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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Finding closed expression for the output of an LTI system
I'm having a problem with two exercises. Dealing with LTI systems, how can I get the analitic expression of the output in a closed form of these two problems? Can someone help me?
1st problem:
$$y[n] − 0.4y[n − 1] = x[n]$$ $$y[−1] = 1$$
$$x[n] =…
Bullel
- 11
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Fast moving object, how to remove noise from observations?
I have an object that I am tracking with bluetooth indoor positioning system (angle measurement). The object usually moves with velocity around 30-50 km/h, but it can peak over 150 km/h. The object also makes sharp turns.
I have the absolutely raw…
user496118
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1 answer
Function that connects impulse to impulse response
This question may seem slightly unnecessary but I'm really curious about the answer.
For a system (LTI ones at least not sure about the rest) the output can be described as some function of the input:
$$y(t) = f(x(t))$$
So surely the impulse…
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Hamming Window - Understanding Formula
I'm trying to understand the Hamming window concept (Signal Processing) and the equation looks like the following:
Where:
N = number of Samples in each frame
Y[n] = Output Signal
X(n) = Input Signal
W(n) = Hamming window
First Question: I have…
Phorce
- 219
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1 answer
Is this discrete-time system time-invariant?
For a discrete-time system, the input signal is $x(n)$, the output signal is
$y[n] = x[n+1] - x[1-n]$
I think it's time-invariant, but the solution's manual says it's not.
My procedure is:
$T\{x[n-k]\} = x[n - k + 1] - x[1 - (n - k)] = x[n - k + 1]…
Johnny Ji
- 531
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1 answer
Shannon reconstruction formula: who can prove alternative form?
I am familiar with the standard formulation of the Shannon-Whittaker reconstruction formula which is
$$s(t) = \sum\nolimits_{n = - \infty }^\infty {s(nT){\mathop{\rm sinc}\nolimits} (B(t - nT))}$$
where B = 1/T.
However, in the standard book…
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Mathematical operator that describes rectifying a signal
In analog communications an AM signal is composed of a message signal with an offset that is mixed/multiplied into a carrier signal of a higher frequency, so that:
$$
(V_{DC} + cos(f_m)) *cos(f_c) = V_{DC}*cos(f_c) + cos(f_c + f_m) + cos(f_c -…
Brant Geddes
- 13
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1 answer
Impulse response should we take for one sided or two sided?
Question is given like this
I did it like this here i have taken for one sided frequecny response
Method1
But in the solution they have calculated it with two sided filter
Method 2
Now clearly i am getting the different answer that is i…
Rohit
- 247
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1 answer
How do I take the discrete derivative of Cosine, and show that it still equals -Sine?
This is really stumping me. I have a signal that is being modulated at frequency $f$, and is sampled every $\Delta t$ seconds for $N$ samples. I'll index these samples with $k$.
The signal is $S(k\Delta t) = -A \cos(2 \pi f k \Delta t)$
The…
Bunji
- 113
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2 answers
What is the right terminology / methods for this standard signal processing task?
Say we have a signal s = [1,2,2,1,3,3,2,2,1,1] or similar (only 1,2,3 can occur). I want to look for a particular pattern, e.g. [1,3,3,2], which can occur anywhere (0 or many times) in the signal. I would like to perform the computation as a…
svangen
- 299
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Mathematics of a leading signal for a sine wave
Taken from elsewhere on the web : -
"The derivative of a sine function is
d SIN(ω*t) / dt = ω * COS(ω t)
where ω = angular frequency = 2 π *frequency
and this derivative leads the original function by 90
degrees (a quarter period) because a cosine…
babelproofreader
- 215
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3 answers
What is the z-transform of $\frac{1}{n}$
given that $n \geq 1$ and $x(n) = \frac{1}{n}$, how can I get the z-transform of $x(n)$?
Thanks
Feng Shi
- 19
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2 answers
Chirp: Why do you need to integrate the frequency function?
From the Wikipedia page on chirp, if I provide some time-dependent frequency function $f(t)$, this has to be integrated if I want to use it as the argument to, say, a sinusoid. Suppose $f(t) = f_0+kt$; then
$x(t) = \sin\left(2\pi\int_0^t…
Dang Khoa
- 237
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2 answers
LTI system difference equation with input
Let's say I am given a difference equation describing an LTI system:
$$y[n] = F(y[n-k],x[n]),$$
where $$x[n] = 2\cos\left(\frac{n\pi}2 + \frac\pi3\right). $$
I know how to find its frequency response and magnitude response. However, I cannot find…
Avatrin
- 1,527
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LTI system response to series $\sum_{k=0}^\infty c_k x_k$ is $\sum_{k=0}^\infty c_k y_k$?
Ok so in a typical "signals and systems" course taught to engineering students (usually electrical engineers, from what I understand), an LTI (linear and time-invariant) system is defined as a "system" (which is just an operator) $T$ that…
user45453
- 179