Questions tagged [fourier]
The fourier tag has no usage guidance.
0
votes
1answer
50 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
79 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
11 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
vote
1answer
21 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
49 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
69 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
134 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
votes
1answer
74 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
77 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
83 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
43 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
42 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
29 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
votes
0answers
252 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
153 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
votes
0answers
52 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
447 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
84 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
116 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
278 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
vote
1answer
1k 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
311 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
146 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
283 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
votes
1answer
71 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},$$ can we call it a Fourier Series representation of $x(t)$ right away?
Suppose we are given the ...
2
votes
3answers
313 views
Periodicity of the discrete-time Fourier Transform
The DTFT of a sequence $x[n]$ can be written as $$X(e^{j\omega}) = \sum_{n = -\infty}^{\infty} x[n] e^{-j\omega n}.$$
Is the smallest (fundamental) period in frequency of the DTFT always $2\pi$? Or ...
0
votes
1answer
87 views
What is the exact meaning of the output of the Discrete Fourier Transform
I'm fairly new to the subject, but so far my understanding that this would be a transform you could use to go from a discrete set of data, say [1, 0, 1, 2] to a continuous sinusoidal function in the ...
0
votes
2answers
71 views
Duality of the continuous-time Fourier transform - derivation and notation
Suppose we have the Fourier transform pair $x(t)$ and $X(\omega)$ such that
$$X(\omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} \mathrm{d}t$$
The duality property states that $X(t)$ and $2\pi ...
0
votes
1answer
71 views
Inverse Discrete-Time Fourier Transform of $X(Ω)=jΩ$
I am trying to solve it by using the properties but I can’t seem to find the same solution as on my book.
0
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0answers
141 views
Understanding Subband Filtering?
I fully understand how a Fourier Transform and FFT work, however, something I've seen before, which confuses me is subband filtering.
I've heard of application of subband filtering with audio where ...
5
votes
2answers
90 views
Deriving the integration property of the Fourier Transform
I want to derive the property of the Fourier Transform that states that if $X(j\omega) = \mathcal{F} (x(t))$ then $$\mathcal{F} \left( \int_{-\infty}^{t} x(\tau) \mathrm{d} \tau \right) = \frac{1}{j\...
0
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1answer
42 views
Pulse wave question
Wikipedia, fount of all knowledge (Ha! LOL), gives a formula for a pulse wave here:
The formula is:
$$f(t)=\frac{\tau}{T}+\sum_{n=1}^{\infty}\frac{2}{n\pi}\sin\left(\frac{\pi n \tau}{T}\right)\cos\...
0
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0answers
108 views
Equation for impulse train
I am looking for a formula (Fourier series) to generate an impulse train waveform - a spike-wave with amplitude and period both $1$ – so that $f(x)$ has value $1$ at $x = 1,2,3,4...$ and $f(x)$ has ...
2
votes
1answer
180 views
struggling to understand why Fourier basis is orthogonal
Studying DSP on my own time on Coursera.
Was given a proof to why the Fourier basis is orthogonal, but I can't figure it out. Here is how it is proof goes.
Consider the Fourier basis
$$
\left\...
0
votes
1answer
49 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?
$$\...
0
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0answers
38 views
Suppressing a frequency using filtering Matlab [duplicate]
Below I have the following frequency representation of a signal. Using Matlab, I need to suppress the two peaks because they represent a beep. I added the notch filter to suppress one peak. But my ...
0
votes
2answers
237 views
Convolution effects width of the signal?
Let's say there are two signal with different frequency:
\begin{align}
X_1(\omega) &= 0\quad\text{for}\quad \lvert \omega\rvert > 1000\pi\\
X_2(\omega) &= 0\quad\text{for}\quad\lvert \omega\...
0
votes
1answer
173 views
MATLAB's $\tt cpsd$ and $\tt pwelch$ - different results for cross spectral power density
I am wondering why the following code does not yield the same results for Sxy1 and Sxy2, where ...
3
votes
1answer
127 views
Time domain basis
I have some troubles with understanding time domain, not on the intuitive level, but in math terms.
For example I have a vector signal $$ x = [x_0,x_1,x_2,...,x_{N-1}]$$
I understand that generally ...
0
votes
1answer
122 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
262 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 ...
-1
votes
1answer
58 views
Plotting a sampled signals DTFT using its CTFT
So I know the connection between the DTFT and the CTFT is the following:
Where the left-hand side is the discrete time fourier transform.
I need to choose a sampling rate which won't cause any ...
2
votes
1answer
376 views
Bandwidth and Bit rate
I'm kind of confused about digital transmission.
Is the bandwidth occupied by some digital signal the Fourier spectrum of the bit (pulse) format,or the one determined by the bit rate?
1
vote
2answers
364 views
Separation of overlapping frequencies
I have a signal with multiple frequencies, and two of them, one of which is my main frequency, overlap.
Are there any techniques that could separate two frequencies that almost overlap?
I can ...
1
vote
0answers
78 views
Fastest PC configuration for FFT [closed]
I'm currently implementing rotation-invariant phase correlation algorithm, which is a variant of phase correlation algorithm (https://en.wikipedia.org/wiki/Phase_correlation) to estimate relative ...
1
vote
1answer
40 views
Modulation and filtering
When I modulate a signal $x(t)$ with $\cos(2 \pi f t)$ and the modulated signal passes through a HPF, what output do i get in the frequency domain?
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0answers
165 views
Inverse Fourier Transform of the real part of fourier transform, and inverse transform of the imaginary part of fourier transform [closed]
How can I calculate the inverse fourier transform of the real part of the fourier transformation?
0
votes
0answers
114 views
Implementing a ram-lak filter in javascript implementation of fast fourier transform?
Having a non-mathematical background I'm trying to understand how to implement filtering of data in the frequency domain as part of FFT.
A javascript implementation of a discrete FFT is found here.
...
1
vote
1answer
659 views
Prove the dirac delta contains all frequencies
I'm looking for a mathematical proof that the dirac delta contains all frequencies.
I just read in a text book that the frequency spectrum of a dirac is just a horizontal line of amplitude 1, whereas ...
3
votes
1answer
573 views
How to “scale” the FFT when using it to calculate discrete convolution?
As you probably know, the discrete convolution $ H = F \ast G $ of some $ F \left[ x \right] $ and some $ G \left[ x \right] $ can be calculated using the Fast Fourier Transform (FFT).
To do this, ...
