Questions tagged [fourier]
The fourier tag has no usage guidance.
0
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2answers
51 views
What is the interpretation of Fourier Transform containing only imaginary part?
The FT of a unit step function is taken as:
$$
X(\omega) = \int_0^\infty e^{-j\omega t}dt = \frac{-1}{jw}e^{-j\omega t} \Biggr |_{0}^{\infty} = \frac{j}{\omega}
$$
The transform only has the ...
2
votes
2answers
160 views
Do Fourier frequencies actually exist in real life in form of “instantaneous frequency”?
For me, this is a very awkward question to be asked, as at this point in my studies I'm supposed to be quite expert with elementary mathematical tools like Fourier transforms, but this has always ...
1
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1answer
115 views
Autocorrelation of sinc function
I'm having trouble on computing the autocorrelation of the sinc function
I want to compute
$$R_{hh}(\tau)=\int_{-\infty}^{\infty}\operatorname{sinc}(t) \ \operatorname{sinc}(t-\tau) \ \mathrm{d}t$$
...
-1
votes
1answer
26 views
How to get descrete fourier tarnsfom [closed]
Could anyone explain me please how to produce descrete fourier transform of such signal? There are no anymore information besides the picture in this task.
3
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2answers
84 views
Fourier Transform of Alternating Periodic Rectangular Pulse
I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem.
Given the signal is periodic I could use formula for Fourier transform of periodic signals:
$$...
1
vote
1answer
28 views
How would I find the function given the magnitude plot and the phase response?
I'm wondering how I'd find the Fourier Transform X(jw) given the following information:
My understanding is that the expression for the continuous time fourier transform (CTFT) is magnitude(CTFT)exp(...
0
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0answers
33 views
Filtering out different narrow-band frequencies at once
I have asked a closely related question on SO at https://stackoverflow.com/questions/55168460/python-implementation-for-filtering-out-multiple-distinct-narrow-band-frequencie
but I am still unclear ...
0
votes
1answer
37 views
Help me understand the stages involved in filtering a signal using Discrete Fourier Transform
I have a series of discrete values measured from a sensor. I want to filter the frequencies coming from this sequence of values. Then, if I understood the process correctly this is what I do:
I ...
0
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1answer
21 views
How to detect the maximum resolvable spatial frequency of camera?
I am trying to calculate the minimum line pixel width that can be distinguished from noise as shown in the camera test chart in Figure 1 where the thinner lines on the left are getting more and more ...
0
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0answers
36 views
Fourier decomposition in Matlab
I am doing a Fourier decomposition of sea level series ( to find out one particular contribution within the sea level height). it should be applied subsequently on shifted (by one hour) windows of 96 ...
0
votes
1answer
89 views
Detrend data with no clear secular trend prior to Fourier analysis?
I am completing Fourier analysis on many different time series of sediment particle flux exiting an experimental flume. Data is collected at a resolution of 1 Hz for durations ranging from ~5,000 to ...
0
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2answers
88 views
What is the basic idea behind Fourier transform? [closed]
What is the basic idea behind (discrete and continuous) Fourier transform (FT)? In short, what is the difference between discrete and continuous FT?
I have read multiple answers on the web related to ...
0
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0answers
13 views
Extracting straight line and curves from an edge image using fourier coefficients
I came across Fourier coefficients and my understanding is that it is very efficient in analysing image properties such as shape etc.. I know we can use Fourier descriptors to describe shape... But in ...
1
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1answer
22 views
Linearity with Difference Period in Fourier Transform
I know that a system is linear if it satisfies
$$\mathscr{F}\{ a\,x(t)+b\,y(t) \} = a\,X(\omega)+b\,Y(\omega)$$
for Fourier transform, $X(\omega)\triangleq\mathscr{F}\{x(t)\}$
But what if $x(t)$ ...
0
votes
1answer
60 views
Calculating fourier transform
I have just recently started doing fourier transforms and I'm a little confused.
Can someone walk me through in detail how to calculate the Fourier transform of
I'm not looking for answer, just an ...
0
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1answer
109 views
Ambiguity in the IFFT process in OFDM
I am still trying to iron out some ambiguities in my understanding of the IFFT component of OFDM modulation schemes.
So here we have a QAM symbol $s_0$ being multiplied with the subcarrier for that ...
