Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/
0
votes
0answers
21 views
Signal approximation using linear combination of functions
How I can approximate the signal $x(t)=0.001\,t^3 \exp(-0.1t)$ in the interval $[0,100]$ using a linear combination of the following functions:
$f_1(t)=A_1$
$f_2(t)=A_2\cos(0.05t)$
...
1
vote
2answers
39 views
What is the inverse z transform of 1/(z-1)^2?
I'd like to know how to calculate the inverse z transform of $\frac{1}{(z-1)^2}$ and the general case $\frac{1}{(z-a)^2}$
3
votes
2answers
32 views
Problem with Discrete Parseval's Theorem
I think I must be missing something obvious, but I can't for the life of me see what it is. The discrete version of Parseval's theorem can be written like this:
$\sum_{n=0}^{N-1} |x[n]|^2 = ...
2
votes
0answers
21 views
Mathematically inclined books on Signal Processing Theory
First off, i know this may seem off topic but i could not find help in signal processing communities so i was hoping there would be people here who both love mathematics and have interest in signal ...
1
vote
1answer
20 views
Scale Space - Scales and Octaves
So I'm desperately trying to understand scale space for signals, specifically for 2D images...
I'm having trouble with algorithms that discuss creating a pyramid. Specifically, I don't understand how ...
0
votes
0answers
20 views
Zero-Padding seems to CHANGE FFT of signal! [migrated]
I am having trouble with zero-padding. As I understand it, in theory, zero-padding in the time-domain should 'sinc-interpolate' the FFT of the signal in the frequency domain.
This would mean, that ...
0
votes
0answers
32 views
Find the magnitude and phase spectra of H(s) = 1/s+1
Find the magnitude and phase spectra of
H(s) = 1 / s+1
I have no clue what this is asking. My teacher kind of left me hanging could someone help me get started.
1
vote
1answer
17 views
How to show quantisation error for frequency coefficient
I have the following question from an exam which reads:
For the second question my answer is:
24 5 2 3
9 2 1 3
2 3 2 2
1 1 1 0
I am unsure of what formula ...
4
votes
2answers
30 views
partially reconstruct information of function convoluted with boxcar kernel
the function (f) I want to reconstruct partially could look like this:
The following properties are known:
It consists only of alternating plateau (high/low).
So the first derivation is zero ...
1
vote
1answer
33 views
Nyquist criterion
When using the Nyquist stability criterion, amplitude-frequency characteristic etc. we go from the Laplace image $G(s)$ to $G(j\omega )$. By definition of the Laplace transform, $s=\sigma + j\omega$. ...
2
votes
2answers
37 views
I need to calculate the period, I need help to verify my answer
I need to determine if $x(t) = 9\cos(2t) + 4\sin(\pi t)$ is periodic. If it is periodic I need to find the period. this what I have done
\begin{align*}
T_0 &= 2\pi/w\\
T_1 &= 2\pi/2 = \pi \\
...
0
votes
1answer
59 views
Is the convolution an invertible operation?
If I have a signal $f(x,y)$ (discrete) and I convolve this signal with a kernal $h(x,y)$:
$y(x,y) = f(x,y) \star h(x,y)$ (where $\star$ is the convolution operator)
Can I obtain $f(x,y)$ given only ...
1
vote
1answer
24 views
Extracting independent sources from available signals.
I have four signals in time domain, in the format of 4 vectors (a,b,c,d). I know there are 3 sources contributing these signals.
One is a source that is shared between all four signals.
One is a ...
1
vote
0answers
14 views
Checking if (discrete) signal is stationary, BIBO stable and
I have this discrete signal
y[n] = sum (x[k+1]h[k-1]), where k goes from -inf to +inf.
I need to check if this signal is stable, stationary, and if it's invertible, i need to find it's inverse ...
0
votes
0answers
15 views
Measuring how “non-noisy” a sound signal is [migrated]
Given a sound clip (whose source is an FM radio signal) I'd like to measure how different from background noise (the "in-between channels" noise) the sound clip is, so that I can compare the ...
1
vote
0answers
46 views
How can I find the compact trigonometric Fourier series from these signals?
I've been stuck on this for a while, but how exactly would I go about calculating the compact trigonometric Fourier series for both of these signals? I have a general formula down for it, but I just ...
-1
votes
0answers
12 views
How to make SciPy Hilbert transform faster [closed]
I'm using Python 3.2.4 and running scipy.signal.hilbert on a numpy array with shape (2**20,1). It's the bottleneck in my code right now. Any way I could make it faster? What I'm really after is the ...
