1
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0answers
12 views

Minimum phase non-rational transfer function: Hilbert transform between log magnitude and phase

In Signal Processing literature, it is well known that a minimum phase sequence with rational transfer function ('zeros' and 'poles' in unit circle) has Hilbert transform relation between log ...
0
votes
1answer
24 views

Why does the discrete cosine transform compact the information at the “low frequencies”?

I've been investigating about the discrete cosine transform. I think I understand the practical applications it has and how it is used in image/audio compression. I also know it is related with the ...
2
votes
2answers
41 views

A simple Fourier Transformation

I am a bit stuck with this small basic signal. I have this $$y(t)=\frac{\sin(200\pi\,t)}{\pi\,t}$$ and I want to take its Fourier Transformation. Obviously it looks like the sinc function. But that ...
1
vote
1answer
43 views

Convolution: $ f (-)*g = g(-)* f$ does this mean both $f$ and $g$ have to be even functions?

Assuming $f$ and $g$ are different functions, does $ f (-)*g = g(-)* f$ mean both $f$ and $g$ have to be even functions? In fact, this is equivalent to $f\star g = g \star f$ (i.e., cross-correlation ...
0
votes
1answer
16 views

Fourier transform and Z transform question?

Lets suppose we have an exercise where I have to find the Z transform and its region of convergence.I find the Z transform and the region.How do I determine if the Fourier transform exists from this ? ...
0
votes
1answer
19 views

Frequency response of unit impulse function

Could someone throw some light on how to get the frequency response of unit impulse function. I am not from EE, but I need it for my wavelet study.
0
votes
1answer
36 views

Fourier transform of a continuous non-periodic function in matlab

I would like to use matlab to find an Fourier transfom of a function which is known only on a grid. As an example I take the function f(x) = exp (-x^2), which Fourier transform is known and is equal ...
0
votes
1answer
48 views

Why would the discrete fourier transform “see” signals like this? What is the origin of spectral leakage?

The discrete fourier transform of $x = (x_{0},\dots,x_{N-1})$ is defined as $\displaystyle X_{k} = \sum_{n=0}^{N-1} x_{n}\omega^{kn}_{N}$ where $\omega^{kn}_{N} = e^{-2\pi ik/N}$ and ...
0
votes
1answer
26 views

Help for understanding Danielson-Lanczos lemma

The Danielson-Lanczos lemma is the basis for fast Fourier transform algorithms. Now, I do understand this step $\displaystyle X_{k} = \sum_{n=0}^{N-1} x_{n}\omega^{kn}_{N} = \sum_{n=0}^{(N/2)-1} ...
0
votes
1answer
60 views

Looking for a nice expression of these functions in terms of trig functions

I have come across three sinusoidal functions f1, f2, and f3 which, up to scaling and translation, are very close to each other. When normalized and plotted together, they are hard to tell apart. ...
0
votes
1answer
54 views

Parseval's theorem.

We consider two signal $h(t)$ and $g(t)$ such that $$\int_{-\infty}^\infty |g(t)|^2dt<+\infty$$ $$\int_{-\infty}^\infty |f(t)|^2dt<+\infty$$ Parseval's theorem states that: ...
0
votes
1answer
26 views

Top and bottom power spectral density of a height profile

Imagine I have a simple 1D height profile which is NOT symmetric. Now, what is truly important for me is to know what are the frequency content of the top profile (i.e. a cut profile above the ...
0
votes
0answers
44 views

Covariance between real and imaginary parts of Fourier transform of a stationary time series

Since Fourier transform of a random stationary time series(in the case of existence) is not necessarily real, my question is what is the relation between the covariance of real and imaginary parts of ...
0
votes
1answer
29 views

Discrete Time Fourier Transform of a real signal

I want to prove that if we have a real signal x[n] then for the DTFT it is applied that we have an even symmetry: | X(Ω+1/10) | = | X(-(Ω+1/10)) | (I mean the ...
3
votes
1answer
65 views

Image Reconstruction:Phase vs. Magnitude

Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. $$ ...
0
votes
1answer
44 views

Fourier and $Z$ transform of a signal?

We have $$X(k)=4[u(k-2)-u(k)* d(k-3)]$$ I need to find the Fourier transform,$Z$ transform,as well as dhe magnitude and phase spectra. First of all I think that I need to convert the $u(k)$ and ...
1
vote
1answer
42 views

How do we determine the duration of a fundamental frequency using the DFT (or FFT)?

