Questions tagged [fourier]

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2answers
147 views

Explanation of fundamental filtering's consequences on signal

Can anyone explain why exactly an "Overshooting" phenomena is observed when the fundamental harmonic is removed as seen on the figures? Is it technically right to call this "overshooting" at all ? If ...
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2answers
602 views

Non Periodic, Deterministic Power Signals

Any one know of work on non-periodic but deterministic power signals? Now one member in this class would be the quasi periodic signals. I wonder if there is a generalized Fourier analysis of non-...
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1answer
192 views

Meaning of transform's area - Fourier

What is the graphic meaning of the transform's area? $$\int_{-\infty}^{+\infty}{X(f)df}$$ Where $X(f)$ is the continuous Fourier transform of the signal $x(t)$. Thank you very much.
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1answer
436 views

Difference between frequency components and harmonic components - Fourier

What is the difference between frequency components and harmonic components? The first concern the continuous domain of frequency, while the second concern the discrete domain of frequency ($f_{k}=kf_{...
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5answers
1k views

Fast & accurate convolution algorithm (like FFT) for high dynamic range?

It seems that FFT-based convolution suffers from limited floating-point resolution due to evaluating everything around the roots of unity, as you can see in the $10^{14}$-factor error in this Python ...
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2answers
191 views

Filter design to realize Cauchy product

I come from Computer Science so please pardon for my possibly wrong terminology. I need to design a filter which has coefficients $$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...
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1answer
1k views

Fourier Transform of a signal using direct integration and properties

Am trying to compute the Fourier Transform of a function using the properties of the Fourier Transform once and checking my answer using direct integration. My problem is that am not getting the same ...
2
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1answer
554 views

Fourier Slice Theorem - Reconstruction Fourier Space

I've stuck in one problem. I need to perform Fourier Slice Theorem on sinogram of medical image. I read a lot about this theorem. I write a matlab code but results are always non-sense after inverse ...
3
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1answer
113 views

estimating spectral optimization

I'm relatively new to DSP so excuse my simplified words, and my detailed explanation. if the signal have non-coherent sinusiod, it will induce energy spreading into the frequency domain. One of the ...
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1answer
675 views

Fourier series approximation: DC component and fundamental frequency

In the linked image below, what is meant by plotting the DC component and fundamental frequency for a Fourier series approximation? For dot point 1 does it want me to graph just the DC component ...
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1answer
191 views

Why can Fourier series be used on a non-repetitive function?

I was just wondering why Fourier series can be used on the function in the linked image. This is since I thought the function had to repeat itself to use Fourier series on it. Or is it saying a period ...
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4answers
1k views

The Number of Sine and Cosine Waves in an $ N $ Point DFT

This is bound to be an embarrassingly simple question, but here it goes... I was reading the chapter on discrete Fourier transforms (DFT) of this really didactic online book, The Scientist and ...
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1answer
2k views

How to get the data (pointwise frequency, amplitude and phase) in a FFT performed on ImageJ?

How to find pointwise readouts of the amplitude, frequency and phase of the DFT underpinning the FFT image? Once an image is FFT-ed in ImageJ, placing the cursor over any points on the FFT plot ...
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2answers
965 views

How can understand periodicity of a Signal from frequency domain representation?

Is it possible to say a signal is periodic from its frequency domain representation? A periodic signal is sum of its sinus and cosinus. Frequency translation of sinus and cosinus functions are ...
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3answers
193 views

Effects of interchanging sine terms with cosine terms

Suppose we have a real signal $x(t)$. Now, we know that $x(t)$ can be represented as a sum of sines and cosines. w be the angular frequency. If $a(\omega)$ be the coefficients of the cosine terms, ...
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1answer
608 views

Fourier convolution of a histogram

Notation: $\mathcal F\left\{a\right\}$ denotes applying the discrete forward Fourier transform to the histogram $a$. Similarly for $\mathcal F^{-1}\left\{a\right\}$ and the discrete inverse Fourier ...
2
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2answers
282 views

Is the frequency spectrum dependant on frequency, or on imaginary angular frequency? [duplicate]

The frequency spectrum of a time domain signal x(t) can either be written as X(f) or $X(j\omega)$. But how is the later correct? I mean, the frequency spectrum is clearly dependant on the frequency, ...
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1answer
371 views

The DTFT of $\{1,1\}$ is $1+e^{-j\omega}$ but what is the DTFT of $\{1,-1\}$?

