The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
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1answer
24 views
Given a plot of both the magnitude $|H(\omega)|$ and its angle, How can you find the $H(\omega)$?
I'm specifically trying to use an inverse Fourier Transform to find $h(t)$, but I'm finding it difficult to get $H(\omega)$ in the first place.
I'm under the impression from my textbook that $H(\...
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1answer
19 views
Fourier Transform of ECG signal in Python
I have an ECG signal which I am analyzing using Python, as opposed to the mainstream MATLAB. So, I have digital form ECG in .dat file with .hea (header file). Below is the Fourier transform
The ...
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1answer
34 views
Denoising a signal using eigendecomposition
I have a complex observable series $Y(t)$ which is the result of summing two complex r.v $X(t)$ (unobservable) and a $\epsilon(t)$ (unobservable).
$$Y(t)=X(t)+\epsilon(t)$$
Assume that $X$ and $\...
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0answers
18 views
Apply the DTFT transform to calculate the magnitude of the spectrum [on hold]
Assume you are given the following discrete signal, which has an amplitude x(0)=8
and x(1)=3:
Apply the DTFT transform to calculate the magnitude of the spectrum, if = 3,1
radians.
You need to ...
0
votes
1answer
42 views
What Is the Point of Doing the Zero Padding? [duplicate]
What are the advantages and disadvantages of doing Zero-padding, in particular the case of speech signals?
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0answers
11 views
Where do I place my filter matrix in the frequency domain?
I need to create a matrix as big as the image but the kernel is way smaller. size of the image is 100x100 and the kernel's is 5x5. I create a 102*102 matrix but where I am supposed to put the numbers ...
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vote
2answers
56 views
How do you apply a filter after DFT on an image?
Let's say size of the image is 100 x 100 and the kernel matrix is 5x5. I took the DFT of both the image and the kernel. But how do I multiple these two matrices? And which parts involve in these ...
0
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1answer
53 views
Fourier transformations of discrete time signals [on hold]
How does one Fourier transform the following signals? $$x[n]=[0,9,0]$$ and $$y[n]=[9,0,19,0,9]$$
I've tried to get it along the way of $$X[\omega]=e^{-i\omega n}$$
but this seems incorrect. I'm not ...
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1answer
31 views
How to get general projection of rect function?
To be more clear I want to get a general expression for
PƟ(t)= ∫∫rect(x)rect(y)δ(xcosƟ+ysinƟ-t)dxdy
I also want to find particular projection for Ɵ=0 and Ɵ=45 and also Fourier Transform of the ...
0
votes
2answers
61 views
Discrete inverse Fourier transform
I have a question regarding discrete inverse Fourier transform, and no answer I found on the internet seem to be satisfying. This might be because I do not fully get some of them, so please excuse my ...
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0answers
57 views
Express mathematically what happened to the spectrum of
Express mathematically what happened to the spectrum of a signal with known Fourier spectrum that has been inverted/decimated/modulated.
I have made inversion and decimation in Mathlab.
I'm not sure ...
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0answers
39 views
Fourier Transform applied on time series data
I am willing to apply Fourier transform on a time series data to convert data into frequency domain. I am not sure if the method I've used to apply Fourier Transform is correct or not? Following is ...
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0answers
52 views
2D Signal Properties of Fourier Transformation [closed]
I was asked this question below.
I have to match i-v to a-j (matching could be one to many or many to one) and i should prove the matchings.
If conjugation is not made, i can assume that $h(n_1,n_2)$...
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2answers
29 views
Sampling with an alternating impulse train
The have the following question:
A signal $m(t)$ with bandwidth 500Hz is first multiplied by a signal
$g(t)$ where $\displaystyle g(t)=\sum_{k=-\infty}^{\infty}(-1)^k \delta(t-0.5*10^{-4}k)$. The ...
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1answer
38 views
Partial Fraction Expansion for Inverse Fourier Transform
In many textbooks, I've seen the application of Partial Fraction Expansion (PFE) to find an inverse Fourier Transform. Let's stick to the discrete time case, and let me give you an example.
Let's say ...
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2answers
67 views
How to do DFT of this signal
I am trying to get $X[k]$ when $x[n]$ is equal to
$$x[n] = \cos\left(\tfrac{\pi}{4}n-\tfrac{\pi}{4}\right)$$
I'm using this equation:
$$X[k] = \sum_{n=0}^{N-1}x[n]e^{-j \frac{2 \pi}{N}kn}$$
but ...
2
votes
1answer
65 views
Does the Fourier series coefficient of AC components remains same if DC component is subtracted form the given signal?
