Questions tagged [dtft]
The dtft tag has no usage guidance.
133
questions
2
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0answers
60 views
DTFT and Eigenvalues in frequency domain
Consider an LTI system with impulse response $h[k]$. Does the frequency response $H(e^{j\Omega})$ equal the eigenvalue corresponding to an eigensignal of frequency $\Omega$?
So if I convolve an ...
1
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1answer
28 views
Moving average frequency response over an image
I'm studying image denoising by linear filtering with cross-correlation, in particular with a moving-average kernel (K x K kernel of all equal elements which sum is 1).
For clarity, I'd like to refer ...
3
votes
1answer
43 views
Where did we get the DC term of the Accumulator from DTFT?
Define $y[n]:=\displaystyle\sum_{m=-\infty}^{n}x[m]$. The DTFT is found as follows:
\begin{align*}
y[n]&=\sum_{m=-\infty}^{n}x[m]\\ \\
&=\sum_{m=-\infty}^{n-1}x[m]+x[n]\\ \\
&=y[n-1]+x[n]\\...
0
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1answer
56 views
Zero padding DFT intuition
I'm trying to grasp some intuition about why zero-padding the time domain sequence $x[n]$ interpolates the frequency domain bins of the $DFT\{x[n]\} = X[k]$ and how does this relate to the $DTFT$ of $...
1
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1answer
57 views
Proof of DTFT equal to DFT when signal is periodic?
I was using the Wikipedia page on the discrete time Fourier transform to understand the connection between DFT and DTFT. The following is claimed in the article - I was wondering if anyone had a proof ...
3
votes
2answers
130 views
DTFT of sine wave using freqz
As mentioned in the title, is it possible to use freqz to find the DTFT of a sine wave? I am confused about what the 'a' and 'b' vectors would look like, since there are only impulses in the numerator....
0
votes
1answer
22 views
DTFT Pairs confusion
When I am in the DT Fourier Domain, and I want to come back to the time domain, which pair do I use? Asking because both pairs have the exact same "form" in the Fourier domain, and that is ...
1
vote
1answer
43 views
Recovering DTFT from Z-transform
The relationship between the Z-transform and DTFT can be expressed like:
$$ H(e^{j \omega}) = H(z)|_{z = e^{j \omega}}$$
Graphically, evaluating the Z-transform on the unit circle is shown as sweeping ...
1
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1answer
74 views
Why do the DTFT and FFT give me completely different results for magnitude at a specific frequency?
I am trying to write a program to compute the magnitude and phase of a specific, non-integer frequency component (i.e. given a sampled finite signal of length $N$, I want to know the magnitude and ...
1
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1answer
45 views
Evaluate expressions without computing DTFT
Let $X(\omega)$ be the DTFT of the sequence $x[n]$ given by:
$$
x[n] = \{4, 2, -1, 5, -3, 1, -2, 4, 2\},\quad\text{for}\quad n \in [-6, 2]
$$
I do want to compute
$X(0)$
$X(\pi)$
$\displaystyle\int_{-...
2
votes
5answers
245 views
How is the DTFT of a periodic, sampled signal linked to the DFT?
I am trying to understand the connection between FT, DTFT and ultimately the DFT. But I am failing to link the DTFT to the DFT.
This is how far I am getting: Say I have a function $f(t)$, and its ...
0
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1answer
45 views
Discrete-time Fourier transform of $a^{|n|} u[n]$
I have a problem calculating the DTFT of this pair:
Could anyone tell me why the DTFT for $a^{|n|} u[n]$ is different from $a^{n} u[n]$'s?
4
votes
1answer
155 views
Why DFT is used for approximating CTFT when you can approximate CTFT-integral itself?
I was using MATLAB for approximating FTs. Why DFT is used if we can approximate the transform-integration using summation.
0
votes
0answers
111 views
Can different Discrete-Time-Fourier-Series(DTFS) coefficients have the same discrete sequence in the time domain?
Please, check the following discrete periodic sequence when the period $N=2$.
$x[k]=\exp(j\frac{2\pi}{N}k), N=\text{period}$
$..., x[0]= 1, x[1]= -1, x[2]= 1, x[3]= -1, ... , N=2$
According to my ...
1
vote
3answers
343 views
Does Zero Padding Distort the Spectrum of a Signal?
It's said to "sample the DTFT", revealing what "DFT fails to see". And I fail to see how this sampling isn't distortion.
The "spectrum" aims to provide the sinusoidal ...
1
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0answers
43 views
Deriving Fourier Transform of Time-Windowed Discrete Signal
I'm trying to derive the Fourier Transform of a finite-length discrete signal to show the effect of windowing,e.g. spectral leakage and resolution, but I can't seem to arrive at the same answer.