So I know that the DTFT of $\{1,1\}$ is equivalent to $1+e^{j\omega }$. But what is the DTFT of $\{1,-1\}$ equivalent to? Is it equivalent to $1-e^{j\omega }$?
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3answers
235 views

Real world application of signal sparsity?

There are theories based on signal sparsity in frequency domain like Compressive Sensing, Sparse FFT, etc. Throughout searching and studying papers I found out Cognitive Radio is a good example of ...
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3answers
2k views

What is meant by “correlation” when referring to spectral coherence

I've been reading that coherence measures the correlation between two waves as a function of frequency. I also read that difference in phase does not mean less coherence at a given frequency, and that ...
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1answer
98 views

Finding frequency respone of a differential/integral LTI system

So suppose that we have an LTI system defined by the differential/integral equation below, where $x(t)$ and $y(t)$ denote the system input and output, respectively. How would I find the frequency ...
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1answer
693 views

Can we use Tiva C series TM4C123GXL for signal processing experiment purposes? [closed]

I've newly bought texas instruments Tiva C series TM4C123GXL processing board for developing DSP application project. Is that processing board is good for that purpose? Is that well work with Matlab? ...
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1answer
800 views

Effect of DC component on the whole signal - comparison between normalised and non normalised

I have a fourier analysis signal as in the picture attached, where red represents the FFT of movement of the hand of a stroke subject and the blue one is the movement of a healthy subject. I am doing ...
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1answer
1k views

Time-differentiation property of Fourier transform for $\sin(\omega_0t)$ and $\cos(\omega_0t)$ [duplicate]

As I know, the Fourier transform has the below property which is called time-differentiation: $$ \frac{dx(t)}{dt}\leftrightarrow j\omega X(j\omega) $$ and the Fourier transform of the cosine and the ...
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3answers
2k views

“Fourier Transform can localize signals in frequency domain, but not in time domain.” — What does it mean in layman's terms?

I was studying the introduction to wavelets and its benefit over the frequency domain. I said that: Fourier analysis can't localize signals both in time and frequency domain. Fourier analysis can ...
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3answers
836 views

Trying to decompose a signal into sine waves whose wavelengths aren't restricted to 1/N times sample range?

I am trying to essentially do a Fourier transform - I want to fit some data with sine/cosine functions. At first I was trying to do this using FFT, but my problem is that the FFT algorithm doesn't ...
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2answers
2k views

Frequency Analysis (DFT / FFT) of a Signal Without a Constant Sampling Frequency (Non Uniform Sampling in Time Domain)

I'm a stack exchange user for some time and now I'm registering to ask a simple question (I think!). I have a vibration signal with an amplitude and time (sampling frequency not constant) in a $...
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1answer
649 views

Why can FFT only operate on images with specific properties?

Can FFT only operate on Grayscale images? If Yes, why? Can FFT only operate on images with dimensions of power of two? If Yes, why?
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3answers
504 views

Can use of Fourier transform be minimized completely with the help of Laplace and Z transform?

Fourier transform has different types like continuous Fourier transform (CFT), Discrete time Fourier transform (DTFT) and Discrete Fourier transform ( DFT). CFT can be used in case of continuous ...
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1answer
1k views

How to prove that the peak of the autocorrelation function is at zero lag?

Show that for a signal $f(\tau)$ with finite energy and energy autocorrelation function $\phi^e_{ff} (\tau),$$$|\phi_{ff}^e (\tau)| \leq \phi_{ff}^e (0), \ \ \forall \tau.$$ According to my textbook ...
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2answers
121 views

Fourier transform of $ne^{-an}u[n]$

I need to find the Fourier transform of the following signal: $$ne^{-an}u[n]$$ The answers start by using the rule of the basic signal: $$a^nu[n] \rightarrow \frac{1}{1-ae^{-j\omega}} $$ and then ...
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1answer
2k views

LTI system response to periodic input

I'm trying to find the zero-state response (ZSR) of an LTI system to a one sided periodic input, like a square wave that is equals to zero for $t < 0$. I know that I can use the Fourier series of ...
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1answer
149 views