I'm still in the process of learning the details of the DFT (and FFT) and I've just made a test .wav file in Audacity by joining 3 one-second sine waves together. .wav file 1 = 440 Hz, sample rate ...
0
votes
0answers
35 views

Plotting the frequency spectrum of a signal

I've found this algorithm here on Mathematica.SE to plot the frequencies of a signal using Fourier. It works beautifully, but I'm having some trouble understanding ...
0
votes
1answer
16 views

Representing a real sampled signal with N samples as a complex sampled signal with N/2 samples

I am studying the discrete Fourier transform, and in its most basic definition it is an invertible linear transformation on the complex numbers. From Wikipedia: The sequence of $N$ complex numbers ...
2
votes
1answer
25 views

Problem about average of cos square (nt) where n is arbitrary

I often see people just say time average of cos^2(nwt) is 1/2, I want to know in what cases this is not valid? w is just the frequency, can be assumed as a constant. Assuming you are always ...
1
vote
1answer
16 views

How do I deal with a seemingly fractional delays in discrete time fourier transforms?

Is a transfer function of a discrete time system is $H(e^{j\Omega})=e^{-j\Omega/4}$ and I feed it an impulse, what will be it's response? I know that technically a transfer function of ...
4
votes
1answer
59 views

Finding the period of the solution to $y'(x) = y(x) \cdot cos(x + y(x))$ with Fourier transform; how to interpret complex result?

A question elsewhere on this site asks about detecting the frequency of oscillations in a system defined by differential equations. The equation is $y'(x) = y(x) \cdot cos(x + y(x))$. The solution ...
0
votes
0answers
13 views

Is there a better approach than DFT for identifying known pitches in a sound sample?

I've been using DFT to extract information about which notes are being played in a sample of music. My understanding of it is fairly basic but what I have so far works a at least in principle. ...
2
votes
3answers
200 views

Any good introductory book/tutorial on Fourier Transform (up to FFT) with plenty of exercises and solutions?

I wonder what could be a good book to start learning in depth all aspects of the Fourier transform up to the FFT algorithm, and beyond. I am going to dedicate quite some time on the subject, so I ...
1
vote
1answer
81 views

Wavelet or FFT for Transient signal analysis?

For now I use FFT to analyze the response of an electrical system to some transient signal. The transient signal is $x(t)$, which translates to $X(w)$ in the frenquency domain. On the other hand I ...
0
votes
2answers
59 views

Fourier Transform: why do all segments generate the same magnitude response?!

I'm working on a DTMF program, and what I've done is to break the one long input signal I initially receive into a bunch of smaller components. I perform an FFT on each of the small components and ...
1
vote
2answers
82 views

What's the point of Dirac delta function?

I have heard that The main useful property of Dirac delta function is it's fundamental property that $$ \int_{-\infty}^{\infty}f(x)\delta(x-a)dx=f(a) $$ I don't understanding why this equation is ...
0
votes
1answer
42 views

Why divide by N (length of input sequence) during IDFT?

During DFT of a input sequence of length N, we find X(k). We find inner product with a basis vector to get the coefficient: X(k) = <x[n], e[k, n]>    |  k = 0, 1, 2, ... ...
0
votes
1answer
36 views

Question about the frequency domain and the fourier transform

if you have a signal say x(t) in continuous time and you transform it using the Fourier transform for continuous time you get X(w) which is the frequency domain representation of this signal x(t). ...
0
votes
1answer
43 views

Amplitude Spectrum, Nyquist Frequency, mixed/min/max wavelets

The problem is here. Now I know the definition of mixed/max/min phase wavelets, whether the roots lie within the unit circle or not. Starting from n = 1, let $$ x_t = ( 5, 6) $$ $$ X(z) = 5 + 6z $$ ...
0
votes
2answers
67 views

Fourier transform of 1 cycle of sine wave

Consider the signal: $\begin{align*} f(t) &= \sin(\omega t) \tag{$0 \leq t \leq 2\pi/\omega$}\\ &= 0 \tag{elsewhere} \end{align*}$ How to compute the Fourier transform of $f(t)$? I ...
0
votes
0answers
28 views

Fourier transform, what is the signal we're analyzing?

I studied Fourier Transform at university (very basic) and I know that it is a mathematical tool to get the frequencies out of a time signal (of some kind). There's something I have always wondered: ...
0
votes
1answer
34 views

What is the relationship between periodicity in a time domain signal and periodicity in the frequency domain representation of the same signal?

