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1answer
35 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 ...
0
votes
1answer
79 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} - ...
3
votes
2answers
83 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 ...
3
votes
2answers
97 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 : ...
0
votes
3answers
55 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 ...
0
votes
1answer
68 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 ...
2
votes
2answers
93 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 ...
0
votes
2answers
91 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 Alan Oppenheim. "The ...
0
votes
2answers
50 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} ...
0
votes
2answers
59 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 ...
1
vote
1answer
97 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*} ...
0
votes
1answer
36 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 ...
0
votes
4answers
89 views

Why Fourier series if Fourier transform can be calculated for both periodic and aperiodic?

While learning about Fourier Transform after Fourier Series, That we can calculate Fourier transform of periodic signals too. If we can take the Fourier transform of periodic signal too then my ...
1
vote
1answer
77 views

Determining Fourier Series coefficient for Discrete time

I am trying to solve the proof for determining the Fourier series representation of a periodic signal. I understand fourier series equation for Discrete time which is $$x[n] = \sum^{}_{k=<N>} ...
0
votes
0answers
81 views

Proof of Properties of Fourier series in CT

I feel problem in understanding the proof of Fourier series properties Time scaling $$b_k = \frac{1}{T}\int_{T}x(t)e^{jk\omega_0t}dt$$ $a$ - scaling factor $$ = ...
-1
votes
3answers
72 views

magnitude and phase Fourier coefficients

While solving Fourier series coefficients in example, i found couple of things which confuse me. How the minus sign changes to plus sign $a_1= 1-\frac{1}{2j} = 1+\frac{1}{2}j$? After plotting the ...
2
votes
1answer
90 views

Mathematical model of a signal in Compressive Sampling

Currently I am reading a paper on Compressive Sampling, and trying to understand each and every parts of it. When I came across the mathematical model of the signal in paper, I got confused. I have ...
1
vote
1answer
81 views

Proof for determining Fourier coefficients

While determining Fourier coefficients we have this equation $$\int^{T}_{0} x(t) e^{-jn\omega_0t} dt = \sum^{+\infty}_{k\ =\ -\infty} a_k [\int^{T}_{0} e^{j(k-n)\omega_0t}dt]$$ I want to ask that how ...
0
votes
1answer
36 views

Value of $A_k$ in Fourier series

Fourier series in continuous time domain while representing $a_k$ in rectangular form $$ a_k = B_k + jC_k$$ But when using the value of $a_k$ in the main equation: $$ x(t) = a_0 + ...
0
votes
1answer
31 views

Fourier Series Proof

I want to ask Question about the Fourier series in continuous time domain while reading a book signals and systems Alan Oppenheim. I have confusion in understanding the statement on page 189 of its ...
0
votes
1answer
39 views

Fourier series in continous time domain

I want to ask Question about the Fourier series in continuous time domain. I am following signal and systems 2nd Edition by Alan Oppenheim. I have confusion in understanding the statement that ...
0
votes
0answers
36 views

the DFT of a periodic signal represented by a fourier series

If I have a signal represented by a Fourier series(like in the photo), which is sampled with $T_s$: $$x[n]=x(t=nT_s) = \sum_{m=-\infty}^{\infty}a[m]e^{j2\pi m(nT_s)/T_0} $$ How do I find its DFT? I ...
1
vote
6answers
153 views

When is the Fourier transform of a signal periodic?

I mean not the time-domain signal being periodic, but the Fourier transform being periodic.
0
votes
1answer
54 views

Bartlett's and Welch's Method for PSD

Lets say. I have an image of 100 samples, and I want to find the presence of smaller image of 24 sample using cross-correlation in the fourier domain. I use Bartlett's and Welch's method for PSD, ...
0
votes
1answer
72 views

Finding Correlation response in fourier domain

Lets say I have a system that is trying to find a small image (assume all images are grayscale) within in an image by using correlation. So this system has the baseline image, and I input 5 different ...
1
vote
1answer
59 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
vote
1answer
94 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
vote
1answer
75 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 ...
-3
votes
1answer
56 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 ...
1
vote
2answers
63 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
votes
0answers
21 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
votes
2answers
154 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) \\ ...
-1
votes
1answer
70 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
votes
1answer
72 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 ...
-1
votes
1answer
52 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
votes
0answers
28 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 ...
1
vote
3answers
139 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
votes
0answers
25 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 < ...
3
votes
1answer
103 views

Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
1
vote
2answers
164 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 ...
-1
votes
1answer
47 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
80 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
votes
1answer
56 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: $$ x_{(m)}[n] = \begin{cases} x[n/m], & n=0,\pm m, \pm 2m,...\\ 0, & otherwise \end{cases} $$ ...
3
votes
0answers
111 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
vote
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
731 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
votes
0answers
86 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
vote
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
vote
1answer
52 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
157 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) ...