim is to generate the original ...
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2answers
495 views

Convolution in frequency domain

Simple math question. The convolution theorem states that multiplication in time domain is equal to convolution in frequency domain and vice versa. There is a condition that the signal has to be ...
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4answers
5k views

About Fourier transform of periodic signal

In Fourier transform for periodic signal, I checked different books and I found a different explanation in each book. Let's take the explanation in Signals and Systems by Rajeshwari & Rao: The ...
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2answers
521 views

Finding Fourier Series Coefficients

I'm just beginning to learn about Fourier series and I'm trying to figure out how to find the Fourier series coefficients for $$x(t) = e^{j100\pi t}$$ I know that $$x(t) = \sum_{-\infty}^{\infty} a_{...
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2answers
5k views

Derive Frequency Representation of Impulse Train Function

I want to walk through the derivation of the frequency representation of an impulse train. The definition of the impulse train function with period $T$ and the frequency representation with sampling ...
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1answer
206 views

Fourier Transform/Series DFT/DFS textbook problem (simple?)

Suppose $x_c(t)$ is a periodic continuous time signal with period 1 ms and for which the Fourier series is \begin{align*} x_c(t) &= \sum\limits_{k=-9}^9 a_k e^{j(2000 \pi k t)} \\ \end{align*} ...
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1answer
2k views

Relation between a Fourier series harmonic component and its power

My question is about the meaning of power spectrum derived from the Fourier series coefficients. Fourier series is shown below: $$f(t)=a_0+\sum_{n=1}^{\infty}a_n\sin(\omega_n t)+\sum_{n=1}^{\infty}...