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What are the DTFTs of the following two signals? $$x[n] = e^{j \pi n}\left\{u[n] - u[n-8]\right\}\quad\text{and}\quad h[n] = (-1)^n\left\{u[n] - u[n-4]\right\}$$ I am trying to find $X(\omega)$ and $... 3answers 4k views Why DTFT coefficients are periodic and why continuous Fourier transform coefficients are not periodic? As I understand, when the input signal is discrete in time and we want to find the coefficients of Fourier transform, DTFT is used and the coefficients in frequency domain are periodic, but I can't ... 1answer 727 views Tricks for plotting the magnitude of a DTFT? To preface, this isn't a homework question but rather a self-study question to help me to understand the basics of finding the DTFT and magnitude of the DTFT based on a discrete time signal sampled ... 1answer 534 views DTFT of$x[-n-1]$How can I determine the DTFT of$x[-n-1]$? I searched for DTFT problems and checked several references but I couldn't find a similar case. My background is a little lacking, so excuse me if it's too ... 2answers 666 views Frequency Response with Delta Function? I am trying to find frequency response and magnitude of the frequency response of the following system impulse response: $$h[n] = 2\delta [n] + 2\delta [n-1]$$ I understand, that through the DTFT: $$... 1answer 390 views Why is this DFT of a real symmetric signal resulting in complex valued coefficients? I am trying to understand exactly how sampling the DTFT to get the DFT works. The signal I'm trying to analyze is x(n) seen below.$$x(n) = \delta(n\pm2) + 2\delta(n\pm1) + 3\delta(n)$$Taking the ... 1answer 616 views 2D Fourier Transform of Rotated Discrete Domain Signal Assume we know that the Fourier transform of a signal x(n_1,n_2) is \mathcal{F}(x(n_1,n_2))=X(\omega_1,\omega_2). What is the Fourier transform of the signal after being transformed by a rotation ... 2answers 374 views Discreteness and periodicity in Fourier transform Why discreteness in time / frequency domain dictates periodicity in the other frequency / time domian? For example the DTFT is perodic in frequency? Why it doesn't contain all the frequencies? Why ... 1answer 465 views Finding the deterministic autocorrelation function (ACF) from its power spectrum The power spectrum of a stationary discrete-time random signal is$$\Phi_{xx}(e^{j\omega})=\begin{cases} 1 & |\omega|<\pi/2 \\ 0 & \pi/2 <|\omega| \le\pi \end{cases} $$(a) ... 1answer 1k views DTFT and Inverse DTFT Homework Problem I'm trying to solve this signals homework problem: So for part a, since multiplication in the time domain is convolution in the frequency domain, I just used a DTFT table, found the DTFT for \left(\... 2answers 2k views Difference between Fourier Transform and DFT? - Example I have read many excellent answers to similar questions, but never one this specific. Here is another way to ask it. Why is the modulation transfer function (MTF) of \textrm{rect}(x/5) = \textrm{... 2answers 3k views Relation between the DTFT and the spectrum of a sampled signal In the \rm DTFT (Discrete Time Fourier Transform) the spectrum is periodic with period of 2\pi . A continuous signal when sampled has a spectrum which is a repeated version of its original ... 1answer 316 views What is the interpretation of the discrete-time spectrum? The CTFT of an analog signal is a representation of that analog signal in terms of the frequency parameter of sinusoidal (cosine specifically) functions whose weighted sum make up that signal. The ... 2answers 451 views Why this DTFT plot from CTFT? [closed] I have a sample test with an answer but don't understand how they got to the answer: x(t) has info only between 2 < |\omega| < 4 X^F(\omega) = 0 for other frequencies. All ... 2answers 50 views DTFT inconsistency Let x[n] = u[n] - u[n-4] (a discrete pulse of length 4), and X(\omega) is its DTFT. Let x_1[n] = x[n]*x[n]. I expect DTFT of x_1[n] to be same as X(\omega), because x_1[n] has the same ... 4answers 936 views Formulas of the Fourier transform family It has annoyed me that there doesn't seem to be a source online where the complete complex Fourier transform family is presented with every variable defined. The lack of definitions can be a nuisance ... 1answer 39 views Given a discrete time signal, what is the sequence of possible frequencies I can get from DTFT? I know that when I have a discrete time signal, let's say: The definition of the DTFT is given by: Now, my question is regarding Omega(n). I know the frequencies will be discret because we can't ... 2answers 2k views Multiplication property DTFT I was truing to solve an example of DTFT which is following multiplication property. The problem is$$ a^n \sin(\omega_0 n) u[n]$$we know that the definition of DTFT is$$ X(j \omega) = \sum _ {n=-\... 3answers 476 views Question about z transform After studying z transform from different books and literature on internet I want to ask few which makes me confuse. a) From the Discrete Time Fourier Transform we have drive equation for z ... 1answer 158 views why$-$sign in DTFT pair for constant In discrete time Fourier transform, The DTFT of constant 1 is $$\sum_{l=-\infty}^{+\infty} \delta(\omega-2\pi l)$$. I have confusion that why there is$-$sign, why it can't be $$\sum_{l=-\infty}^{+\... 0answers 108 views Confusion in understanding the Proof of DTFT While understanding the proof of DTFT from Signals and Systems by Oppenheim, I have confusion in understanding few steps.$$ x'[n]=\sum_ {k=<N>} a_ke^{jk(2\pi/N)n} a_k= \frac{1}{N} \sum_ {... 1answer 74 views Find the Fourier transform of$g(k)$from$G(z)$for frequency$=1/2$$$G(z)=\displaystyle \frac{\frac{1}{z}}{1+\frac{5}{6z}+\frac{1}{6}z^{-2}}$$ I found: $$g(k)=\displaystyle \left(\frac{-1}{3}\right)^k - \left(\frac{-1}{2}\right)^k$$ I don't understand how I can ... 3answers 291 views Finding Fourier transform of a discrete signal from its Z-transform Is it possible to find the Fourier transform of a discrete signal if you know its$\mathcal{Z}$-transform of? 1answer 280 views Finding values of DTFT without explicitly computing My attempt : a) Summation of all values? b)c)d) Failed e) Parserval's theorem 3answers 5k views How condition for existence of Fourier transform is valid? The condition for Discrete time Fourier transform to exist for function$f(n)$is given as $$\sum_{-\infty}^\infty |f(n)| < \infty.$$ In case of continuous Fourier transform the difference is ... 1answer 190 views Inverse DTFT Problem Having trouble finding the inverse DTFT of$\ X(\ e^{j \omega}) = \frac{3 - \frac{1}{4} e^{-j\omega}}{1 - \frac{1}{4} e^{-2j\omega}} $Given the IDFT of$Xe^{j \omega}$as :$x(n) = \frac{1}{2\pi} ...
We know that Fourier transform $F(\omega)$ of function $f(t)$ is summation from $-\infty$ to $+\infty$ product of $f(t)$ and $e^{-j \omega t}$:  F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^...