Just ...
0
votes
2answers
70 views
Inverse DTFT of phase shifted complex exponential
I have been working on this problem for a few days now and I think this is the closest I have gotten.
I am getting an Answer of zero and I would like to know if that is correct and if someone could ...
0
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0answers
29 views
find time domain sequences using DTFT definition (NOT IDTFT)
The sequence is X(e^jw) = 3 + 2cos(w) + 4cos(2w), and the problem asks to use the definition of the DTFT to find the corresponding sequence.
I have tried using the IDTFT and integrating, but I could ...
0
votes
1answer
65 views
How to find minimum length of a FIR symmetric filter if I am given DTFT
I am practising for upcoming exams and came across this question.
Let $h[n]$ be an FIR filter such that $h[n] = 0$ when $|n| > M$ and $h[n] = h[−n]$. A plot of $H(e^{j\omega})$ (DTFT of $h[n]$) is ...
0
votes
1answer
59 views
Inverse discrete time Fourier transform with differentiation
Consider a signal x[n] and its DTFT $X(e^{jω})$ . Assume $X(e^{jω})$ is differentiable. Compute the inverse DTFT of
$j\frac{dX(e^{jω})}{d\omega}$
You should write your answer in terms of $x[n]$ and ...
0
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1answer
59 views
How to calculate DTFT of cosine function divided by n
I'm having a hard time to calculate the next function, and I don't really know Matlab good enough to calculate it there.
Help would be appreciated:
$$h[n]=\frac{A_1 \cos[\theta_1(n-N/2)]}{n-N/2}$$
0
votes
1answer
37 views
Evaluate phase of $X(\omega)$ without computing $X(\omega)$
$$x(n) = \{ -1, 0, 1, 2, 1, 0, 1, 2, 1, 0, -1 \}$$
Let $X(\omega)$ be the DTFT of $x(n)$. I need to find the phase of $X (\omega)$ without computing $X(\omega)$. I notice that $x(n)$ can be a type I ...
0
votes
1answer
57 views
Finding causal impulse response given the imaginary part of the frequency response
I understand that I would need to calculate inverse Discrete Time Fourier Transform (iDTFT) to find $h(n)$. Since $h(n)$ is real, iDTFT of the imaginary part of $H(e^{j\omega})$ gives the odd part of ...
1
vote
1answer
60 views
Expressing DTFTs in terms of one another with similar time domain signals
I cam across a question in my DSP book asking this:
1). Express $X_2(e^{j\omega})$ in terms of $X_1(e^j\omega)$ without explicitly computing $X_1(e^{j\omega})$. ($X_1(e^j\omega)$ represents the DTFT ...
2
votes
1answer
50 views
Is my solution to the DTFT of a delta function correct?
I am newer to signal processing math and just figured out something cool (hopefully). I was trying to see how the DTFT of the delta function is 1, because thats what my book says. I could only find ...
1
vote
1answer
55 views
DTFT and a Downsampled Sinc Function
I found the answers to this question and this question to be extremely helpful in understanding the derivation of the downsampling or decimation property of the DTFT. Thank you! I am now struggling ...
1
vote
2answers
96 views
Question on N point DTFT - Fourier transform
I have been trying to use the logic that both X and Y should have same Z transform, but according to the definition, Y is not anti causal.
0
votes
2answers
877 views
Continuous frequency vs discrete frequency? [closed]
I have understood idea of discrete time and continuous time but I am feeling difficult to comprehend this idea in regard to frequency.
As for example the DFT output is discrete and the DTFT output ...
1
vote
1answer
64 views
Evaluating discrete spectral density at only a few frequencies
I'm trying to obtain the spectral density at three particular frequencies for a computational chemistry problem that I'm working on (if you are curious, it has to do with the estimation of Nuclear ...
0
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0answers
35 views
$2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal
please help me find the error in the following counter example.
Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
0
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0answers
44 views
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 ...
0
votes
1answer
100 views
Why is there a negative in front of the phase response equation for this complex exponential?
first time on here!
I'm working through "Digital Signal Processing using MATLAB" by Vinay and Proakis. Good book.
I am stuck on this example tho.
Shouldn't the imaginary part in the denominator (...
0
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0answers
19 views
How do you change an instance of dsp.DigitalDownConverter object in MATLAB to work with filters other than the ones it is originally defined with?
If you look at this website:
https://www.mathworks.com/help/dsp/ref/dsp.digitaldownconverter-system-object.html
you will see an example (with code) that attempts to up convert and down convert a ...
