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3 votes
4 answers
221 views

Why is sampling not “idempotent”?

This answer describes succinctly what sampling a continuous signal means in the frequency domain: $$ \begin{align*} x(t)\sum_{n=-\infty}^{\infty}\delta(t-nT) &\leftrightarrow \frac{1}{T}\sum_{k=-\...
jelly's user avatar
  • 31
0 votes
0 answers
11 views

Matching closed form BER with integrals for QPSK modulation

I am trying numerically compute the $\bar{P}_b$ for QPSK in a Rayleigh fading channel according to the formula, $$ \bar{P}_b = \int_0^\infty P_b(\gamma)p_{\gamma_s}(\gamma)\ d\gamma $$ for QPSK $P_b(\...
albusSimba's user avatar
1 vote
0 answers
43 views

Plotting Theoretical Maximum ratio combining

I am try to plot the maximum ratio combining of BPSK on a Rayleigh fading channel by integration i.e, $$ \bar{P_e} = \int_0^\infty Q(\sqrt{2\gamma})p_\Sigma(\gamma) \ d\gamma $$ but I can't seem to ...
albusSimba's user avatar
2 votes
1 answer
119 views

Are complex exponentials the only eigenfunction for arbitrary LTI systems?

After reading a few posts, like this. I know that arbitrary LTI systems always have complex exponential eigenfunctions. And that for specific LTI systems you can also have other types of ...
roobee's user avatar
  • 125
1 vote
1 answer
54 views

What is the effect of multiplication on the value of discontinuities?

I see that the values of a distribution at discontinuities are essentialy equal to the mean of the right-hand and left-hand limit values when dealing with distributions in relation to the Fourier ...
Finn Heijink's user avatar
0 votes
1 answer
24 views

In Bluetooth Low Energy, why are Enhanced Data Rate packets only 3 Mb/s?

In the "Introduction tu Bluetooth Device Testing" document ( https://download.ni.com/evaluation/rf/intro_to_bluetooth_test.pdf ), the modulations for Bluetooth Classic are said to be a ...
Rêve's user avatar
  • 35
3 votes
2 answers
657 views

Why is the reference pressure for dB SPL 20uPa?

The article here says that This 20-micropascal reference was selected because it was the quietest sound pressure level that a group of normal hearing test subjects could detect. which makes me think ...
user13267's user avatar
  • 533
2 votes
1 answer
72 views

FMCW Transmit Signal and Fly-back Effect

I am studying a thesis about nonlinearities in the transmit signal and it mentions the following: The first 2,500 samples, which correspond to the Tmax of each of each sweep period and are affected ...
user avatar
0 votes
1 answer
67 views

how to tune and demo

How does one go about tunning your fm demod algorithm to a given carrier frequency. Consider the following algorithms that are present in this website: DSP Tricks: Frequency demodulation algorithms ...
Ben Madison's user avatar
1 vote
0 answers
208 views

Power Spectral Density and Wiener–Khinchin theorem for 2 different stochastic processes

I know the famous Wiener-Khinchin theorem for stationary random processes: the Fourier transform of the autocorrelation function of a stationary random process is equal to the Power Spectral Density ...
Gospadi's user avatar
  • 21
-1 votes
1 answer
184 views

Shortened linear codes

I've been working on my linear code assignment in my coding theory course and I have encountered a problem I would like to get help with. the question is described below. I will try to expalin what I ...
Ran Greidi's user avatar
7 votes
7 answers
3k views

Qualitative Explanation of Fourier Transform

I am reading the book Fundamentals of Music Processing by M.Muller and I am close to understanding the idea behind the decomposition of a signal into basic frequencies, and would appreciate some help ...
nikos's user avatar
  • 171
2 votes
3 answers
986 views

Are all exponential functions eigensignals of LTI systems?

I know that complex exponential functions are eigensignals to LTI systems. Do these include real exponential functions? E.g. $2^t, e^t, ...$ Thanks for the help!
Phobos's user avatar
  • 425
1 vote
1 answer
619 views

How is time used in this autocorrelation expression?

There are two papers I'm working through that explain applications of autocorrelation. The first - by Monti - is quite clear to me: It runs a sum over the time axis. The second one by Brown makes no ...
Reinderien's user avatar
3 votes
1 answer
299 views

Multiplying signals in discrete-time vs continuous-time

Given two discrete-time signals $a[n]$, $b[n]$ and its product $c[n]=a[n] b[n]$. The ideally interpolated, continuous-time version of $c[n]$ is \begin{align} c_1(t)&=\sum_{n=-\infty}^{\infty} a[n] ...
divB's user avatar
  • 473
1 vote
0 answers
248 views

Validity of applying Heaviside function for signal processing applications

I wasn't sure if this question was more suitable for math.stackexchange, but I suspect it's more-so a signal processing question (albeit, a theoretical one) than a mathematical one. I am currently ...
The Pointer's user avatar
1 vote
1 answer
456 views

How does Overlap-Add work for IIR filter?

