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1answer
28 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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0answers
4 views

Am to measure fatigue in different individuals using EEG based BCI [on hold]

How do I measure the brain activity using BCI i.e where the recorded signals will be viewed How do I interpret signals that constitute fatigue What method is the best for extraction of these signals ...
2
votes
3answers
176 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 ...
2
votes
1answer
111 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
30 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 ...
0
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0answers
18 views

How to calculate Fourier's coefficients of a $T$-periodic function with Scilab?

I have a vector of a size $N>1$ (it represents the values of a $T$-periodic function on a interval). I want to calculate its Fourier's coefficients with the fft, ...
0
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1answer
30 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 ...
0
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1answer
30 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" ...
1
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0answers
45 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 ...
1
vote
1answer
43 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 ...
1
vote
2answers
118 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 ...
0
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0answers
35 views

Fourier Transform of 2D signals

Hello I've been trying to solve this one for a while and I didn't come up with any solution. Given two 2D signals $g(x,y)$ and $f(x,y)$ as that $g(x,y)=f(ax+by, cx+dy)$ and that the Fourier transform ...
0
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0answers
59 views

Fourier transform on Scilab of a Gaussian function

I am trying to do a fourier transform on Scilab, of the Gaussian function $y(x)=\exp(-\frac{x²}{2})$, by using the fft command. So I plotted the graph of ...
0
votes
1answer
36 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 ...
1
vote
1answer
45 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 ...
0
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0answers
44 views

Magnitude Squared Coherence C/C++

I have two questions about the mscohere function in matlab. The first is, is it a requirement for length(N*M) of the image you are trying to find be equal to the length of a column in the image you ...
1
vote
1answer
42 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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0answers
34 views

Is there a way to determine what pitches are present at a given time in a music sample?

I'm sure it would be complicated to do so, but it seems the programs like Melodyne can separate notes in a chord. How complicated would it be to determine with any accuracy what pitches are being ...
0
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1answer
76 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 ...
0
votes
1answer
60 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 ...
1
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0answers
23 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 ...
0
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0answers
42 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_ {...
0
votes
2answers
127 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 ...
1
vote
1answer
50 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{...
1
vote
1answer
128 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*} ...
0
votes
1answer
58 views

Fourier Transform of image convoluting with kernel [closed]

edit: clarifying question. ...
1
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1answer
114 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 ...
0
votes
0answers
37 views

the DFT of a periodic signal represented by a fourier series

If I have a signal represented by a Fourier series(like in the photo), which is sampled with $T_s$: $$x[n]=x(t=nT_s) = \sum_{m=-\infty}^{\infty}a[m]e^{j2\pi m(nT_s)/T_0} $$ How do I find its DFT? I ...
3
votes
2answers
162 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 ...
1
vote
6answers
180 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.
-1
votes
1answer
372 views

Deconvolution in Python in 2D

Referring to this topic, I am interested in a deconvolution using Python. However, unlike the linked topic above, I want to deconvolve a 2D image. The scipy.signal.deconvolve function unfortunately ...
1
vote
2answers
80 views

PSD and $\lim_{T\rightarrow \infty} \frac 1 {2T} \int_{-T}^T x(t)\bar y(t)\,dt$

From Wikipedia, I taken a definition of power spectral density: For continued signals that describe, for example, stationary physical processes, it makes more sense to define a power spectral ...
0
votes
1answer
71 views

Seamless audio loops via Fourier transforms?

I am trying to create short seamless loops of continuous sound. I recorded myself making an "Aaaaah" sound at 44.1 KHz, and cut this recording to a section containing 4096 samples (giving me slightly ...
1
vote
1answer
74 views

Power Spectrum Analysis

In order to find a peak or max response in the fourier domain as in the spatial domain, I have been studying bartlett's method, welch's method, and the blackman-tukey method for more accurate power ...
1
vote
1answer
62 views

Fourier series calculation [closed]

I have tried to solve, but do not know if the answer is correct or not. A person has a periodic voltage input to a circuit. The input repeats itself every 0.02 seconds i.e. the fundamental period is ...
0
votes
0answers
85 views

Difference between summation of motion components and IFFT?

I have a problem using the IFFT command. I want to see if i can go from the frequency domain to the time domain of a signal. I wanted to test this in two parts: 1) first creating a wave time domain-->...
0
votes
1answer
267 views

What is the unit of autocorrelation function?

In general, for autocorrelation of the deterministic signals,from the formula what is the unit of it.
0
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0answers
30 views

Correlation of an image in the Fourier Domain

I have been reading up on correlation in the frequency domain, and I just had two questions which I could not find in the book I was reading nor online: [1] So correlation is the same as a normalized ...
1
vote
1answer
181 views

Fourier transform 4 times = original function (from Bracewell book)

I was glancing through "The Fourier Transform & Its Applications" by Ronald Bracewell, which is a good intro book on Fourier Transforms. In it, he says that if you take the FT of a function 4 ...
0
votes
1answer
21 views

Amplitude of an image

If I take a two dimensional image and conduct a fourier transform on it, I would get a two dimensional matrix of complex values. If I want to find the amplitude of each value, is that the same as ...
0
votes
2answers
188 views

Generate fourier transform signal

I'm newbie in DSP (maybe the question title is misleading for this reason, I apologize for this, please feel free to edit it) but not in programming. I want to experiment with Fourier (or FFT) ...
1
vote
1answer
105 views

frequency spectrum of the conjugate of x(t)

Is the frequency spectrum of x*(t) the same as the one of x(t). I'm telling this because I found that X*(f) = (X(-f))* . So to find X*(f), intuitively i would just flip X(f) because of the minus sign ...
0
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0answers
38 views

ًWhy we use fourier transform in most of spectrum estimation approaches?

I wonder why in all spectrum estimation techniques, the analysis depend on the Fourier transform? Why not deal with the signals in time domain?
2
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2answers
112 views

Compare between JPEG and JPEG2000

JPEG image compression is Fourier based DCT while modern image compression technique like JPEG2000 is based on more multi-scale technique like Wavelets.I want to know how Fourier and Wavelets are ...
1
vote
1answer
35 views

List of Fourier coefficientes to simulate musical instruments

I'm trying to find a list of Fourier Coefficients (frequencies/amplitudes, ie, spectral data) to simulate different musical instruments using additive synthesis. Are these data published somewhere? ...
1
vote
2answers
73 views

Find the Differential Equation of an Analog Band Pass Filter

I don't even know how to start. We're supposed to find the differential equations that links $V_{in}$, $V_{out}$, and $V_{io}$, as well as the values of $C_1$, $C_2$ and $R$ so the filter works in the ...
0
votes
1answer
401 views

Shift in Time-Domain after FFT-Convolution

To my understanding, multiplying a signal in the frequency-domain is equal to a convolution in the time-domain. I wrote a small python program, but i always end up with a shift in the time domain. ...
2
votes
3answers
158 views

Power Spectral Density computation and units

I want to make some calculs of power spectral densité of signal. For example a real voltage signal (physical unit : $V$) in time $g(t)$, its fourier transform $G(f)$ and $S_g(f)$. As far as I know,...
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2answers
598 views

Frequency spectrum of signal - Matlab

Here is the code I use to plot a function in frequency domain in Matlab: ...
0
votes
1answer
144 views

Increasing the number of points in the frequency spectrum

I have an image with few pixels in length and height. For this image I calculated the two dimensional Fourier transformation. What I got for the frequency spectrum in one direction was a very ...