Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/
Questions tagged [signal-processing]
2068 questions
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Why Fourier Transform uses the notation X(jw) and X(e^j$\Omega$)
Usually books (e.g. Oppenheim) use the notation X(jw) for the continuous time Fourier Transform and X(e^j$\Omega$) for the discrete time Fourier transform.
AFAIK the only parameter is w o $\Omega$, respectively. Why they include these other…
Freeman
- 171
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1 answer
Instant frequency of sine sweep function?
Firstly, I'm not a mathematician, I'm an engineer, so you can freely make fun of the question.
I have the following counter-intuitive behaviour in a sweep function. I have a sweep sine function (something like $$x(t) = \sin(\omega(t) \times t)$$,…
nodarkside
- 205
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Is that a counterexample to sampling theorem?
Sampling points are $\mathbb{Z}$. Sampling theorem tells us that functions with bandwidth lower than $\frac{1}{2}$ will have no aliases. Take functions with pure frequency $\frac{1}{4}$ as an example.Consider $y=sin(\frac{\pi x}{2})$ and triangle…
user33869
- 1,040
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Single Sideband LSB-SC Demodulation
The problem is how the phase φ effects the outcome when the input(message signal) is the DSB-SC LSB.
It's :
message: $m(t)=A_{m}cos(ω_{m}t)$
carrier: $c(t)=A_{c}cos(w_{c}t)$
I found that the LSB through the…
Nick
- 203
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Why is this defined as $u[n]$?
In LTI systems there are two famous functions the unit step function and the unit impulse functions. And they are defined as follows.
$$ u[n] =
\begin{cases}
1, & \text{if $n$ $\ge$ 0} \\
0, & \text{if $n$ $\lt$ 0}
\end{cases}
$$
$$ \delta[n]…
Padmal
- 595
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1 answer
Graph of the Angle of a Fourier Transform
If I need to graph the magnitude and angle of a discrete Fourier transform which happens to be $X(e^{j\omega}) = 4\cos(4\omega)$, I know how to graph the magnitude, but how do you graph the angle?
I would make an attempt, but I don't even know how…
Austin
- 680
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1 answer
A signal on a noisy channel is input to a filter
Question:
A Wide-sense stationary (weakly stationary, (WSS)) random signal {X(t)}t∈R with Power spectral density(PSD) S_X(ω) is transmitted on a noisy channel where it is disturbed by an additive zero-mean WSS random noise {N(t)}t∈R that is…
JKnecht
- 6,543
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1 answer
Is this system time-invariant?
I think this system is not time-invariant, but I'm not really sure how to plug in a couple test cases to check. The system is:
$x(t)$ -->(S)--> $y(t) = \int_{-\infty}^{3t}x(\tau) d\tau$
Without actually doing a proof, could I possibly plug in an…
Austin
- 680
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Why is the cross-correlation an integral?
The cross-correlation of continuous $f,g$ is:
$$(f \star g)(\tau)=\int_{-\infty}^{\infty}f^*(t)g(t+\tau)dt$$
Why is it an integral?
Why doesn't
The cross-correlation of continuous $f,g$ is:
$$(f \star g)(\tau)=f^*(t)g(t+\tau)$$ suffice?
mavavilj
- 7,270
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Why does cross-correlation involve the complex conjugate?
The cross-correlation of continuous $f,g$ is:
$(f \star g)(\tau)=\int_{-\infty}^{\infty}f^*(t)g(t+\tau)dt$
where * is the complex conjugate.
Why is there the complex conjugate?
mavavilj
- 7,270
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1 answer
is a "non-causal" system "memory"?
Is their a relationship between non-causality and memory?
for example: is the system $Y(t) = X(t+1)$ memory or memory-less.
I got confused because the memory system is defined to depend only on the (same time) input, when the memory-less depends on…
Abdo Kamal
- 13
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Math required to solve Fourier Transform for periodic functions?
In my Signals & Systems course my professor said that although it's possible to solve the standard Fourier transform for periodic signals, it requires advanced math beyond what we've learned, so we instead solve for the Fourier coefficients and then…
Austin
- 680
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1 answer
Assist on finding the impulse response fom a simple LTI graph
Could you please advise on the impulse response from this $LTI$ graph? I need to plot it and find if it is stable and causal...
LTI system with response to unitary step ($t$):
Angel Rmz
- 13
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Sampling theorem - signal reconstruction
Hi and thank you for your help.
I got stuck for the last days with this chapter in this book
https://ccrma.stanford.edu/~jos/mdft/Sampling_Theorem.html.
What I do not understand…
ggs
- 9
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1 answer
How to determine the states of ideal diodes in simple circuits with only DC sources and resistors
How can the states of ideal diodes be determined in simple circuits with only DC sources and resistors without a trial and error approach?
I posted this question on Electronics SE and found out that there is none.
This is one of the situations…
Hashir Omer
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