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1answer
44 views

Fourier series calculation [closed]

I have tried to solve, but do not know if the answer is correct or not. A person has a periodic voltage input to a circuit. The input repeats itself every 0.02 seconds i.e. the fundamental period is ...
1
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1answer
80 views

How to simplify the Fourier Series Using an Approximation?

I have a signal, $f(t)$. I know a function that can be used to generate this signal, such that I can determine its Fourier series. I want to express this Fourier series in simpler terms so that the ...
1
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1answer
69 views

What is difference between outputs of Fourier transform and Fourier series of a periodic square waveform?

We can use Fourier transform of an aperiodic signal and Fourier series of periodic signal. But we can use Fourier transform formula for periodic function also. Now, let us consider a periodic square ...
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1answer
50 views

How Fourier decomposition is performed?

The Fourier decomposition explains a time series entirely as a weighted sum of sinusoidal functions and with the Fourier series,it is possible to do it. But I have some doubts Suppose ,for any ...
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2answers
58 views

why fourier series gives lower amplitude for max value of signal

I want to approximate below signal using fourier series on Matlab. My code is below ...
0
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0answers
19 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 ...
0
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2answers
151 views

Signal decompositon

I am not a good in writing algorithm but please follow below steps 1.There are 4 1D sinusoidal periodic signals.3 of them are given by \begin{cases} x(t)=4\sin(10\pi t) \\ y(t)=8\cos(20\pi t) \\ ...
0
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1answer
43 views

Change of discrete summation to definite integral

The Exponential Fourier Series for a signal is written as, $$x(t) = \sum_{n=-\infty}^{\infty} X_n e^{jnw_0t}\tag{1}$$ and, Fourier Coefficient, $X_n$, is written as, $$X_n = \frac{1}{T} ...
0
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1answer
67 views

how to create synthetic $1/f$ noise? [duplicate]

I am writing an app to work with synthetic time series data from a physics experiment. In our experiments we always have $1/f$ noise in our time series, but I haven't been able to find code/packages ...
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1answer
47 views

Exact formula for alias of Discrete Fourier transform for periodic sigals

Suppose that $f(t): \mathbb{R} \to \mathbb{C}$ is a $T$-periodic signal, with highest frequency $f_h$. Now suppose that our sampling rate frequency is lower than $f_h$, and is not any multiples of ...
0
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0answers
27 views

How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

Suppose there is signal $f(t)$ that is continuous and periodic. It is known that this $f$ is $T$-periodic. (but it's not necessarily a single cosine $f(t)$.( I'd like to make the mean of samples be ...
0
votes
1answer
88 views

Can I study continuous time Fourier Transform and treat the rest as special cases

Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to Lapace transform, Z transform, DTFT, DFT, Fourier sequence ...
0
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0answers
24 views

energy and power type signals [duplicate]

How can I determine if the signal $$\begin{array} \\g_1(t)=A\cos (2\pi f_c t), & \frac{-T}{2}<t<\frac{T}{2} \\ 0, &\text{otherwise} \end{array}$$ and: $$g_2(t)=\cos(t), -\infty < ...
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1answer
92 views

Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
1
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2answers
114 views

A clarinet has no even harmonics. What would produce no odd harmonics?

According to this link, the waveforms of clarinets do not have even-numbered components in their harmonic series: A closed cylindrical air column will produce resonant standing waves at a ...
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1answer
44 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 $x(t) = > \cos4t +\sin8t+3$?
0
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1answer
74 views

Why does Fourier Series have $\sin$ and $\cos$ Components

While we look at Fourier Series there are both $\sin$ and $\cos$ components.But I think $\sin$ component is ony needed to describe wave.why there is also an $\cos$ component in Fourier Series? ...
0
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1answer
38 views

Deriving time-scaling property for Fourier Series

thanks for taking the time to help with this problem! I have to prove the time-scaling property: $$ x_{(m)}[n] = \begin{cases} x[n/m], & n=0,\pm m, \pm 2m,...\\ 0, & otherwise \end{cases} $$ ...
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0answers
104 views

