# Questions tagged [dtft]

The tag has no usage guidance.

92 questions
Filter by
Sorted by
Tagged with
350 views

### $|X(e^{jω})|^2$ - Power or Energy Density?

If $x(n)$ is an aperiodic signal and $X(e^{jω})$ its DTFT, then, what is $|X(e^{jω})|^2$? Power or Energy Spectral Density? My understanging of Fourier transforms so far tells me that its energy ...
81 views

### Difference in Interpretation: $ω$ (rads/s) vs. $ω$ (rads) and $X(ω)$ vs. $X(e^{jω})$

The fourier transform of a continuous time signal $x(t)$ is $X(ω)$ where the unit of $ω$ is radians/second. And for a discrete signal $x(n)$, the DTFT is $X(e^{jω})$ where the unit of $ω$ is radians. ...
864 views

### Circular vs Linear Convolution

When deriving DFT from DTFT,we sample the frequency domain with uniformly spaced samples,hence adding periodicity to time domain. But DFT requires a limited support: we take only 1 period. Does that ...
264 views

### How is a continuous spectrum for the DTFT possible?

So we that a complex sinusoid of the form $e^{j\omega_0n}$ is periodic over $N=2\pi/\omega_0$ only if $\omega_0$ is a rational multiple of $\pi$, otherwise the exponential is not periodic. (see EDIT!) ...
93 views

### DTFT of $f[k] = 3^k u(-k-1)$

Find the Discrete-time Fourier transform of $f[k] = 3^k u(-k-1)$ (then sketch it and find its magnitude & angle). It doesn't fit any templates on the Fourier table, and I don't see how one ...
2k views

### Link between DFS, DFT, DTFT

My understanding of DFT is as follows For a signal $x[n]$ of finite-length, the DFT is DFS of the periodic extension, $\tilde{x}[n]$, of that signal $x[n]$ and also another way to view DFT is that it’...
228 views

### FFT-like algorithm for fast DTFT computation? [duplicate]

Good morning! I'm coding up a project on a microcontroller to read in some analog audio (specifically, the sound of someone whistling: a near perfect sine wave) and determine which piano note tones ...
4k views

### DTFT of any finite sequence in matlab

I think freqz in a MATLAB toolbox, is the way to obtain DTFT of sequence. freqz can calculate frequency response of: H(z)=(Num)/...
446 views

### Calculating the inverse DTFT of a signal

There is a signal $y[n]$ with a differentiable DTFT $Y(e^{i\omega})$. How do I find the inverse DTFT of $i\frac{dY(e^{i\omega})}{dw}$ in terms of $y[n]$ (where of course $i = \sqrt{-1}$)?
145 views

### Does $H(-z)$ produce aliasing? [closed]

Given $H(z)$ is the z-transform of a signal, I know that $H(-z)$ results in shifting of frequencies in DTFT by $\pi$ or $-\pi$. Does it produce aliasing ? How ?
551 views

### Magnitude and phase of $-\delta[n]$?

I was reading this document and it shows the computation of the magnitude and phase of $h[n]=-\delta[n]$. We can get the DTFT as: $$H(e^{j\omega})= -1$$ So the magnitude will be $1$, and according ...
333 views

### DTFT reconstruction

I have a sampled DTFT. If we assume that there isn't aliasing in time domain, what is the best way to reconstruct DTFT from its equidistant samples? I though about Dirichlet interpolation. Do you know ...
312 views

### What additional information do we get from z-transform that we don't get from DTFT? [duplicate]

As an engineer analyzing a system (whether it be a circuit or an audio sample), you should know when to apply the analysis tools you've been given--such as Discrete Time Fourier Transform and Z-...
307 views

### Mathematical advantages of the ZT, DTFT and DT?

I apologize if this question is too general to answer concretely, but I was hoping more to perhaps be pointed towards some resources that could help more extensively. Essentially, I have a Discrete-...
327 views

### The DTFT of $\{1,1\}$ is $1+e^{-j\omega}$ but what is the DTFT of $\{1,-1\}$?

So I know that the DTFT of $\{1,1\}$ is equivalent to $1+e^{j\omega }$. But what is the DTFT of $\{1,-1\}$ equivalent to? Is it equivalent to $1-e^{j\omega }$?
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 $... 3answers 4k views ### Why DTFT coefficients are periodic and why continuous Fourier transform coefficients are not periodic? As I understand, when the input signal is discrete in time and we want to find the coefficients of Fourier transform, DTFT is used and the coefficients in frequency domain are periodic, but I can't ... 1answer 883 views ### Tricks for plotting the magnitude of a DTFT? To preface, this isn't a homework question but rather a self-study question to help me to understand the basics of finding the DTFT and magnitude of the DTFT based on a discrete time signal sampled ... 1answer 584 views ### DTFT of$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 883 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: $$... 1answer 434 views ### Why is this DFT of a real symmetric signal resulting in complex valued coefficients? I am trying to understand exactly how sampling the DTFT to get the DFT works. The signal I'm trying to analyze is x(n) seen below.$$x(n) = \delta(n\pm2) + 2\delta(n\pm1) + 3\delta(n)$$Taking the ... 1answer 866 views ### 2D Fourier Transform of Rotated Discrete Domain Signal Assume we know that the Fourier transform of a signal x(n_1,n_2) is \mathcal{F}(x(n_1,n_2))=X(\omega_1,\omega_2). What is the Fourier transform of the signal after being transformed by a rotation ... 2answers 432 views ### Discreteness and periodicity in Fourier transform Why discreteness in time / frequency domain dictates periodicity in the other frequency / time domian? For example the DTFT is perodic in frequency? Why it doesn't contain all the frequencies? Why ... 1answer 539 views ### Finding the deterministic autocorrelation function (ACF) from its power spectrum The power spectrum of a stationary discrete-time random signal is$$\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 408 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 489 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 53 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 1k 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 47 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:$$f(t_n),\;t_n=\dfrac{n}{F_s}$$The definition of the DTFT is given by:$$F_n(\omega)=\sum_{n=0}^{N-1}f(t_n)\cdot e^{-i\omega_nt_n}$$Now,... 2answers 2k views ### Multiplication property DTFT I was truing to solve an example of DTFT which is following multiplication property. The problem is$$ a^n \sin(\omega_0 n) u[n]$$we know that the definition of DTFT is$$ X(j \omega) = \sum _ {n=-\... 3answers 606 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 170 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 $$\sum_{l=-\infty}^{+\... 0answers 111 views ### Confusion in understanding the Proof of DTFT While understanding the proof of DTFT from Signals and Systems by Oppenheim, I have confusion in understanding few steps.$$ 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 650 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 309 views ### Finding values of DTFT without explicitly computing My attempt : a) Summation of all values? b)c)d) Failed e) Parserval's theorem 3answers 6k 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 209 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^...