Questions tagged [dtft]
The dtft tag has no usage guidance.
107
questions
2
votes
1answer
29 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
23 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 ...
0
votes
0answers
21 views
Find the inverse DTFT of the following signal: [closed]
Can someone please help me out here in solving this question.
2
votes
2answers
38 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. So, I am clueless!
0
votes
2answers
45 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
49 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
27 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
votes
0answers
43 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
38 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
votes
0answers
12 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
17 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
58 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
votes
1answer
90 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:
$$X_s(j\Omega) = 6000 \pi \sum \limits_{...
2
votes
2answers
81 views
Effect of changing sample rate, window duration and zero padding on DTFT and DFT
Let $T$ be the window duration, $N$ be the DFT size, $F_s$ be the sample rate, and $F_{max}$ be the frequency of the highest bin. In the context of image below:
halving the $F_s$ (keeping $T$ ...
0
votes
1answer
67 views
Ideal high pass filter for discrete signal
there. I currently get stuck on a question. I was asking to find an inverse discrete-time Fourier transform for the ideal high pass filter.
Here is the question
It is getting more confused after I ...
0
votes
0answers
22 views
Characterizing a non-LTI system
How should we characterize a non-LTI system? For example we have: $y[n]=x[3n]+x[2n]+x[n]$ which is clearly not LTI. Also, the impulse response will be $h[n]=3\delta[n]$ and if we take the DTFT of this ...
1
vote
2answers
95 views
Getting the DTFT from the DFT samples
How would you get the DTFT from the DFT samples?
How will the DFT indexes map to the discrete frequency and what kind of an interpolation would be required?
0
votes
1answer
46 views
What is the formula for the frequency spectrum?
A signal $f[n]$ is given, the corresponding DTFT as $F(e^{j\omega})$ and a plot of the frequency spectrum $f(t)$. Unfortunately I can't find a formula for the frequency spectrum in my documents.
When ...
1
vote
1answer
111 views
Real-valued DTFT
Now this is a simple question, but I still ask it for clarification:
I know that an even signal $$h[n] = h[-n]$$ results in a real-valued DTFT (we have proven that in class). Now my question is the ...
0
votes
1answer
35 views
Orthogonality of filter impulse response to its even shift
I meet this problem but still do not know how to solve it.
Could you guy give me some guides?
Upsampling by 2 ($U_2$) followed by filtering by $g$, with operator $G$
And given: $<g_n,g_{n-2k}>...
0
votes
1answer
24 views
DTFT of inverse of any function
In my book solution is given like this.
But i am solving like this , am i doing wrong??
0
votes
1answer
47 views
From Orthogonality to DTFT
I have met this question, but cannot prove it using DTFT definition.
Given: $g$ is a discrete sequence filter and:
$$ g \in l^2(Z)$$
$$\langle g_n, g_{n-2k} \rangle = \delta_{k}$$
Prove:
$$|G(e^{j \...
0
votes
1answer
79 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
vote
1answer
80 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
1answer
80 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
61 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 ...
1
vote
1answer
27 views
Linearity and time-shifting of $\mathcal{F}\{0.8^n\cos(0.1Ļn)u[n]\}$
To preface, this is not a homework related question but purely for self-study purposes.
Hi there, I try to calculate $\mathcal{F}\{0.8^n\cos(0.1Ļn)u[n]\}$ by using the properties of Discrete time ...
1
vote
1answer
60 views
Why is DTFT of $e^{jn\omega_0}$ an impulse train?
update : After asking the question, I figured out that DTFT result is an impulse train. Now my question evolved to, how it is derived in this way?
Using the DTFT formula seems not to be working, ...
2
votes
2answers
143 views
What is the meaning of the DTFT of the unit impulse sequence?
In an exercice, I'm asked to draw the $X_{imp}(\omega)$ Discrete-Time Fourier Transform (DTFT) of the $x_{imp}(n)$ unit impulse sequence defined as:
$$
x_{imp}(n) = \begin{cases}
1 & \text{if } ...
2
votes
2answers
36 views
Invertibility of Time-Dependent Fourier Transform
I am reading Oppenheim & Schafer's (O&S) Discrete Time Signal Processing (2nd or 3rd edition, does not matter) and I find hard to understand a technicality behind the Time-Dependent Fourier ...
0
votes
1answer
46 views
DTFT of window function applied to input signal
$$x[n] = cos(\omega_1n) + cos(\omega_2n)$$
$w[n] = 1/N$ for $0 \leq n < N, 0$ for everything else
Find the DTFT of $y[n]=x[n]w[n]$ expressed by the DTFT of $w[n]$, $W(\omega)$
I was thinking ...
2
votes
1answer
131 views
Discrete Time Fourier Transform (DTFT) cross correlation property
I came across this property of the Discrete Time Fourier Transform (DTFT) and I am having a tough time proving it.
In general, consider two real signals $x[n] \: \& \: y[n]$. If
$$ x[n] \...
2
votes
1answer
74 views
Frequency estimation of circularly shifted single tone signal
I have a discrete signal $y[n] = <e^{j ~ 2 \pi f ~ n}>_J + ~w[n]$ with $n \in [0, N[$ and $w[n]$ AWGN, $<x[n]>_K$ denotes the signal $x[n]$ circularly shifted by $K$ samples. Let's define $...