3
votes
1answer
144 views
Discrete Harmonics - Why multiplying digital frequency by k does not get next harmonic
For continuous time $ e^{jk\Omega_0t} $ gives a complete set of orthogonal harmonics for fourier decomposition but for discrete $ e^{jk\omega_0n} $ does not form a complete set orthogonal basis set ...
2
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1answer
81 views
Does the Fourier series coefficient of AC components remains same if DC component is subtracted form the given signal?
Suppose a signal is defined by
$
x(t)= \begin{cases}
t & 0\leq t \leq 1 \\
2-t & 1\leq t\leq 2 \\
\end{cases}
$
Since $x(t)$ has even symmetry, I can calculate fourier coefficient as
$$
a_n = ...
1
vote
3answers
78 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
vote
3answers
107 views
Intuitively, what is fourier series representation of a signal? Also intuitively what is frequency response? [duplicate]
I know these formulae and can solve problems mechanically but i never got the core concept. Please help me out with this.
0
votes
1answer
50 views
help in understanding cosine filter
I was referring to this link https://cdn.selinc.com/assets/Literature/Publications/Technical%20Papers/6059_HowMicroprocessor_Web.pdf?v=20180606-230156 . I am not very clear about the derivation of the ...
0
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1answer
60 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:
$ ...
0
votes
0answers
32 views
From Fourier (k space) to wavelet domain in MRI sensing
In compressed sensing MRI (cSENSE MRI) technology the idea seems to entail sampling from the Fourier domain (k space) in a way that, when transformed to the wavelet domain ("sparsification"), the ...
0
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0answers
376 views
Cosine Fourier Transform and Phase
If we do FT of cosine wave, then sine wave will be orthogonal. So, the imag parts of FT will be 0. This is my think. But, the result isn't show that. Like this.
Figure 1. Real and Imag parts (Y label ...
1
vote
3answers
210 views
Deconvolution Using Complex Division in The Frequency Domain
Consider these two signals:
a = [1 1 0 0 0 0 0 0]
b = [1 0 1 0 0 0 0 0]
their convolution is
c = a * b = [1 1 1 1 0 0 0 0]
...
0
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0answers
55 views
Finding essential bandwidth of the given function
Let the function to be $x(t) = e^{-2t}u(t)$.
I want to find the essential bandwidth of the function to be the frequency at which $|X(jw)|$ drops to $1\%$ of its peak value. With a search, I found that ...
1
vote
2answers
503 views
Hilbert transform of unit step function
How to calculate Hilbert transform, if it exists, of the signals like $u(t)$, $sgn(t)$.
What properties should a function satisfy for existence of Hilbert transform.
Absolute integrability of a ...
1
vote
1answer
118 views
Averaging magnitude squared coherence across multiple time series
In a previous post, A. Donda had suggested that, in order to calculate the average magnitude squared coherence of more than one pair of time series (e.g. y1 and x1, and y2 and x2), one ought to follow ...
1
vote
2answers
123 views
Resampling with and without replacement for estimating significance of spectral components
In order to test the significance of spectral components, it seems reasonable to randomly sort the data in order to destroy all the serial correlations / spectral order e.g. 100,000 times, and then ...
0
votes
3answers
423 views
Correct magnitude spectra of a cosine DFT?
I've just started my course on DSP and haven't laid my hands on MATLAB yet. I was wondering if the plot of the magnitude spectra was correct for the below shown $x(n)$:
1
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1answer
2k views
Impulse response of ideal filters
I am aware that an ideal low-pass filter in both continuous time and discrete time has a $\mathrm{sinc}$ impulse response. What would the impulse response of an ideal high-pass or band-pass filter ...
1
vote
2answers
375 views
BIBO Stability and the convergence of the frequency response of a system
It is my understanding that an LTI system is BIBO stable if and only if its impulse response $h(t)$ is absolutely integrable. This also happens to be one of the Dirichlet conditions for the ...
1
vote
1answer
212 views
Time scaling of discrete-time sequences and the DTFT
In the second edition of Signals and Systems by Alan Oppenheim, he discusses the DTFT of a "time-expanded" sequence that is effectively a slowed down version of the original sequence and can be ...
1
vote
2answers
367 views
Fourier transform of even/odd parts of a complex signal
Why does Oppenheim state the following properties:
\begin{align}
\mathcal F\big\{x_e (t) \big\} &= \Re\big\{ X(j\omega) \big\}\\
\mathcal F\big\{x_o (t) \big\} &= j \Im\big\{ X(j\omega) \big\...