Is it true that the frequency domain representations of signals are always periodic? If so, is there intuition as to why? I'm having some trouble understanding what periodicity in the frequency ...
0
votes
2answers
31 views

Finding transfer function with Fast Fourier Fransform.

I have two signals with input = a(t) and output = b(t) that have been sampled every 0.01s and as such the fast Fourier transform has been used on both and utilised to produce a transfer function. The ...
0
votes
0answers
29 views

Determining valid frequency domain DTFT's

This question may or not be off-topic but it concerns Fourier Transforms so I'm assuming it's of some relevance here. One of my problem set questions is... Are the following frequency domain ...
1
vote
1answer
40 views

What is the meaning of a continuous curve in the frequency domain?

I am sorry for how rudimentary this question will sound. I approach the frequency domain thinking in discrete terms. The plane is frequency on the x axis and amplitude on they y (ignoring phases). ...
1
vote
1answer
49 views

How does this phase shift in x-space affect the position of a spectrum in k-space?

I'm working on a new form of signal detection with which I hope to recover both the amplitude and phase of a very small signal. However, doing this requires the use of some Fourier maths that I don't ...
0
votes
2answers
44 views

Very short theory question signals?

My teacher asked us this question yesterday in the lecture but it didn't make any sense to me. He asked: What do the coefficients of the exponential Fourier series represent? Also, what's the ...
0
votes
1answer
52 views

2-D Fourier Transform of complex exponential with 2-D quadratic phase

I've been looking around to see if there is either an exact transform pair or an approximation to either of the following but have not been able to find anything: $$ \mathcal{F}_{xy}\left( ...
2
votes
1answer
118 views

Need to learn wavelet, suggest steps and resources

I am looking for a good introduction to wavelets and wavelet transforms. that covers the following: Basics Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and ...
1
vote
0answers
66 views

Fourier Transform of a Gaussian Signal?

As far as I know this is the formula for FT : On this question on part b) I fint on the answer the part with e^-jwt is changed with cos(wt) I have no idea how cos(wt) came in ... would you please ...
3
votes
0answers
85 views

Artifacts and low frequencies FFT.

I am working on analyzing a time signal and want to preform a FFT. However I run in to some artifacts at low frequencies. I have managed to reproduce the behavior in a test signal. Given by $S(t) = ...
1
vote
1answer
89 views

Given a Poisson-noisy signal, what is the noise distribution of its Fourier transform?

Disclaimer: I'm not a mathematician, but here's my attempt at a mathy version of my question Start with a noiseless, discretely sampled expected signal $I(x_n)$. Construct a Poisson-noisy measurement ...
1
vote
1answer
54 views

Fourier analysis of an exponential function review

I am working through and reviewing some of the examples presented on Fourier analysis from a Modern Digital and Analog Communication Systems book. In one of the examples, the author goes through the ...
0
votes
2answers
132 views

Why is the DTFT (Discrete Time Fourier Transform) unique to each input?

As the title implies. I know the DFT of a signal is unique due to the matrix, but can anyone give a solid explanation as to why the DTFT is unique for each signal input? Thanks for your time!
2
votes
1answer
81 views

Paley Wiener Theorem on sinc function

Use the Paley-Wiener theorem to argue that, although ${\rm sinc}\left(t\right)$ is bandlimited, ${\rm sinc}\left(t^{3}\right)$ is not. Explain how the above result allows reconstruction of some ...
2
votes
1answer
52 views

Complex Integration of DTFT

Question A discrete-time signal $u \in \mathcal{l}^2(\mathcal{Z})$ has DTFT \begin{equation} \hat{u}(\omega) = \frac{5+3\cos(\omega)}{17+8\cos(\omega)} \end{equation} Use complex integration to find ...
0
votes
1answer
47 views

Understanding a step in the proof of the Inverse Fourier transform theorem

I'm trying to understand the proof of the Inverse Fourier Transform theorem in Stéphane Mallat's "A wavelet tour of signal processing". Near the end of the proof, we have: $ \lim_{\epsilon ...
1
vote
1answer
22 views

How do you compute the Fourier Transform of this Unit-Impulse Function?

I have been given this problem from a textbook (not homework, trying to study for an exam. The goal is to find the Fourier transform of this function. $\sum_{k=0}^\infty a^k*\delta(t-kT), |a|<1$ ...
0
votes
0answers
35 views

DFT one-dimensional vector

That's a way to define one-dimensional Discret Fourier Transformation (DFT)? If I have a signal $x \in \mathbb{R}^N$ and I take a rectangular window of lenght M: $y = (x_m, x_{m+1}, x_{m+2}, .., ...