Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

learn more… | top users | synonyms (1)

1
vote
0answers
48 views

System stability

I need to do an absolute integral of my impulse response of my LTI system so I can find out if the system is stable or not. The general formula is: $\int_{-\infty}^{\infty} \! |h(t)| \, \mathrm{d} t$ ...
0
votes
1answer
48 views

Using Product rule to take derivative

I'm trying to take the derivative of: $\frac{-1}{6}(e^{-3t}-1) u(t)$ The $u(t)$ is the step response. So the answer I get is by just doing product rule: ...
2
votes
0answers
291 views

Understanding Discrete Cosine Transformation

I'm currently working on some software and a key component is 2D DCT. But my question is more general, as I'm trying to understand the DCT in general, let's say from engineers point of view. For ...
0
votes
0answers
390 views

Fourier Series Coefficients for Signals

The question is: We specify the fourier series coefficients of a continuous-time signal that is periodic with period 4. Determine the signal x(t). $a_k=\begin{cases} 0, & k=0\\ ...
0
votes
1answer
130 views

Fourier Series with Signals

So the question is: Determine the fourier series representations for the following signal: Here the formula for the fourier series $$C_k=\frac{1}{T}\int_T \! x(t)e^\frac{-j2\pi kt}{T} \, \mathrm{d} ...
1
vote
1answer
197 views

Should mean be subtracted before convolution?

Suppose I have a signal in the form of N real numbers. I am searching for a continuous pattern within this signal. The pattern is represented by M real numbers. (M < N) To find the pattern's ...
0
votes
1answer
63 views

what is an integral multiple of a period?

Suppose i have a sinusoidal waveform. What does it mean when I need to truncate it corresponding to an integral multiple of a period?
0
votes
2answers
200 views

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) = ...
1
vote
1answer
333 views

Maximum Eigenvalue of Autocorrelation Matrix Bound

I am reading Detection and Estimation by Kay. In problem 2.7, one of the parts is to show that the maximum eigenvalue of the autocorrelation matrix is less than the maximum value of the PSD. The ...
1
vote
0answers
214 views

Projection Slice theorem getting rid of artifacts?

I have employed the fourier(projection) slice theorem in matlab. I have a 3D image, P(x,y,z) defines their pixel intensities at a given location int he image volume, it is discrete and uniform. I ...
2
votes
1answer
3k views

How to plot this signals or functions?

i´m taking a course in signals and systems, and i really don´t know how to plot this signals Consider the pulse signal written as $p(t)=u(t+0.5)-u(t-0.5).$ where $u(t)$ is the Heaviside step ...
0
votes
2answers
129 views

Why is $1 - 2\cos^2(\frac{\pi n} {4})$ the same as $ -\cos(\frac{\pi n} {2}) $?

Why is $$1 - 2\cos^2(\frac{\pi n} {4})$$ the same as $$ -\cos(\frac{\pi n} {2}) $$ I think the 1 in here, I can just neglect when I look at borders from $[-\infty , \infty]$. But what's going on ...
0
votes
1answer
501 views

Autocovariance of white noise convolved with function on L2

I want to compute the autocovariance of a Gausian zero-mean white noise process convolved with a function $f(t) \in L^2$. Could anyone show me how I'd do this or provide a reference? $L^2$ is the ...
1
vote
3answers
10k views

square wave matlab code

I'm having some trouble generating a square wave in matlab via my equation. Just wondering if anyone has some insight on what I am missing here in my code? I was thinking I could easily generate a ...
3
votes
1answer
716 views

Is there a time-domain proof of Nyquist sampling theorem?

For a continuous-time signal $x(t)$ that is bandlimited (in the baseband) to $[-W,W]$, the standard proof of Nyquist sampling theorem proceeds in the frequency domain by examining the Fourier ...
8
votes
2answers
12k views

Integration of sawtooth, square and triangle wave functions

Context After a discussion about how to plot the results of a frequency modulation between two signals on Stack Overflow, I understood that I need to find the time-integral of the following wave ...
0
votes
1answer
685 views

What is the difference between FWHH and FWHM?

The title says it all really. I wanted to know if there is a situation where full width half height half maximum is more appropriate than full width half height or vice versa. Thank you
1
vote
1answer
94 views

Boundary condition error, correlation of a function with a wavelet.