DSP interview question: use of the identity in development of a significant transform

I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform? How the simple identity $$xy=\frac{1}{2}x^2 ...
1
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1answer
61 views

Fourier synthesis

I know what I am attempting is not easy but I have a spectrum with peaks at 10Hz 20Hz and 30Hz. I also have various amplitudes at these peaks. I want to recreate my original signal. I initially ...
0
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1answer
475 views

Determine spectrum amplitudes for half-wave rectified sine

I am trying to learn how to solve a bunch of digital signal problems and I have trouble understanding the solutions provided by this book I'm using. Basically, this problem asks me to determine ...
3
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0answers
73 views

Estimate the Discrete Fourier Series of a Signal with Missing Samples

Assuming we have a discrete signal $ { \left\{ x \left[ n \right] \right\}}_{n = 1}^{N} $. Which has a Discrete Fourier Series. Now, assume I'd like to estimate its Discrete Fourier Series ...
1
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0answers
36 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 ...
1
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1answer
50 views

Synthesis discrete time signal from fourier coefficients

Following information is given about a signal $x[n]$ $x[n]$ is real and even signal $x[n]$ has a period $N=10$ and Fourier coefficients $a_k$ $a_{11}=5$ $\frac1 {10}\sum_{n=0}^9 |x[n]|^2=50$ How ...
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votes
2answers
139 views

Trignometric Fourier series representation of a continous time signal

While learning Fourier series I read the definitions of representation for a continuous time signal $x(t)$ as: $$x(t)=A_0 + 2 \sum_{k=1}^{\infty} A_k \cos(k \omega_0 t) - B_k \sin(k \omega_0 t) ...
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4answers
179 views

Why does the Fourier series not include phase information?

From my understanding, the Fourier series is a way to describe an arbitrary continuous signal in terms of sinusoids of varying frequencies and amplitudes, as shown here in Equation 1. Why are the ...
0
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1answer
118 views

Discrete Fourier Transform and Opposite Convolution Theorem

I am reading the Wiki for DFT. There is a part for circular convolution theorem which sounds a bit odd saying: $$ \mathcal{F} \left \{ \mathbf{x\cdot y} \right \}_k \ \stackrel{\mathrm{def}}{=} ...
1
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1answer
63 views

Why we need fourier transform of periodic signal although we have fourier series for periodic signal?

I was going through some of the basics of fourier series and fourier transform. And I came across one topic "Fourier transform of periodic signal". But I am not able to understnad why we need to go ...
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3answers
68 views

Fourier Transforms and Series for the NON mathematically inclined.

This would most likely be the opposite of this question ( Mathematically inclined Signal and Systems/Signal Processing book? ) I figured I'd ask here if there are any good books that while, ...
0
votes
1answer
36 views

Reason for bimodal behavior while low second fourier coefficient

If I have a time series (for eg. for 23 timestamps) and if I plot it and see that it is bimodal, that means it might be having high value of second fourier coefficient (with frequency = 2). But when I ...
0
votes
1answer
47 views

How to check if Fourier components are in phase of out of phase?

I have a time series (of 23 timestamps) of which I take the Fourier transform. Now the fourier transform has 23 imaginary values and each has an amplitude and a phase. When I get the phase angle, it ...
1
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1answer
61 views

Similarity theorem in Fourier analysis

I have a homework problem that I'm not quite sure how to complete. The problem is as follows: PROBLEM Write the definition of the Fourier coefficients, and show that $$f(t + \frac{1}{2}T) = f(t) ...
1
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1answer
347 views

Calculation of cosine in frequency domain instead of calculatin in time-domain followed by a FFT

I got an $N$, in my case 512, point FFT of a real-valued signal. Based on some calculation in my application I determine the parameters $k \in [1, N-1]$, the number of oscillations per period, $\phi ...
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1answer
79 views

Disadvantages of wavelet transform

I have a question related to wavelet transform: we know that while the Fourier transform is good for a spectral analysis or which frequency components occurred in signal, it will not give information ...
0
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1answer
184 views

Book recommendations on Gabor filter and Fourier series

I'm starting to learn about Gabor filters and Fourier series. I need to make a presentation on Gabor filters in a few months, so I need quality references for the presentation. Does anyone have any ...
0
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1answer
204 views

How to prove $cos(t) + cos(\pi t)$ is non periodic function? Also can I represent this signal using fourier series?

