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Questions tagged [fourier]

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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 ...
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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 ...
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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 ...
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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
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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
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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
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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 = ...
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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 ...
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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.
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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: $ ...
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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 ...
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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 ...
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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] ...
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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 ...
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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
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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
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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
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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 $x(n)$:
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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 ...
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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
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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
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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\...
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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
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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
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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
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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
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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.
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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 ...
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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\...
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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\...
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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
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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\...
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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? $$\...
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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
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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
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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
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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
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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
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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
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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?
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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 ...
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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 ...
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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?
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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. ...
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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
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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, ...