I'm trying to compute some wavelet transforms and I seem to be running into some boundary condition errors. I have a randomly generated signal pictured at the top of the figure, and the real part of ...
3
votes
2answers
748 views

Need a formula for a quadratic spline

I'm trying to reproduce some results from a paper and I need an explicit formula for a specific quadratic spline to do so. The problem is, I've only got a plot of it. The quadratic spline is from ...
1
vote
1answer
649 views

FFT with a real matrix - why storing just half the coefficients?

I know that when I perform a real to complex FFT half the frequency domain data is redundant due to symmetry. This is only the case in one axis of a 2D FFT though. I can think of a 2D FFT as two 1D ...
2
votes
2answers
971 views

How can I apply a low pass filter to a Fourier Series?

I have a square wave signal and its Fourier Series. This signal pass through an ideal low pass filter,H(f), which has a cutoff frequency of 4KHz. What is the resulting baseband bandwidth of the ...
3
votes
2answers
3k views

How do you calculate the frequency perceived by humans of two sinusoidal waves added together?

I'm not sure if this is on topic or not. The tag may also not actually fit. If you add together two sinusoidal waves of different frequencies, how do you calculate the frequency of the resulting ...
3
votes
1answer
81 views

Estimating the input to a system from a system state

[ Cross-posted to: http://dsp.stackexchange.com/questions/3098/estimating-the-input-to-a-system-from-a-system-state-using-ekf ] I have a system for which I have obtained a non-linear time-varying ...
0
votes
1answer
169 views

Solving Difference Equation

I have the following equation: $$\frac{Z-1}{{Z^2}-2Z+6}$$ I tried to apply difference equation on it: $$y_{n+2}-5y_{n-1}-6y_n = x_{n+1}-x_n$$ I need to find equation expressed as $y_n$ I have the ...
2
votes
1answer
4k views

Plotting a one-sided amplitude spectrum

I have a continuous signal $x(t)$ such that $$x(t)=12\cos(6\pi t)+6\cos(24\pi t)+3\cos(30 \pi t)$$ and is asked to sketch a $1$-sided Amplitude Spectrum of the signal $x(t)$ if sampled above the ...
1
vote
1answer
772 views

Finding Fourier series with function not centered at the origin

I am trying to find both Fourier cosine and sine series which represent the function F(t) in the interval $(0, \pi)$ where $F(t)=\begin{cases} \frac{\pi}{2} & \ \ 0<t< \frac{\pi}{2}\\ 0 ...
1
vote
1answer
84 views

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 ...
0
votes
2answers
141 views

Z-Transform Identity

I've come across an identity and would like to know if it has some sort of formal name or derivation or explanation or something! Also, I'm curious as to whether others are aware of such an identity. ...
1
vote
1answer
1k views

Visualize a difference equation with Matlab [closed]

I have a difference equation for a Single Pole Infinite Impulse Response Filter, defined on a discrete time-series: $y[n]-(1-\alpha)*y[n-1]=\alpha*x_n$ While the []s brackets refer to a position n ...
3
votes
3answers
121 views

Detecting significant decreases in a signal

I'd like to find a way to detect a significant drop/decrease in a signal. Below is an actual example of what I'd like to accomplish, with the arrow denoting the change that I'd like to detect (only ...
2
votes
1answer
6k views

$y(n) = x(-n)$ , causal or not , memory or memoryless?

$y(n) = x(-n)$ , causal or not , memory or memory-less ? it's a question in digital signal processing course . My guess it's memory less , causal because $x(-n)$ is only the inverse of the ...
1
vote
0answers
121 views

Worst-case error related to Cramer-Rao bound

I would like to understand the relation (if any) between the Cramer-Rao Lower Bound of estimation theory and the following simple definition of "reconstruction accuracy" which doesn't use any ...
3
votes
1answer
534 views

95% of energy of Bessel Functions

How can we determine what which Bessel function amplitudes contain the majority of the the energy? Similar to the Carson bandwidth rule, I want to determine which sidebands help make up the 95% of ...
0
votes
0answers
452 views

proof that orthogonal signals not interrupting each other

I know that signals that are orthogonal do not disturb each other. What I am curious is what is the proof behind why orthogonal signals in a single signal (i.e. a single signal can be broken down ...
2
votes
1answer
115 views

MA process ACF proof - don't understand it

I've got the proof but I don't understand a small detail. As you know for an MA process: $X_n = \sum _{i=0} ^q \beta_i Z_{n-i}$ where $Z_n$ is WGN (pure Gaussian random process). Then the ACF is: ...
2
votes
0answers
181 views

How to solve the recursive relation in Kalman filter?