I would just want to prove $\cos(t) + \cos(\pi t)$ is non periodic. I don't know where to start it. Also I know that individually these signals ie $\cos(t)$ and $\cos(\pi t)$ are periodic with ...
0
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1answer
73 views

Two basic questions related to complex Fourier series

Doing excersies from Richard Hammings book about digital filters I've got two questions about them: 1) Fourier expansion of $g(x) = \sin^5(x)$. Provided answer is: $\sin^5(x)=5\sin(x)-20 \sin(3 ...
1
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1answer
84 views

Multiply FS Coefficients by 0 or 1 to get Low Pass Filter?

I have written a bit of code to upsample and interpolate a sample waveform in MATLAB. It's at the point where I have taken a signal, upsampled it 2x and filled in the gaps with 0's, and then I found ...
1
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1answer
111 views

g(x)=x odd and even expansions

I'm studying book about digital filter by Richard Hamming. And there is exercise to get odd and even expansion of g(x)=x where x is from 0 to $\pi$. I understood even expansion, but can't get into odd ...
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2answers
67 views

Why can't we just make all wireless networks use integer multiples of base frequency?

I always wondered why transmission capacity depends on bandwidth. For example, let us say that there is an isolated island. In this island, people decide that all wireless networks use frequencies ...
1
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3answers
55 views

Ambiguity in the term 'dimension'?

We used to classify signals as 1D and 2D etc ie one dimensional and two dimensional. For example a periodic square wave signal is 1D and an image is a 2D signal etc (reference - Signals and systems by ...
0
votes
2answers
103 views

Reason of Fast Fourier and Inverse Fast Fourier [closed]

I am not very good at mathematics I was doing some image processing so I came to know about FFT and IFFT I was learning about ...
1
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0answers
1k 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 ...
1
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1answer
180 views

What is the physics behind the width of a main lobe?

We know that the square window gives the lowest main lobe width possible, and that other windows after that trade main lobe width for side lobe height. I also understand that the main lobe width is ...
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1answer
2k views

Graphical fourier series of a square wave

This is probably off-topic since it isn't really a question, but I thought that this GIF of the fourier series of a square wave was too cool not to share.
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1answer
41 views

Number of zeros of a sum of Shah functions by applying Rice's formula?

There is a Dirac pulse train following the scheme of the Shah function (or $\delta$-cumb function) with its Fourier series of the form: $$\varsigma(t,T)=\sum_{n=-\infty}^{\infty}\delta ...
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3answers
2k views

How to remove the periodic oscillations from a signal

The task that I have is to remove the annual and semiannual oscillation from a set of temperature measurements, taken over several years, by means of least squares method. I found the method ...
2
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1answer
200 views

Gain function calculation (frequency response)

Define moving average process $y_t := 0.5 x_t + 0.5 x_{t-1}$ where $x_t := e^{i2 \pi t}$. Its frequency response is then: $$H(f) = 0.5 + 0.5 e^{-i2\pi f}$$ Recall that the frequency response in ...
2
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1answer
206 views

Benefit to know Fourier series for image processing? [closed]

I know there's a benefit of knowing the Fourier Transform for image processing, but is there a benefit to know Fourier series, or could you just skip them? Would you recommend skipping Fourier series ...
0
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2answers
446 views

Fourier series - time and frequency domain confusion

I am computing the fourier series of the following function between $[-0.5, 0.5]$ $$\displaystyle f(t) = \frac{1}{2} - |t|$$ According to the definition of Fourier Series the coefficients are given by ...