Questions tagged [dtft]
155 questions
2
votes
1 answer
How to find the DTFT of unit step with $(-1)^n$ scalar multiplied?
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 $H(\omega)$ and the scalar $(-1)^{n}$ is throwing…
Gary
- 345
- 1
- 4
- 14
1
vote
1 answer
DTFT of sawtooth wave through DTFT of rect signal
In a course i'm currently taking, the lecturer computed DTFT for the following signal:
$$r[n] = \begin{cases}
1& 0 \le n \le N\\
0& \mbox{otherwise}
\end{cases}
$$
For $N = 32$ i pictured $\frac{1}{N}\frac{\sin{\omega*N/2}}{\sin{\omega/2}}$:
The…
Yola
- 121
- 5
1
vote
1 answer
DTFT of $(-1)^n \cdot \mathrm{sinc}()$
I'm trying to find the DTFT of $$(-1)^n \cdot \frac{\sin (\pi n/2)}{\pi n}$$ I know the DTFT of $\frac{\sin \pi n/2}{\pi n}$ = a box function of amplitude 1, cutoff $\pi/2$. And I know that multiplication in time domain = convolution in frequency,…
python_
- 11
- 2
1
vote
1 answer
Finding values of DTFT without explicitly computing
My attempt :
a) Summation of all values?
b)c)d) Failed
e) Parserval's theorem
usfmohy
- 66
- 3
0
votes
1 answer
DTFT Pair Transformation of unit step
I am not seeing a direct pair of DTFT transform of the unit step.
0
votes
1 answer
Understanding graphs of DTFT with time shift of$~y\left[n\right]=x\left[n-2\right]~$
$$x\left[n\right]:=\text{discrete time signal}\tag{1}$$
The following plot is DTFT of$~x\left[n\right]~$
What I know so far are as below.
$$x\left[n\right]=\frac{1}{2\pi}\int_{0}^{2\pi}X\left(\exp\left(j\omega\right)\right)\exp\left(j\omega…
electrical apprentice
- 105
- 4
0
votes
0 answers
A DT sequence y[n] is constructed from another DT sequence x[n]
A DT sequence $y[n]$ is constructed from another DT sequence $x[n]$ according to the
formula $y[n]=x[nN]$, where $N$ is a constant positive integer greater than one. (This process is usually called decimation, although this name would strictly be…
John
- 1
- 1
0
votes
1 answer
FFT-like algorithm for fast DTFT computation?
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 are present in the signal.
Although the FFT is the…
Mahkoe
- 131
- 4
-1
votes
1 answer
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 trivial.
What I tried is to substitute $t=(n+1)$,…
Val9265
- 91
- 7
-1
votes
2 answers
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 sample values. But it is actually a convolution:…
Aswartha
- 1
- 2