# Tagged Questions

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### 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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### 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, ...
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### 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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### 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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### 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 ...
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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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 ...
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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### When is the Fourier transform of a signal periodic?

I mean not the time-domain signal being periodic, but the Fourier transform being periodic.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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-->...
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### What is the unit of autocorrelation function?

In general, for autocorrelation of the deterministic signals,from the formula what is the unit of it.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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) ...
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### 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 ...
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### ً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?
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### 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 ...
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### 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? ...
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### 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 ...
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### 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. ...
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### 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,...