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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How do you find the intersection of multiple lists of sine waves using only the sine wave sums of each of the lists of sine waves?
If I have, for example, two finite lists of sine waves and all the sine waves in each of these lists are summed to create 2 new sine waves a and b, then is there any way I can figure out whether or not the 2 lists of sine waves contained any common…
CCS
- 143
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Trouble finding the right DTFT pair
i have a periodic signal $x[n] = \cos (\frac{2 \pi}{10}n)$.
I found this DTFT pair:
That's the only pair for a cosine function i found.
But what is $\delta _{2\pi}$ ? Is it just a Dirac $\delta$ function for every period ?
And the $\pi$ before the…
madmax
- 439
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1 answer
Inverse system of $y(t)=\int_{-\infty}^te^{-(t-\tau)}x(\tau)d\tau$
How to find the inverse system of $$y(t)=\int_{-\infty}^te^{-(t-\tau)}x(\tau)d\tau$$ with input $x$ and output $y$?
The solution for this is $y(t) = x(t) + \dot x(t)$. I am confused about how to get this answer. Thanks!
sleeve chen
- 8,281
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How to express the interconnection of LTI systems as the impulse responses?
For the interconnection of the LTI system as the diagram shows, how can we express and simplify this interconnection to one LTI system using each impulse response?
I know that you are supposed to convolve the impulse responses when you go through…
Kaihua Hou
- 119
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Derive the function for a given symmetric impulse response
i have a symmetric impulse response: $h[n]=-h[M-n]$ , $0\leq n \leq M$
Frequency response is: $H(e^{j\omega})=je^{-j\omega N}R(e^{-j\omega})$
$R(e^{-j\omega})$ is a real-valued function.
I want to derive the function $R(e^{-j\omega})$ for $h[n]$…
madmax
- 439
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1 answer
Discrete autocorrelation function
I'm trying to solve following and already tryed some approaches, but seems to be I not really understand how I should start to solve it.
The following relationship is given x[n]=v[n-1]+w[n]+v[n+1], v[n] is a mean free
white noise with variance one…
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Relating the infinite operator to finite difference
I'm reading a book (Digital Signal Processing by Jonathan Steyn) which defines the infinite sum:
$$r\equiv\sum^\infty_{m=0}z^{-m}x_n$$
This is just the sum of $x_1 + x_2 + x_3 +\dots +x_n$ to infinty. Then it defines the finite difference as…
moinudin
- 129
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Difference between x(2t-3) and x(2(t-3)).
Ofcourse x(2(t-3))=x(2t-6), but my question is in terms of operations on signals. In what order does the shifting and scaling happens in the case of x(2(t-3)) and how is it different from the ones that happens with x(2t-3). And is this different in…
leena
- 31
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Find the values of $k$ , for which the system is stable.
I have a multiple choice question , that says , if $y(t) = (k^2 -3k -4)\log(x) + \sin(x)$ , find the values for which the system is stable ( I guess it means BIBO stable) .
$$a. 1
\ \ \ \ b. 3 \ \ \ \ c.-1 \ \ \ \ d. 5 \quad e. 4
\quad f. 2$$
We…
tonythestark
- 817
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linearity test of a piecewise function
I'm struggling to find any youtube videos for piece-wise examples.
Apologies for not knowing the math syntax yet.
Given $y[n]=
\begin{cases}
x[n] & n\geq 1 \\
1 & n=0 \\
-x[n] & n\leq 1
\end{cases}
$
Determine if the system is…
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Linearity and stationarity of a system with integral
How can I demonstrate the linearity and the stationarity of system with integrals? For example I have this signal $ y(t)= \int_{t}^{t-T} x(\tau ) d\tau $ and I know from theory that’s a filter so I should have both linearity and stationarity but I…
Elena Martini
- 261
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What is the Hilbert transform of $e^{-jwt}$?
What is the Hilbert transform of $e^{-jwt}$ ?
I know how to do it via convolution , but i am looking for a less formal, more intuitive explanation such as the phase shift it imparts
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What does it mean to downconvert signals within a bandwidth, centered at another bandwidth?
So, conceptually, when a book talks about down-converting signals within a bandwith of say, $25$ MHz, with the bandwidth centered at say, $50$ MHz, down to baseband, what exactly does it mean?
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Prove a necessary condition so that a complex discrete exponential function is periodic.
Consider the discrete complex function $f(n) = e^{iwn}$ with w is nonzero and n is in the set of integers. Assume f is periodic, which means there is an integer N st, $f(n+N) = f(n)$. From the book "Signal and System", there must exist an integer m…
Jesse
- 183
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What propability distribution could be fitted to a noisy sinus signal
i'm currently working on feature extraction from noisy (real world measurement) sinusoid measurements. I was thinking about fitting a propability distribution over my signals propability to use the fitting parameters as signal features for further…
