Questions tagged [fourier-transform]

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

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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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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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369 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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127 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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77 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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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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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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331 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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44 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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171 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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104 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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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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149 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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245 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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552 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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120 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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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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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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100 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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173 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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31 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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51 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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134 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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114 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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109 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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581 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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106 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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84 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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146 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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152 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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253 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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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: $ ...
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239 views

Image zooming with Fourier transform

I want to go from this image into this one: So basically I need to scale the white square. The authors of the paper claim that this can be done in four steps: zero-padding in real space (image is ...
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102 views

Application of Parsevals theorem with Welch method

For my project I had to manually code the welch method using the code below. Pretty much it involves finding the spectral density through fft and incorporating windowing and segmenting with overlap. ...
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114 views

Impulse response from Frequency response: why using $e^{j\omega}$ as an input?

Every resource that I can find uses this identity when deriving impulse response: $h[n] = IDTFT \Big\{H(e^{j\omega}) \Big\}$ Suggesting that the input signal was $e^{j\omega}$. But by definition ...
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172 views

Bridging CTFT and DTFT for a cosine

I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT. For example if I take a basic example: $$ x(t) = cos(\omega_x \cdot t) = \frac{1}{2} \cdot \left( e^{j\...
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145 views

While finding the ESD/PSD of a signal why we always prefer to find it via Auto-correlation function then the square of the FT of the signal? [closed]

In a video i saw that while calculating ESD or PSD of a signal time auto correlation function was used when it can be also done by the square of FT of the signal.Why we followed that approach even ...
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71 views

trying to understand fast fourier transform in matlab

Y = fft(X); P2 = abs(Y/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); 1) I dont understand what lines 2-4 are acheiving, why must lines 2-4 be ...
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964 views

Scaling property of Fourier Transform

Problem 4.6(b) from Oppenheim, Wilsky & Nawab (2nd ed) reads: Given that $x(t)$ has the Fourier transform $X(j\omega)$, express the Fourier transform of $x(3t - 6)$ in terms of $X(j\omega)$. The ...
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797 views

How to get around the circular shift property of Discrete Fourier Transform?

I understand that when we introduce a linear time shift using DFT on a finite sequence, the algorithm assumes that the signal repeats itself outside of the given range. Here is an example explaining ...
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1answer
56 views

Maximum of cross-correlation not moving

I already asked this question here yesterday, but it was very poorly worded I think. I made a much more detailled post explaining my problem of stackoverflow, as it might also be a code problem. Here ...
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graph display problem [closed]

I have a problem with the end of my code. I would like to display the last two curves, the problem is that at the beginning the size of YY is 288 and then after the equality with diff, my size goes to ...
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337 views

Orthogonal signals in frequency and time domains [closed]

I have 3 orthogonal signals obtained by Fourier transformation. But when I do the inverse Fourier transform in Matlab, my signals are no longer orthogonal in the time domain. Here is my question: ...
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60 views

What frequencies are present in the Fourier transform of the Dirac impulse?

When I do the Fourier transform of the Dirac impulse I get a pure sinusoid (or complex exponential, however you wanna call it) but I read in several places that all frequencies are present in the ...
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98 views

How to understand the relationship between the filter time constant and the half-power cutoff frequency

I learned that the time constant can be computed as $\frac{1}{2 \pi f_0}$, where $f_0$ is the half-power cutoff frequency of a high-pass filter. However, I was wondering how the time constant and the ...
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23 views

detection of periodicities in n-dimensional signals

Generally speaking, what analyses are necessary and sufficient for the detection of periodicities in an n-dimensional signal amounting to a discretely sampled density distribution over n-dimensional ...
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97 views

interpolate 1D signal depending on 3D parameter space

I have a 1D array of data d(x,p) in which a number of "bumps" or "dips" appear and/or move in the spacial dimension x, depending ...
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845 views

Amplitude of frequency bin in FFT doesn't match time-domain amplitude

I have a sinusoidal current that I am sampling at about 357k SPS. The current signal is about 3A pk-pk @ 750hz (top figure). I am wondering why when I take the fft using numpy/scipy's fft function, ...
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135 views

Get I and Q components from a signal (multple frequency signal)?

Is there anyway to get the I and Q components from a signal in the time domain? The signal has multiple frequencies. So far I have been doing this in a SIMPLE situation: Fast fourier transform to ...
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279 views

Software to extract frequency spectrum data from an audio file

I've been trying to learn how computers recognize musical notes, and I found apps like spectrogram which shows the frequency spectrum of a sound, but what I need is the data which is plotted or the ...