Complex Conjugate Sinusoids in Forward DFT

I hope this isn't such a dumb question, but I'm finally getting to grips with the inner workings of the DFT. What I'm having trouble understanding is why the basis complex sinusoids in the "forward" ...
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0answers
9k views

Flat top sampling to a step shape signal

Flat Top Sampling During transmission, noise is introduced at top of the transmission pulse which can be easily removed if the pulse is in the form of flat top. Here, the top of the samples are flat i....
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1answer
522 views

Real Time Goertzel Algorithm

Why is Goertzel Algorithm considered a block algorithm? Given that my input is bounded, couldn't I just run it forever (taking every sample that comes out after some length N) given a big enough word ...
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3answers
18k views

Two-Sided Frequency Spectrum

I am trying to make FFT simulation in Matlab by generating noise added two sinus waves in 60Hz and 100Hz. After adding the noise into these signals then I have applied the FFT as I put my Matlab code ...
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1answer
2k views

Inverse Fourier Transform problem

One of my tutorial questions for communication systems asks me to find the time function $x(t)$ which has the Continuous-Time Fourier Transform: $$X(\omega) = \frac{3}{(1+j\omega)(2-j\omega)}$$ So far ...
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1answer
243 views

Fourier Transform of triangle function $x(t)=\Delta\left(\frac{t-1}{2}\right)$

Can you please tell me if my working is right for the Fourier Transform of this function: $$x(t)=\Delta\left(\frac{t-1}{2}\right)$$ My workings are: I have used the fourier transform standard ...
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1answer
253 views

Fourier transform 4 times = original function (2D and higher)

The Signal Processing SE post linked below shows how the Fourier Transform applied 4 times to a 1D function returns the original function, i.e. F{ F{ F{ F{ g(x) } } } } = g(x) Link to 1D case: ...
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1answer
137 views

Calculating original signal from Discerete Fourier Transform

I am trying to calculate the original equation using a DFT. I start with a equation, generate values from this equation and then get the dft of these values. The aim is to generate the original ...
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1answer
404 views

Fourier Transform of exponential

While solving Example 4.1 of Signals and Systems by Alan Oppenheim. Example 4.1 is: $$ x(t)=e^{-at}u(t), a>0$$ and the transform I get is: $$ X(j\omega)\frac{1}{a+j\omega}, a>0$$ The problem is ...
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0answers
46 views

Is there a way to go from a set of (F/D)FT values to FIR coefficients?

I'm not yet well educated on the DSP subject, but I've initiated a project where I will do some audio filtering. My intuition tells me that there is a link between the coefficients of a FIR filter and ...
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0answers
115 views

Confusion in understanding the Proof of DTFT

While understanding the proof of DTFT from Signals and Systems by Oppenheim, I have confusion in understanding few steps. $$ x'[n]=\sum_ {k=<N>} a_ke^{jk(2\pi/N)n}$$ $$ a_k= \frac{1}{N} \sum_ {...
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4answers
16k views

About Fourier transform of periodic signal

In Fourier transform for periodic signal, I checked different books and I found a different explanation in each book. Let's take the explanation in Signals and Systems by Rajeshwari & Rao: The ...
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1answer
212 views

Frequency translation of an ideal low pass filter

I am trying to create a discrete-time filter with a Fourier transform as follows. $X(\omega) = \begin{cases} 1, & T - W \leq \omega \leq T + W\\ 0, & \text{all other values of } \omega \end{...
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1answer
306 views

Fourier Transform/Series DFT/DFS textbook problem (simple?)

Suppose $x_c(t)$ is a periodic continuous time signal with period 1 ms and for which the Fourier series is \begin{align*} x_c(t) &= \sum\limits_{k=-9}^9 a_k e^{j(2000 \pi k t)} \\ \end{align*} ...
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1answer
166 views

Fourier Transform of image convoluting with kernel [closed]

edit: clarifying question. ...
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1answer
1k views

Numpy's real fft (rfft) - losing power

Related to another problem I'm having, I was looking into the workings of numpy's rfft2 and ...
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2answers
2k views

Fourier transform artifacts

My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in ...
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6answers
4k views

When is the Fourier transform of a signal periodic?

I mean not the time-domain signal being periodic, but the Fourier transform being periodic.