1
vote
1answer
524 views
Find the period of a signal with the DTFT plot
I have an exercise and I'm struggling to resolve it. Here it is :
My problem is about the DTFT. I've always been taught that we use DTFT for infinite-lenght signal that are not periodic (if the ...
0
votes
1answer
124 views
Continuous-time vs Discrete-time Fourier transform
case 1) to calculate the Fourier transform of discrete-time signal(sampled signal) we use Discrete-time Fourier transform.
but my question is:
case 2) if I consider that discrete-time signal as ...
2
votes
1answer
75 views
Method for determining probe angle by analyzing skewed sine wave
I've got a fun problem and would be curious to get feedback on how some of you would go about solving this.
Imagine I have a probe and am scanning the surface of some material. This material surface ...
0
votes
2answers
150 views
What is the interpretation of Fourier Transform containing only imaginary part?
The FT of a unit step function is taken as:
$$
X(\omega) = \int_0^\infty e^{-j\omega t}dt = \frac{-1}{jw}e^{-j\omega t} \Biggr |_{0}^{\infty} = \frac{j}{\omega}
$$
The transform only has the ...
0
votes
1answer
124 views
Matlab FFT not producing symmetric spectrum
I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset.
...
0
votes
1answer
124 views
Calculating DTFT
When calculating DTFT of (1/2)^n u[n]. We evaluate the sum as follows:
Please correct statements and answer questions below:
1) So to go from STEP 1 to STEP 2, the limits of the series are changed ...
2
votes
1answer
514 views
Proving that the IDTFT is the inverse of the DTFT?
The DTFT is given by:
$$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty}x[n]e^{-j\omega n}$$
The IDTFT is given by:
$$x[n]=\frac{1}{2\pi}\int_{0}^{2\pi}X(e^{j\omega})e^{j\omega n}d\omega$$
I have been ...
3
votes
2answers
434 views
Proof that first difference filter amplifies noise
I'm a bit befuddled by noise's effect on derivative filters.
I've always 'known' that straightforward first difference derivative filters of discrete signals amplifies noise, but I'm struggling to ...
3
votes
2answers
150 views
Support of the convolution of two rectangular signals
I'm trying to convolve two rectangular signals in the frequency domain $$H_1(\omega) = u[\omega +.2\pi] - u[\omega -.2\pi]$$ and $$H_2(\omega) = u[\omega +.1\pi] - u[\omega -.1\pi]$$
My result is a ...
1
vote
1answer
109 views
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 $\...
0
votes
1answer
42 views
system function $H(\omega)$ relationship to odd and even components of h[n]
What qualities of $h[n]$ are necessary for:
$$
H(e^{j\omega}) = DTFT\{h_{even}[n]\} + j\ DTFT\{h_{odd}[n]\}
$$
Do all real / causal h[n] have the property that:
$$
H(e^{j\omega}) = DTFT\{h_{even}[n]...
5
votes
1answer
144 views
Is possible reach the DFT if I have the DTFT?
My teacher told me that DFT is DTFT sampled, i.e.:
$$X[k] = X(e^{j \omega})\Bigg|_{\omega = \frac{2\pi k}{N}}$$
But, if I have the sine
$$ x[n] = \sin(\omega_0 n) $$
the DTFT is:
$$X(e^{j \...
0
votes
1answer
41 views
Conversion between DTFT in radians/sample to DTFT in cycles/sample
I have found that most commonly the DTFT is defined as:
$X(\omega) = \sum_{n=-\infty}^{\infty} x[n]e^{-j \omega n}$.
However the class I am taking frequently uses the DTFT expressed in "normalized ...
1
vote
1answer
282 views
Relationship between the IDFT of a sampled DTFT and its discrete-time domain signal
Suppose we are given an input signal s[m,n] with DTFT $S(\omega_1, \omega_2)$.
We sample it at $\omega_1 = \frac{2 \pi k}{256}$ and $\omega_2 = \frac{2 \pi l}{256}$ to get a 256 point DFT S[k,l]. ...
2
votes
3answers
200 views
Maximum Magnitude Deviation between DFT and DTFT
Let $x[n]$ be a finite-length discrete-time signal with length $N$. The continuous DTFT $X(\omega)$ is then
$$
X(\omega) = \sum_{n = 0}^{N-1} x[n] e^{-j \omega n}.
$$
The length-$N$ DFT of $x[n]$ is
$...
0
votes
1answer
156 views
Using the given identities, find the inverse DTFT
Using the given identities,
$$ a^nu[n] \Longleftrightarrow \frac{1}{(1-ae^{-jw})}$$
and
$$\delta[n-k]\Longleftrightarrow e^{-jwk}$$
Find the inverse DTFT of,
$$ H(e^{jw}) = B\cdot\frac{e^{-jw}}{(...
4
votes
1answer
520 views
Bridging CTFT and DTFT for a cosine
I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT.
For example if I take a basic example:
$$\begin{aligned}
x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