0
votes
2answers
36 views
Complex expression for periodic binary sequences
We have infinite binary sequences of type
$$\langle g_n \rangle_{j=4}=\{0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,...\} \,;\, n\to\infty$$
where $j$ indicates the length of a period that starts/ends with a $1$; ...
0
votes
0answers
32 views
fourier series coefficients for power signal
Given a signal
$$x(t) = -5 +3\cos(3000\pi t-\pi/6) -3\sin(4500\pi t+\pi/2),$$
a) Determine the Fourier series coefficients $X[k]$ for $x(t)$ (do not do any integrals).
b) Suppose that $x(t)$ is ...
1
vote
1answer
36 views
FFT for a single frequency
I was looking for a more efficient way of finding the magnitude and phase of a signal at a certain frequency without performing an FFT because it produces more information than I need and I came ...
2
votes
1answer
31 views
Check the orthogonality of two functions
This is a part of two Passband Signals. My question involves inner product. Is
$$
\left < \cos(2\pi ft + \phi) , \sin(2\pi ft + \phi) \right>
$$
where $\phi \in [-\pi, \pi)$
equal to zero, i.e. ...
0
votes
1answer
49 views
solve an difference equation's particular solution with unit step input
I have a question like this $y[n] - \frac 2 5y[n-1] = 2x[n]$ and $x[n] = 2u[n]$, the manual say that $y^p[n] = k u[n]$ and subtitute it into the equation will become $ k - \frac 25k = 4$.
But I think ...
1
vote
1answer
32 views
How can I calculate the bode magnitude and frequency as well as their plots?
I've been trying to figure this problem out for a while now. I've been given a transfer function $$H(s) = \frac{s(s+100)}{(s+2)(s+20)}.$$ I'm supposed to calculate the bode magnitude and frequency for ...
0
votes
0answers
24 views
Calculation of the error function.
I have the next two signals:
$X(t)$ and $G(t)$ and a random process $Y(t)=G(t)X(t)$ where $X(t)$ and $G(t)$ are wide sense stationary with expectation values: $E(X)=0, E(G)=1$.
Now, it's also given ...
1
vote
0answers
18 views
Discrete time fourier transform of partial sum
I came across the following property of the DTFT:
$ \mathcal{F} \Bigg(\sum_{m=- \infty}^{n}x[m]\Bigg) = \frac{1}{1- e^{-j \omega}} X(e^{-j \omega}) + \pi X(e^{-j0}) \sum_{m= ...
1
vote
1answer
808 views
Prove of the Parseval's theorem for Discrete Fourier Transform (DFT)
If $x[k]$ and $X[r] $ are the pair of discrete time Fourier sequences, where $x[k]$ is the discrete time sequence and $X[r]$ is its corresponding DFT. Prove that the energy of the aperiodic sequence ...
0
votes
0answers
18 views
is there a Kalman filter for distribution function?
The standard Kalman filter uses a series of measurements observed over time, to decomposite the signal and noise.
However, when I'm modeling the distribution (pdf or cdf) of a variant, is there a ...
0
votes
1answer
49 views
Find the non null complex Fourier coefficients
I'm doing my homework on signal processing in MatLab and I'm stuck on an exercise.
I'm given this signal $x(t)=1 + 2\sin(12\pi t+\frac{\pi}{4})\cos(21\pi t);$ and I have to get the non null complex ...
0
votes
1answer
38 views
The science of pearson product moment correlation coefficient
I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the ...
2
votes
2answers
34 views
Express $\cos(5t)$ with the help of Euler formula
I can't figure out, how to express $\cos(5t)$ in the form $e^{j\omega t}$. I don't even know the right answer. How would you deal with this task?
1
vote
1answer
39 views
How does one verify if a vector is really recovered?
In compressed sensing, how to verify if a vector is really recovered or how does one plot the figures on recovery rate? Since in numerical experiments, there is always a difference between the ...
1
vote
1answer
74 views
How to determine the function of this “black-box”?
Imagine a black box which accepts a digital input signal which is a pure sine wave and outputs the area between this input signal and some constant data set over a sample window.
Given the input ...
0
votes
1answer
38 views
response impulse function
my question is related to time series modeling in signal form,i have such question,suppose we have time series data $y_1........y_n$,how can we represent in impulse response form?as i ...
3
votes
1answer
57 views
Find the expression and the system impulse response
I've started to learn signal fundamentals and I have to do one exercise and I can't understand something.
It is said that $$x[n]=1.5\cos(0.025 \Pi n)(u[n+40]-u[n-40]))$$ and that the signal $u[n-m]$ ...
