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1answer
36 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
58 views

how to create synthetic $1/f$ noise?

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 ...
-1
votes
1answer
43 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
25 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
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1answer
55 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
23 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 < ...
2
votes
1answer
84 views

Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
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2answers
80 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
43 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
votes
1answer
71 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
35 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
101 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
votes
1answer
359 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
57 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 ...
0
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0answers
33 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
vote
1answer
48 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 ...
2
votes
2answers
129 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
173 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
votes
1answer
87 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
vote
1answer
55 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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0answers
38 views

Fourier Transform in 2D? (image processing) [duplicate]

In audio signal processing, Fourier Transforms are widely used to convert the mono-dimensional signal, expressed in time, into the frequency domain. It is not clear to me how this is extended to the ...
0
votes
3answers
66 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
31 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
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1answer
37 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
53 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) ...
0
votes
1answer
285 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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0answers
52 views

Disadvantageous of wavelet transform

i have question related to wavelet transform:we know that while Fourier transform is good for spectral analysis or which frequency components occurred in signal,it will not give information about at ...
0
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1answer
153 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
votes
1answer
176 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
72 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 ...
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1answer
81 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
110 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 ...
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3answers
54 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 ...
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2answers
102 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
vote
0answers
968 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
vote
1answer
158 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
1k 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.
3
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1answer
39 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 ...
4
votes
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
votes
1answer
181 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
votes
1answer
194 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
votes
2answers
361 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 ...
1
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0answers
94 views

A Laymans Fourier transform and harmonics explanation?

Please bear with me, I know some of you will scoff but I have looked on Wiki and in various literature (see below) and can't quite get a handle on a few things. I am a general business programmer, ...
4
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1answer
430 views

Gibbs phenomenon in Hamming's digital filters

In 'Digital Filters' by Hamming there is a cryptic section where he describes how the Gibbs phenomenon can be viewed as the displacement between the centers of two functions as they are convolved ...
2
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1answer
717 views

FFT has unexpected DC component

I have a mixture of Gaussians and I want to look at their power power spectrum. The spatial distribution looks like this: It's already been convolved with a Gaussian window function. I subtract ...
6
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1answer
227 views

Intuition behind the scaling property of Fourier Transforms

The Fourier transform of $f(ax)$ is $\frac{1}{|a|}F(\frac{u}{|a|})$. So the frequencies are scaled horizontally but the magnitudes are also scaled when the graph of $f$ is scaled horizontally. On the ...
3
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2answers
308 views

Given the Graph of a Fourier Series $\sum c_k e^{2\pi ikx}$ Find the Graphs of $\sum c_{3k} e^{2\pi ikx}$ and $\sum (c_k)^2 e^{2\pi ikx}$

Define a 1-periodic function on $\mathbb{R}$ by: $f(x) :=$ $\left\{\begin{matrix} 1 & if & 0<x<\frac{1}{10}\\ 0 & if & \frac{1}{10}<x<1 \end{matrix}\right.$ with ...
3
votes
3answers
5k views

The Fourier Series Of This Triangle Wave

I am using matlab to study digital signalling and have come across a problem which i was wondering if anyone with more experience could help me with. I need to work derive the Fourier series of a ...