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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Function to take discrete sample of a continuous sinusoid function?
Say I have continuous sinusoid function such as:
$$x(t) = \cos(2\pi f_0 t)$$
where $f_0$ is the frequency and $t$ is some time in the function.
I want to take samples of this function at some sample rate using a function of this form:
$$x(n) =…
jfenwick
- 111
1
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2 answers
Calculate phase and amplitude of a sampled sine wave
I have an electronics project where I sample two sine waves. I would like to know what the amplitude (peak) and difference in phase is. Actually I just need to know the average product of the two waves.
A caveat I have is that the two sine waves…
1
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1 answer
Using the FFT to align two instances of the same signal
I'm working on a program that has a software oscilloscope-like viewer for audio signals. The scope basically takes in blocks of signals at a regular rate and adds them to its existing signal data. When requested by the system, it renders the signal…
dsharlet
- 161
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DSP, discrete time, how to calculate the frequency
this is from Digital Signal Processing, 4th ed, Sanjit K Mitra, problem 2.39b.
The question is: Determine the fundamental period of
$x[n] = cos(0.6n\pi + 0.3\pi)$
Since x[n], is in square brackets, this means discrete time, not continuos time, thus…
duane
- 11
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1 answer
Frequency bound for Hermite interpolation'
The Nyquist limit for interpolation by trig functions states that one must give at least two data points per wavelength, because data just above and just below this "folding frequency" cannot be distinguished. I am currently playing with Hermite…
Philip Roe
- 1,140
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1 answer
Short question to a pole-zero plot
I worked out this output of a sequence:
$$Y(z) = \frac{(z-1)(z+\frac{3}{2})}{z^2 (z-\frac{j}{2})(z+\frac{j}{2})(z-\frac{1}{2})}$$
My problem is the $z^2$.
$$z^2 = z * z = (z - 0)(z-0)$$
So I think that are 2 poles in the center.
But does that have a…
madmax
- 439
1
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1 answer
How to find the zeros and the poles of a FIR notch filter?
The question is as follows:
Design a simple digital filter of the form $$y[n] = a_0 x[n] + a_1 x[n-1] + a_2 x[n-2]$$ to remove a narrowband disturbance with frequency $f_0 = 70 \,\rm{Hz}$. Let $f_s = 280 \, \rm{Hz}$ be the sampling frequency. a)…
Priit
- 11
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0 answers
Why is the periodogram the FT of the autocorrelation?
Roughly speaking, the periodogram can be used to determine which frequencies are found in a signal.
However, why is the periodogram defined as the Fourier transform of the signal's autocorrelation? Why don't we take the Fourier transform of the…
Garp
- 33
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1 answer
Signal compression
I believe I have an extremely simple question but I can't seem to figure it out.
This image shows $x[n]$
and I have to draw $y[n]=x[2n-4]$ by first doing a compression and then a time shift.
The image from the compression $y[n] = x[2n]$ is…
Favolas
- 803
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Approximation of Saturation function
"Saturation" or "clipping" function: clip(x)=min(max(x, -1), 1)
The context where I encountered this is LTI (linear time-invariant) system analysis (in classic control theory).
I tried to take its laplace transformation and mix it into the system's…
smilekzs
- 31
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0 answers
How to Relate Engineering Writing of Sifting Property of Dirac $\delta$ to Its Rigorous Form in Tempered Distribution
The normal writing of sifting property in signal processing is
\begin{equation}
\psi\left(x\right) = \int_{-\infty}^{\infty}\delta\left(x - y\right)\psi\left(y\right)\mathrm{d}y,
\end{equation}
where $\delta$ is defined…
Ziqi Fan
- 1,816
1
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2 answers
Max frequency of a signal?
Having
$$ f(x) = \cos(x) + \sin(10x)$$
How Can I know which is the max frequency of this signal?
I need it to set the right Nyquist frequency ($2\cdot\max\text{frequency}$)
I can use Matlab if it's needed
dynamic
- 310
1
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1 answer
Express a signal by another signal?
I am having trouble understanding and getting the solution to this question:
Let $x : \mathbb Z \to \mathbb C$ denote a discrete-time sequence and for $N \in \mathbb N$ let $x |_N$ be the restrictin of $x$ to $\{0, \ldots, N-1\}$ i.e., the mapping
…
madmax
- 439
1
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1 answer
Sawtooth wave spectrum
The Fourier transform of a periodic signal is a pulse train, but for a sawtooth wave, what is the fundamental frequency of the spectrum?
Thanks
JMFS
- 247
1
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1 answer
Find peak output value using transfer function
I have a filter with Transfer function $H(z)=(1-0.5z^{-1})(1+0.5z^{-1})$ designed for a sampling rate of 800 samples/s.
How to find peak output if a sine of 200Hz and amplitude 4 is applied as input?
khan
- 13