2
votes
1answer
66 views
Relationship between DFT index values, frequency in a Fourier series and Hz.
I have a sound file recorded at 44.1 K samples per sec, and some FFT and IFFT algorithms. The sound file is a vector with about $ 2^{17} $ elements.
My objective is to find which of the index values ...
0
votes
0answers
75 views
Frequency estimation by Prony's method
My question is related to Prony's method, from Internet there is direct link for this method, but also i would like to show you method
Now i am a little confused, I have read about Pisarenko ...
0
votes
0answers
21 views
Pre-Emphasis of a signal
I'm trying to describe the process of Pre-Emphasis (of a signal) in my equations, but I don't know whether or not this makes sense.
$Y[n] = X[n] - 0.95 \cdot X[n-1]$
Where Y = pre-emphasis after, X ...
1
vote
1answer
59 views
Discrete time signal and unit step
I've started to learn signal fundamentals and I have to do one exercise and I can't understand something.
It is said that $$x[n]=3\cos(0.1 \Pi n)(u[n+55]-u[n-55]))$$ and that the signal $u[n-m]$ is a ...
-1
votes
1answer
119 views
How to determine the step response using convolution of the signal's impulse response?
The step response can be determined by recalling that the response of an LTI to any input signal is found by computing the convolution of that signal with the impulse response of the system.
...
1
vote
1answer
23 views
Finding two highest peaks in a chunk of samples
Supose I have a list of 600 samples of numbers, and the histogram of the samples looks like the following:
As can be seen, there are two 'mountains' of values around 16 and 48, and a outlier in 95. ...
0
votes
1answer
41 views
Cleaning a signal and computing period
I am working with a signal which is a periodic square signal with some kind of noise and some outliers. I would like to know which is the best solution in order to get the period and clean the ...
1
vote
3answers
72 views
What course sequence should I study in order to build a foundation for studying cryptography and signal processing?
I studied mathematics about two decades ago, but unfortunately, I remember little of it. I'm hoping to start studying cryptography and signal processing, but I'm not entirely sure what ...
0
votes
2answers
70 views
When writing out the wave equation isn't the phase shift just adding to the frequency?
I hope someone here could clarify for me.
With the waveform function f()=(A)sin(wt + theta)
where
A=magnitude of the wave,
sin= type of wave form,
wt=frequency rads/sec,
theta = phase shift
...
0
votes
1answer
66 views
Power spectrum for discrete signals.
If $x(t)$ is a real (aperiodic) power signal, i.e.
\begin{equation}
0<\lim_{T\rightarrow\infty} \frac{1}{T}\int_{-T/2}^{T/2}|x(t)|^2 dt<\infty
\end{equation}
$x_T (t)$ is a truncated version of ...
0
votes
1answer
228 views
What does upside down “v” ($\wedge$) mean in this equation?
I have a simple question, but it is hard to google it. I have this equation here:
$$y(t, x) = \sum_{i=1}^{d}(|x_i| \wedge t)^{2}
$$
Here $x$ is a size $d$ signal and $t$ is just a scalar. I am not ...
1
vote
1answer
61 views
Recover filter coefficients from filtered noise
I have a digital signal which may be represented as noise filtered with an FIR (finite impulse response) filter. Let us suppose that the noise consists of pulses (nonzero samples on a zero ...
0
votes
1answer
56 views
Filter signal through convolution
I am a little bit unsure if I've set up the following problem correctly:
Consider the signal
$$f(t) = e^{-t}(\sin(5t) + \sin(3t) + \sin(t) + \sin(40t)) \quad 0 \leq t \leq \pi$$
Filter this signal ...
0
votes
0answers
88 views
Looking for all possible combinations: Can we find combinations of “triplets with accompanying pitch” in any arbitrary SOAE spectrum?
By the cochlea: Differentiating and squaring of tone combinations, is one of the main characteristics of the "Heerens / de Ru" auditory model Applying physics makes auditory sense
based on the correct ...
0
votes
0answers
53 views
Two variable PCA using gradients
Let $x$ and $y$ be two random variables. Using principal component analysis (PCA), I can find a linear projection making the two variables uncorrelated. PCA solves this problem through an eigenvalue ...
0
votes
1answer
66 views
(geometric) intuition of whitening
I found this http://cis.legacy.ics.tkk.fi/aapo/papers/IJCNN99_tutorialweb/node26.html
But I still don't have an intuition of whitening. A diagonal covariance matrix means uncorrelated distributions, ...
