Dtft Definition and 18 Threads

Homework Statement I'm kind of confused between DFT and DTFT. Here is my understanding: Okay, so let's say we have time domain, continuous, analogue signal from a sensor - ##x(t) ## 1. We sample this signal, giving us something like the following with an impulse train Now this is a...

Homework Statement Hi, So we started sampling/sampling theorem, dirac delta, DTFT in a digital signal processing module and I'm kinda confused. I understand how to derive the following formulae but these two formulae are so different to each other that I don't understand why? We are first...

Let's consider a signal which is continuous in both time and amplitude. Now we consider the amplitude of this signal at specific time instants only. This is my understanding of sampling a signal in time domain. When performing a Fourier transform on a time discrete signal, we have to apply the...

Hello everyone. Iam trying to understand the discrete time Fourier transform for a signal processing course but Iam quite confused about the angular frequency.If I have a difference equation given, what values should I choose for my angular frequency if I do not know anything about the sample...

Homework Statement There is a signal y[n] with a differentiable DTFT Y(eiw). Find the inverse DTFT of i(d/dw)Y(eiw) in terms of y[n] (where of course i = √-1). Homework Equations Sifting property ∫eiwndw = 2π*δ[n] from [-π,π] (integral a) leads to ∫Y(eiwn)dw = 2π*y[n] from [-π,π] (integral b)...

Could someone explain the intuition behind the variables of the FT and DTFT? Do I understand it correctly ? For FT being X(f), I understand that f is a possible argument the frequency, as in number of cycles per second. FT can be alternatively parameterized by \omega = 2 \pi f which...

1. Given: The DTFT over the interval |ω|≤\pi, X\left ( e^{jω}\right )= cos\left ( \frac{ω}{2}\right ) Find: x(n) 2. Necessary Equations: IDTFT synthesis equation: x(n)=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}X\left ( e^{jω} \right ) e^{j\omega n}d\omega Euler's Identity...

Homework Statement My book writes the following: using pair for the Discrete Time Fourier Transform: -a^{k}u[-k-1] <---(DTFT)---> \frac{1}{1-ae^{-iw}} for \left | a \right | > 1 Homework Equations Well, for the simple similar pair such as: a^{k}u[k] <---(DTFT)--->...

Hello. I'm stuck on calculating DTFT of 1. DTFT formula is: so dtft of 1 is: 1) in case of w=1, sum becomes: doesn't it diverge? 2) in case of w no 1, how the hell should that sum be calculated? thanks

Given a discrete time signal x[n] that has a DTFT (which exists in the mean square convergence or in the uniform convergence sense), how can we tell if the signal x[n] converges absolutely? I know the following: x[n] is absolutely summable <=> X(e^{j \omega}) converges uniformly (i.e...

So I'm trying to find the DTFT of the following; where u(n) is the unit step function. u \left( n \right) =\cases{0&$n<0$\cr 1&$0\leq n$\cr} I want to find the DTFT of u \left( n \right) -2\,u \left( n-8 \right) +u \left( n-16 \right) Which ends up being a piecewise defined function...

Homework Statement x[n] = Ʃ ck * δ(n-k), from k = -N to N. Plot the DTFT as a function of the number of terms N. This is a finite sum. Homework Equations The equation for the DTFT of a signal, which is Ʃ x[n] * e-j*2∏*∅*n, from n = -∞ to +∞ The Attempt at a Solution I have...

Hello all ! Homework Statement I have the following problem. I have to calculate the DTFT of this : x(n)=u(n)-u(n-4). Homework Equations Fourier Transformations The Attempt at a Solution So far , from what I have studied I have understood, that a DTFT , is actually many...

1. Homework Statement [/b] You are given the following pieces of information about a real, stable, discrete-time signal x and its DTFT X, which can be written in the form X(\omega)=A(\omega)e^{i\theta_x(\omega)} where A(\omega)=\pm|X(\omega|. a) x is a finite-length signal b) \hat{X} has...

Homework Statement You are given the following pieces of information about a real, stable, discrete-time signal x and its DTFT X, which can be written in the form X(\omega)=A(\omega)e^{i\theta_x(\omega)} where A(\omega)=\pm|X(\omega|. a) x is a finite-length signal b) \hat{X} has exactly two...

Can someone explain to me why sometimes I see the DTFT as functions of capital omegas or e^(jomega). I'm failing to see the reason.

Homework Statement Compute the DTFT of the following signal. x[n] = (0.8)^n u[n] Homework Equations Properties of DTFT The Attempt at a Solution Well, my professor tells me to use the properties of DTFT to solve this. I'd love to - except I don't know what the DTFT of (0.8)^n...

I'm considering the 12 –point sequence x[n] which is defined as x[n] = {1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1}. I'd like to use Matlab to find the DFT (X[k] of x[n]) and DTFT (X(e^jw) of x[n]). I realize that the DFT is sampled version of DTFT, and I want to show this graphically using...