I was wondering how to solve the Kalman filter's recursive equation (also see the appendix at the end of this post) for the estimated state $\hat{\textbf{x}}_{n|n}$ at time $n$, over discrete times ...
1
vote
2answers
414 views

Nyquist-Shannon sampling theorem - original version and modern version difference?

I just found out that the original version of Nyquist-Shannon sampling theorem differs from the modern version.. In the original version, it states that the bandlimited signal $x(t)$ can be ...
3
votes
1answer
1k views

Derivative of a random variable w.r.t. a deterministic variable

I'm reading about time series and I thought of this procedure: can you differentiate a function containing a random variable. For example: $f(t) = a t + b + \epsilon$ where $\epsilon \sim N(0,1)$. ...
1
vote
0answers
38 views

every continuous signal being modelled as a function

Can every coninuous signal be modelled as a function, which then can be converted into a series of sine and consine functions with unique frequencies? And let us say that we have some arbitrary ...
0
votes
2answers
108 views

wave separation

Say there is a wave of sines and cosines. (<- one can think of Fourier theory.) A) There is a wave that has the same frequency all the time. However, amplitude (- shape) of each period differs. Is ...
1
vote
1answer
2k views

Nyquist–Shannon sampling theorem shannon's proof

In Wikipedia, there is Shannon's proof on Nyquist-Shannon sampling theorem. ( http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem#Shannon.27s_original_proof ) The original proof ...
1
vote
1answer
218 views

Complex Numbers and polar form

I am given the following information: $$x[n]= s^n,\qquad n=0,\pm 1,\pm 2,\ldots$$ where $s=\sigma + j\omega = re^{i\theta}$ is a complex number in general. I was wondering how the following is ...
5
votes
6answers
537 views

How to generalise the Fourier transform

The Fourier transform approximates a signal using a bunch of sine and cosine waves. The inverse Fourier transform then reconstructs the original signal from this information. I am told that it's ...
0
votes
1answer
45 views

Differences of distributions inside Kalman filter.

I am studying the Kalman filter algorithm but i can't understand one point. The k factor has to be chosen in order to minimize the variance of the signal. This lead to following equation: ...
1
vote
1answer
274 views

Is there an autocorrelation function with a constant integral whose absolute value integral diverges?

Suppose a function $g:\mathbb{R}\rightarrow\mathbb{R}$ such that: $|g(x)|\leq g(0)$; $g(x)=g(-x)$, i.e. $g(x)$ is even; $\int_{-\infty}^{\infty}g(x)dx=C$; There exists a Fourier transform of ...
2
votes
1answer
150 views

How to remove the boundary effects arising due to zero padding in discrete fft?

I have made a python code to smoothen a given signal using the Weierstrass transform, which is basically the convolution of a normalised gaussian with a signal. The code is as follows: ...
1
vote
1answer
2k views

time derivative of discrete data in simulink

I'm implementing a program in Java that was delivered in Simulink. My expertise is limited, and I'm stuck on converting a derivative block. The simulink code applies a du/dt block to the input data. ...
1
vote
1answer
1k views

constructing Feature Vector from given values

I am fairly new to signal analysis, so pardon any noobish questions, but I couldn't find a clear answer by googling. I am using PyLab to calculate certain values from a given data. My data is a 3D ...
1
vote
2answers
102 views

How to simplify the product of two $\exp$ functions

It's been a while since I did any of this. I have the following product: $\exp(-j2 \pi u|k|x) \cdot \exp(-j2 \pi v |k|x)$. This seems like it is something that can be simplified, but how? Note, ...
2
votes
2answers
239 views

An example of a “pathological” power-spectral density function?

Suppose that we are given a wide-sense stationary random process $X$ with autocorrelation function $R_X(t)$. Power spectral density $S_X(f)$ of $X$ is then given by the Fourier transform of $R_X(t)$, ...