0
votes
1answer
160 views
Deriving expression for the DTFT of a rectangular window
Looking at the picture above, how did the author get from point A) to B)?
My Approach: Multiply A) by $e^{j\omega/2}/e^{j\omega/2}$. Now I am stuck with simplying the numerator.
0
votes
3answers
77 views
DFT of the same signal with different values of N
Let $x[n]$ be a discrete signal of 2 samples. We know that its DFT with N=4 is $X[k]=[0, 1+j, 2, 1-j]$. Without calculating $x[n]$, how can we know the DFT with N=2?
I have tried to use the relation ...
0
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1answer
127 views
CTFT to DTFT why can't you always just substitute $\Omega = \omega/T_S$
This is something I've always wondered about in DSP class, but just accept as a fact because I never really fully understand why this is the case:
Given CTFT:
$$X_s(j\Omega) = 6000 \pi \sum \limits_{...
2
votes
2answers
285 views
Effect of changing sample rate, window duration and zero padding on DTFT and DFT
Let $T$ be the window duration, $N$ be the DFT size, $F_s$ be the sample rate, and $F_{max}$ be the frequency of the highest bin. In the context of image below:
halving the $F_s$ (keeping $T$ ...
0
votes
2answers
678 views
Ideal high pass filter for discrete signal
there. I currently get stuck on a question. I was asking to find an inverse discrete-time Fourier transform for the ideal high pass filter.
Here is the question
It is getting more confused after I ...
0
votes
0answers
98 views
Characterizing a non-LTI system
How should we characterize a non-LTI system? For example we have: $y[n]=x[3n]+x[2n]+x[n]$ which is clearly not LTI. Also, the impulse response will be $h[n]=3\delta[n]$ and if we take the DTFT of this ...
1
vote
2answers
230 views
Getting the DTFT from the DFT samples
How would you get the DTFT from the DFT samples?
How will the DFT indexes map to the discrete frequency and what kind of an interpolation would be required?
0
votes
1answer
102 views
What is the formula for the frequency spectrum?
A signal $f[n]$ is given, the corresponding DTFT as $F(e^{j\omega})$ and a plot of the frequency spectrum $f(t)$. Unfortunately I can't find a formula for the frequency spectrum in my documents.
When ...
1
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1answer
225 views
Real-valued DTFT
Now this is a simple question, but I still ask it for clarification:
I know that an even signal $$h[n] = h[-n]$$ results in a real-valued DTFT (we have proven that in class). Now my question is the ...
0
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1answer
66 views
Orthogonality of filter impulse response to its even shift
I meet this problem but still do not know how to solve it.
Could you guy give me some guides?
Upsampling by 2 ($U_2$) followed by filtering by $g$, with operator $G$
And given: $<g_n,g_{n-2k}>...
0
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1answer
24 views
DTFT of inverse of any function
In my book solution is given like this.
But i am solving like this , am i doing wrong??
0
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1answer
68 views
From Orthogonality to DTFT
I have met this question, but cannot prove it using DTFT definition.
Given: $g$ is a discrete sequence filter and:
$$ g \in l^2(Z)$$
$$\langle g_n, g_{n-2k} \rangle = \delta_{k}$$
Prove:
$$|G(e^{j \...
0
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1answer
97 views
About the proof of an equality related to the DFT [sampling the DTFT to obtain the DFT]
This wiki page about the DTFT says that the DFT can be obtained from the DTFT by sampling the latter in one cycle at $N$ points:
When the DTFT is continuous, a common practice is to compute an ...
1
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1answer
207 views
relation between DFT to CTFT
The signal $$x(t)\;\;\;\;0\leq t\leq 0.2s $$
We know that the CTFT of $x(t)=0$ when $|w|>2*\pi*10^4$
We sample $x(t)$ in sample space of $$T=25\mu s$$ or $$F_s=1/T=40000Hz$$and we get a series ...
0
votes
2answers
51 views
Resampling of DTFT
I have a constant digital signal that is 1 for every sample and of length 4.
4 point DFT coefficients are $$[4,0,0,0]^T$$ Obviously. I wonder, if I resample the DTFT such that samples are taken at $$...
0
votes
1answer
272 views
Finite sequence input to DTFT
i'm studying the practical utility of Fourier transforms and i have some questions. I hope to receive answers in layman terms.
1) Does the DTFT take only infinite input sequences?
2) If i apply the ...
0
votes
1answer
120 views
Aliasing and DTFT of a real signal
We are analyzing a real signal with the DTFT. Since we are using a limited number of samples it's like we are transforming a finite signal.
As I remember, the FT of a finite signal has an infinite ...