Suppose a signal is defined by
$
x(t)= \begin{cases}
t & 0\leq t \leq 1 \\
2-t & 1\leq t\leq 2 \\
\end{cases}
$
Since $x(t)$ has even symmetry, I can calculate fourier coefficient as
$$
a_n = ...
1
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3answers
74 views
How the FFT takes a cosine or sine and outputs the frequencies of the complex form?
If i take the Fast Fourier Transform (FFT) of a cosine function, what has turned this cosine function into its complex exponential form which consists of $e^{i \omega t} + e^{-i \omega t}$ ?
Because ...
-1
votes
0answers
21 views
Good reference to study graduate-level DSP course
I'm looking for a textbook on discrete-time signal processing, that has solution in the back of the book, so I can work on practice problems, and validate the result, so that I can study on where I'm ...
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0answers
24 views
Single frequency missing in time domain effect
How to explain effect of a missing frequency in time domain ? As we know it is simple task when we talk about frequency domain and missing a frequency component in there (in spectrum).What about time ...
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1answer
301 views
Practical book in C [duplicate]
Is there any practical “go to” book that demonstrates the main dsp methods for time series written in C for practical applications? (Doesn’t have to be for hardware, but for any raw data such as ...
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1answer
38 views
Signals and Systems - LTI - Transforms - Impulse Response
I have $x(t)-> LTI -> y(t)$ where $LTI=h(t),H(jw)$.
and
$H(jw)=ab/((a+jw)(b+jw))$ where a and B are real numbers.
I am wanting to find the impulse response $h(t)$ as well as the input/...
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2answers
34 views
Identify random repetitive patterns
Forgive me if it’s too basic, I finish engineering a while ago.
Given any time series, not periodic, I would like to find any repetitive pattern that is distinct (by some given measurement) and is ...
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1answer
65 views
Basic confusion about the DFT and convolution
I am learning DSP (with Digital Images) and I have some elementary confusion about the convolution between two discrete periodic signals. Specifically, I have learnt that when filtering an image, we ...
2
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0answers
47 views
How to calculate the Fourier Transform of a solvable chaos waveform?
Recently I am stucking in frequency estimation of a solvable chaos waveform.
Its local analytic expression in time domain is
$$
z(t)=s_m(u_m-s_m)e^{\beta(t-mT)}\cos(\omega_0 t+\varphi),mT\leq t<(m+...
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0answers
39 views
what are the advantages of using Lomb-Scargle over FFT?
I know that lomb scargle is used for non uniformly distributed timepoints, but assuming we had those, Is there any difference between using Fourier transforms and Lomb Scargle. I know this is a ...
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1answer
22 views
Signal in frequency domain with OpenCV dft
I am experimenting with cv::dft: a 1HZ sinus signal is generated, and displayed in the frequency domain. But for some reason it hasn't got the maximum component at ...
0
votes
1answer
61 views
Applying Nyquist's sampling theorem to a real signal
I'm struggling to fully understand the Nyquist-Shannon sampling theorem.
For some message input signal $m(t)$ that is infinite in time (i.e. is not identically $0$ for any interval $t_1<t<\...
0
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0answers
22 views
pulses: Power signals or Energy signals?
I am doing system Identification for a tracking task, and I want to determine in the frequency bounds where I can approximate a baseline model with the chosen signals.
There are two channels, one is ...
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3answers
73 views
Fourier Transform negative amplitude meaning
I am reading this example http://www.thefouriertransform.com/pairs/truncatedCosine.php
What does it mean to have some of the frequency components be negative in its amplitude ? I am not talking about ...
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1answer
42 views
Why do we need the power spectral density?
Since the power spectral density is just the squared of the fourier transform, why is it useful ? Can't I just replace every solution that requires the psd with the fourier transform ?
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2answers
45 views
Why is it called continuous-time frequency?
I'm just wondering about the CTFT. My lecturer refers to capital Omega $\Omega$ in the following as being the continuous-time frequency:
Why is it called continuous-time frequency here but in the ...
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2answers
63 views
Why are edges in spatial images represented as edges in their Fourier transform image?
Here is a well-known image and its Fourier Transform (magnitude).
If I understand correctly the theory behind the FFT, each pixel in the FFT image represents a certain 2D sine wave with frequency ...
2
votes
3answers
66 views
Maximum Magnitude Deviation between DFT and DTFT
Let $x[n]$ be a finite-length discrete-time signal with length $N$. The continuous DTFT $X(\omega)$ is then
$$
X(\omega) = \sum_{n = 0}^{N-1} x[n] e^{-j \omega n}.
$$
The length-$N$ DFT of $x[n]$ is
$...