So let's say I'm trying to implement something like an LPC vocoder. I analyse a speech signal by breaking it up in small chunks and determining their LPC coefficients, which are by design, the ...
Aditya TB's user avatar
  • 129
2 votes
3 answers
576 views

Is there any new scientific capability to build non-causal filters in real world?

According to this post: In discrete-time systems, causality is a requirement only when processing (filtering) signals in real time; i.e. when the index nn corresponds to a physical time n×Tsn×...
Soheil Paper's user avatar
2 votes
2 answers
4k views

Derivation of Nyquist Frequency and Sampling Theorem [closed]

I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
akkab's user avatar
  • 143
17 votes
6 answers
14k views

Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
tjwrona's user avatar
  • 327
3 votes
4 answers
2k views

LTI system and initial conditions

I suspect this is rather obvious once explained; I must be misunderstanding something. From reading various answers here (such as this one), I understand that an LTI system must have zero output for ...
Westerley's user avatar
  • 203
1 vote
1 answer
103 views

Maximizing entropy on a channel

In Shannon's paper "A Mathematical Theory of Communication", in Theorem 8 he states: Theorem 8: Let the system of constraints considered as channel have a capacity $C = \log W$. If we assign $$p^{(s)}...
Giorgian Borca-Tasciuc's user avatar
0 votes
0 answers
31 views

The mean value of phase noise as a stochastic process

What is the mean value of phase noise as a stochastic process? Where can I get a theoretical analysis of this topic? PS: PLL produces cos(2*πfct+φ(t)). The phase noise refers to φ(t). The mean value ...
wu yi's user avatar
  • 1
0 votes
1 answer
118 views

explanation of Hybrid systems?

I want to study Detailed explanation of hybrid systems?Which incorporate both continuous and discrete time signals & systems? for example In which a continuous-time input signal is transformed ...
DSP_CS's user avatar
  • 1,894
1 vote
2 answers
195 views

Is the definition of recursion and iteration in signal processing different from computer science?

I was talking to my advisor today about this. He is a very experienced professor in this field, so I assume he is very knowledgable about it. He pointed out that in signal processing, the word ...
ellamenopee's user avatar
0 votes
1 answer
535 views

Does dividing the magnitude spectrum of white noise by sqrt(2) give an RMS magnitude spectrum?

I understand that the RMS Amplitude of a sinusoidal signal is around 0.707 ($\frac1{\sqrt2}$) times the Peak Value, but this is not true for noise. However, an FFT of a noise signal indicates ...
Aditya TB's user avatar
  • 129
2 votes
1 answer
628 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]. ...
Filip's user avatar
  • 123
0 votes
2 answers
401 views

transfer function and 'causal' signal - evaluate transfer function or use z-transform of input?

From my studying difference equations and transfer functions, I understand that when a complex exponential input $x[n]=z_1^n$ is applied to an LTI system with transfer function $H(z)$, determining the ...
Westerley's user avatar
  • 203
0 votes
0 answers
146 views

should block diagrams in Direct Form 1/2 contain empty branches to fit structure?

When creating a block diagram in a well-recognized structure (Direct Forms 1&2 in particular), does one remove branches where the coefficient is 0? This picture includes a coefficient of $b_1=0....
Jonas Schwarz's user avatar
11 votes
3 answers
88k views

What is the Fourier Transform of a constant signal?

I am trying to figure out what the fourier transform of a constant signal is and for some reason i am coming to the conclusion that the answer is 1. Or better yet a step function.
Micheal C.'s user avatar
8 votes
3 answers
5k views

Is sampling at double the desired reproduction frequency accurate?

This is probably a general principles question, though I'm thinking specifically in relation to sound, which is commonly sampled at a rate of 44.1 kHz in part because the maximum frequency the average ...
aroth's user avatar
  • 183
0 votes
3 answers
341 views

What really means stochastic in field of signal processing

I met two definitions of word stochastic, the first one (cited from wikipedia Stochastic) The word stochastic is an adjective in English that describes something that was randomly determined The ...
matousc's user avatar
  • 667
0 votes
1 answer
754 views

Pulse wave from sum of sinusoids

...
bzrr's user avatar
  • 103
4 votes
1 answer
269 views

Overlapping power-of-cosine windows with constant weight

I would like to refer you to a relevant question I posed on the Math StackExchange: A generalisation of the Pythagorean trigonometric identity. As can be seen from the question and the answer, what ...
Veeno's user avatar
  • 41
6 votes
1 answer
336 views

Is there a strategy for discrete control of a system with dynamics near sample rate?

