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The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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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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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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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 ...
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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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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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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 ...
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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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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 ...
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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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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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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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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 ...
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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 = ...
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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 ...
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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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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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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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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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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 ...
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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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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 ...
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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<\...
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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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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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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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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 ...
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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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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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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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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 ...
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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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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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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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: $ ...