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2answers
68 views
Fourier transform and impulse function $\delta(\omega)$
Why does impulse function $\delta(\omega)$ keep occurring in the Fourier transform expression of standard functions like $\sin(t)$, $\cos(t)$, constant function, unit step $u(t)$ etc? (can someone ...
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2answers
73 views
Different ways of decomposing signals into sine waves? [closed]
Using windowed Fourier transform for time frequency analysis can produce a spectrogram including time/frequency information of a signal. But there should be infinite ways to decompose a finite signal ...
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0answers
52 views
What does the output of a DFT really mean?
I've computed the DFT twice on the function:
$$
f(t) = 2 + 2\cos(2\pi t) + 2\cos(4\pi t)
$$
Once between $t=0\to 3/4$, hence taking 4 readings, and once between $t=0\to 15/16$. The first plot has ...
0
votes
1answer
26 views
Calculating Power of Sinusoidal Term and a Convolution expression
The following is an excerpt from the book Statistical Digital Signal Processing and Modelling (Monson Hayes)
...consider a random process consisting of a random phase sinusoid in
white noise $$ x(...
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votes
1answer
29 views
Mean Square Error and Gibbs oscillations
While studying the convergence of Fourier transform, I got to know two conditions.
$$\sum_{n=-\infty}^{\infty}|x(n)|<\infty$$
$$\sum|x(n)|^{2} \leq [\sum|x(n)|]^{2}$$
While I was reading the ...
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2answers
66 views
Realization of a filter based on its transfer function
How can we check whether the filter is realizable given its transfer function and What are the parameters the realization depends on?
Here is an example:
Show that a filter with transfer function
...
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votes
1answer
101 views
Generalized translation on graph
David I.Shuman in "vertex-frequency analysis on graph" claims that,"we generalize one of the most important signal processing tools – windowed Fourier analysis – to the graph setting and When we apply ...
0
votes
0answers
26 views
FFT based audio convolution (reverb) sample rate dependency
I know it's usually not advicable to ask more than one question in a post but in this case the main question does only work if the basics are correct.
So I was reading more into audio reverb and ...
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1answer
64 views
Transfer function intuition
What is the meaning of the transfer function of a filter? Please explain intuitively with an example if possible.
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2answers
127 views
Why does the Fourier Transform of the impulse look so different from the Fourier Transform of the impulse train?
The fourier transform of the impulse functions is:
$$ \delta(t) \longleftrightarrow 1$$
The shifted delta:
$$ \delta(t-nT) \longleftrightarrow e^{-j \Omega nT}$$
But the fourier transform of the ...
1
vote
1answer
40 views
Find Discrete Fourier transform given the inverse
I don't know if this question is already answered somewhere else but I'm stuck with that and I need help...
Given an inverse Discrete Fourier Transform (IDFT), with N=16 :
How can I find the F(k) ...
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1answer
47 views
given an image and its fourier transform, find another image fft using fourier properties
I managed to solve few of those questions , but I'm not manage to answer 3 of them correctly,
the question is: given an image and its fourier transform, find another image fourier transform ,using ...
1
vote
1answer
56 views
Question about Fourier descriptor and the physical meaning of the coefficients
I would have some questions about the Fourier descriptor and the physical interpretation of the individual coefficients. I'm rather new to this concept, so I would be looking for a simple answer.
To ...
3
votes
2answers
118 views
How to calculate the Fourier transform of absolute-valued sinusoid?
The signal $x(t) = |1+a\sin(\omega t)|,(a>0)$ is a continuous waveform. In order to extract the frequency parameter $\omega$, I conduct the FFT of it and obtain its spectrum showed as follows. The ...
0
votes
2answers
77 views
Why do frequencies of analog signals range from $-\infty$ to $\infty$ while frequencies of digital signals are restricted to $[0,2\pi]$?
In Fourier analysis while dealing with discrete-time signals, frequencies range from $0$ to $2\pi$ why? Intuitively how can i understand it?
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1answer
33 views
Using the given identities, find the inverse DTFT
Using the given identities,
$ a^nu[n]$ <===> $\frac{1}{(1-ae^{-jw})}$
$\delta[n-k]$ <===> $e^{-jwk}$
Find the inverse DTFT of,
$ H(e^{jw}) = B \frac{e^{-jw}}{(1-ae^{-jw})}$
my attempt:
$ ...