I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to ...
tkw954's user avatar
  • 203
-1 votes
1 answer
237 views

Are these Linear and Time Invariant Systems?

We were given the above systems and we were asked to tell whether they are linear (or not) and time invariant(or not). $y(m,n)=x(m,n)+c,\quad c>0$ $ y(m,n)=x(m,n)+x(m,-n)$ $y(m,n)=x(m,n+m)$ $y(m,n)...
johny's user avatar
  • 15
-1 votes
1 answer
775 views

Spectrum of a time-domain impulse train

I am trying to learn DSP. I'm reading the 2nd edition of Oppenheim & Schafer's "Discrete-Time Sig. Proc." book. On the topic of converting a continuous signal to a discrete-time signal the idea of ...
knight's user avatar
  • 77
1 vote
1 answer
46 views

Frequency range for set of all discrete-time sinusoids

Consider discrete time sinusoids of the form $$x[n] = \cos(\omega n) \ ,$$ where $n$ is an integer. What frequency range of $\omega$ would constitute all the possible sinusoids? I'm thinking that $0\...
J. Sanders's user avatar
2 votes
4 answers
1k views

Finding a signals complimentary sound / frequency

I know about complimentary colors and how to get them, since colors are basically frequency / wavelengths. Is it possible to find a signals complimentary, additive or subtractive frequencies in an ...
Rick T's user avatar
  • 199
1 vote
1 answer
284 views

Baseband vs. Passband

I am a bit confused if the following signal is baseband or passband: $f(t) = x(t) \cos(2 \pi f_c t) - j \: y(t) \sin(2 \pi f_c t),$ where $j = \sqrt{-1}$. Since it is clearly not real, I cannot say ...
Noor's user avatar
  • 337
4 votes
1 answer
6k views

Baseband vs Passband modulation

I am taking a graduate level course in Networking theory and applications and I am still a bit shaky on the difference between baseband and pass band scheming. The book I am using is Computer Networks ...
Joseph's user avatar
  • 141
-1 votes
1 answer
12k views

Integral of unit step function [closed]

Can someone help me understand how did we get from the second line to the third one? $$\begin{align} u(t-1)*u(t) &= \int_{-\infty}^{\infty}u(\tau-1)u(t-\tau)d\tau \\ &=\int_{1}^{t}u(t-\tau)d\...
user2692669's user avatar
0 votes
2 answers
139 views

Discrepancy when calculating LTI system output using inverse z-Transform

I'm given a difference equation, $y[n]-0.4y[n-1]=x[n]$, and asked to find the natural response $y_n[n]$, forced response $y_f[n]$ and complete response $y[n]$ if $x[n]=4 (0.25)^nu[n]$ and $y[0]=0$. ...
Westerley's user avatar
  • 203
0 votes
1 answer
1k views

BIBO stability and input at system's pole

My understanding of BIBO stability is that if a bounded input is applied to a discrete-time, linear, time-invariant BIBO system, the output will also be bounded. A sufficient condition for this is ...
Westerley's user avatar
  • 203
2 votes
2 answers
483 views

Output of a discrete-time LTI system different form than input?

This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question ...
Westerley's user avatar
  • 203
1 vote
3 answers
1k views

Output of discrete-time LTI system guaranteed to be same form as input?

I know that in the continuous-time context, if I supply a complex exponential input to a Linear Time Invariant system, the output will be of the same form as the input - for example, if the input is $...
Westerley's user avatar
  • 203
4 votes
2 answers
20k views

What is the difference between wide sense and strict sense stationary processes?

What is the difference between wide sense and strict sense stationary processes (SP) ? According to the definition (by Heinrich Meyr, Marc Moeneclaey, Stefan A. Fechtel in "Synchronization, Channel ...
József Hegedüs's user avatar
1 vote
2 answers
1k views

Does the system matrix being singular tell us anything about the system?

If we have a linear system, represented in State Space and the A matrix is singular (det(A) == 0), can we expect any special properties from the system?
Vorac's user avatar
  • 233
0 votes
1 answer
292 views

DFT independent variable as fraction of sampling rate

When the frequency domain's independent variable is labeled as a fraction of the sampling rate, the values along the horizontal axis always run between $0$ and $0.5$, since discrete data can only ...
Stephen K. Karanja's user avatar
-1 votes
2 answers
2k views

How to compute the Fourier Transform of this ramp-like signal?

I have the following signal: and this as the solution to the problem: $$\begin{align} X(j\omega) &= \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \\ &= \int_0^\tau \frac{E}{\tau}t\; e^{-j\...
Tanatos Daniel's user avatar