0
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1answer
79 views
Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals
If we are given a signal of the form $$x(t) = \sum_{k = -\infty}^{+\infty} a_k e^{j k \omega_0 t},$$ can we call it a Fourier Series representation of $x(t)$ right away?
Suppose we are given the ...
3
votes
3answers
374 views
Periodicity of the discrete-time Fourier Transform
The DTFT of a sequence $x[n]$ can be written as $$X(e^{j\omega}) = \sum_{n = -\infty}^{\infty} x[n] e^{-j\omega n}.$$
Is the smallest (fundamental) period in frequency of the DTFT always $2\pi$? Or ...
0
votes
1answer
104 views
What is the exact meaning of the output of the Discrete Fourier Transform
I'm fairly new to the subject, but so far my understanding that this would be a transform you could use to go from a discrete set of data, say [1, 0, 1, 2] to a continuous sinusoidal function in the ...
0
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2answers
89 views
Duality of the continuous-time Fourier transform - derivation and notation
Suppose we have the Fourier transform pair $x(t)$ and $X(\omega)$ such that
$$X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} \mathrm{d}t$$
The duality property states that $X(t)$ and $2\pi ...
0
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1answer
94 views
Inverse Discrete-Time Fourier Transform of $X(Ω)=jΩ$
I am trying to solve it by using the properties but I can’t seem to find the same solution as on my book.
5
votes
2answers
92 views
Deriving the integration property of the Fourier Transform
I want to derive the property of the Fourier Transform that states that if $X(j\omega) = \mathcal{F} (x(t))$ then $$\mathcal{F} \left( \int_{-\infty}^{t} x(\tau) \mathrm{d} \tau \right) = \frac{1}{j\...
0
votes
1answer
42 views
Pulse wave question
Wikipedia, fount of all knowledge (Ha! LOL), gives a formula for a pulse wave here:
The formula is:
$$f(t)=\frac{\tau}{T}+\sum_{n=1}^{\infty}\frac{2}{n\pi}\sin\left(\frac{\pi n \tau}{T}\right)\cos\...
0
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0answers
134 views
Equation for impulse train
I am looking for a formula (Fourier series) to generate an impulse train waveform - a spike-wave with amplitude and period both $1$ – so that $f(x)$ has value $1$ at $x = 1,2,3,4...$ and $f(x)$ has ...
2
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1answer
185 views
struggling to understand why Fourier basis is orthogonal
Studying DSP on my own time on Coursera.
Was given a proof to why the Fourier basis is orthogonal, but I can't figure it out. Here is how it is proof goes.
Consider the Fourier basis
$$
\left\...
0
votes
1answer
51 views
Integral of the Fourier spectrum?
The integral
$$\int_{-\infty}^{\infty}|X(f)|^2df$$
of the absolute Fourier spectrum squared is the energy in the signal, but what about the integral of the 'simple' absolute Fourier spectrum?
$$\...
-1
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0answers
40 views
Suppressing a frequency using filtering Matlab [duplicate]
Below I have the following frequency representation of a signal. Using Matlab, I need to suppress the two peaks because they represent a beep. I added the notch filter to suppress one peak. But my ...
0
votes
2answers
301 views
Convolution effects width of the signal?
Let's say there are two signal with different frequency:
\begin{align}
X_1(\omega) &= 0\quad\text{for}\quad \lvert \omega\rvert > 1000\pi\\
X_2(\omega) &= 0\quad\text{for}\quad\lvert \omega\...
0
votes
1answer
186 views
MATLAB's $\tt cpsd$ and $\tt pwelch$ - different results for cross spectral power density
I am wondering why the following code does not yield the same results for Sxy1 and Sxy2, where ...
3
votes
1answer
133 views
Time domain basis
I have some troubles with understanding time domain, not on the intuitive level, but in math terms.
For example I have a vector signal $$ x = [x_0,x_1,x_2,...,x_{N-1}]$$
I understand that generally ...
0
votes
1answer
145 views
How to estimate covariance matrix using Fourier representation?
So, I have multidimensional time-series $X \in R^{(d \times T)}$, and I want to determine the covariance matrix of that signal in a specific frequency band.
I might filter the signal to that specific ...
4
votes
2answers
278 views
Relation between samplingrate and frequency
I am working on Fourier Transformation, and applying this for recognizing an audioclip.
I have a 9 second long audio clip of a guitar strumming an A-Minor.
The audioclip has a sampling rate of 44100 ...
