Questions tagged [signal-processing]

Question 1

As stated in the Wikipedia page of the Kosambi-Karhunen-Loève theorem, the Karhunen-Loève (KL) representation of a zero-mean stochastic process $\{\mathsf{x}(t)\}_{t\in[a,b]}$ is $$ \mathsf{x}(t) = \...

Question 2

As the title says: If $\theta(\omega) = - \omega t_0$ what is $t_0$? $$t_0 = -\dfrac{\theta(\omega)}{\omega} \quad \text{or} \quad t_0 = -\dfrac{\text{d}\theta(\omega)}{\text{d}\omega}, \quad \omega \...

Question 3

When the region of convergence (ROC) of a $Z$-transform $F(z)$ is of the form $|z|>r$, meaning it corresponds to the outermost region of the $z$ domain, then $f[n]$ is necessarily right-sided. ...

Question 4

Cross-posted from signal processing stack exchange: Consider the following approach for de-rating proportional feedback gains to account for a measurement delay by controlling a future-projected ...

Question 5

Question Consider the two periodic signals $$ y(t)=B\sum_{n\in\mathbb Z}\operatorname{rect}\!\bigl(2t-n\bigr), > \qquad x(t)=A\sum_{n\in\mathbb > Z}\operatorname{rect}\!\Bigl(\tfrac{t}{2}-6n\...

Question 6

I have heard it often stated without much explanation that ... any orthogonal transformation of [a Gaussian white noise vector] will result in a Gaussian white random vector. In particular, under ...

Question 7

In some applications such as amplitude modulation, one encounters product of cosines of the form: $$x(t) = \cos(\omega_1 t + \phi_1)\cos(\omega_2 t + \phi_2) $$ And for specific values of $\omega_1, \...

Question 8

It is well known that multiplying tempered distributions is generally not possible, especially considering that pointwise values are not defined in general. I am however wondering if a relation can be ...

Question 9

Let’s say I have a signal from angle sensor that gives me the measured angle. Let’s call it $A$. I want to smooth the measurements so I am doing simple FIR with B coeff. like this: $A_e[k] = A[k]*B[0]+...

Question 10

I was reading Signals and systems by Professor Oppenheim. In the first chapter it writes (not in exact words): The discrete-time unit step is the running sum of the unit sample. That is $$u[n]=\sum^n_{...

Question 11

The Allan Variance Sigma Tau Diagram allows one understand the different kinds of noise that are present in a time series; the following two images are taken from the wikipedia page related to Allan ...

Question 12

From Wikipedia: A pulse in signal processing is a rapid, transient change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline ...

Question 13

This series is from a signal processing coding assignment. It is the result of the convolution between two signals, and I need to solve this series to prove that it really equals the convolution. The ...

Question 14

I’m trying to pin down a subtle point about the derivation of the convolution formula for an LTI system $L$. We start with the representation $$x(t) = (x*\delta)(t) = \int _{-\infty}^{\infty} x(\tau) \...

Question 15

I have made great efforts on the derivation, and the results are really close but I am still missing the last step. If someone can help that'd be great! Problem setup Consider this modified Kalman ...

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Questions tagged [signal-processing]

Continuous Karhunen-Loève spectral representation of a discrete-time random sequence

If $\theta(\omega) = - \omega t_0$ is: $t_0 = -\dfrac{\theta(\omega)}{\omega}$ or $t_0 = -\dfrac{\text{d}\theta(\omega)}{\text{d}\omega}$

If the region of convergence of a $Z$-transform is $|z|>r$, the sequence is right-sided, but is it causal?

Compensating optimal PD gains for a simple two-state linear system with different position/velocity measurement delays

Show $\frac{B}{A}=-\frac{C_3}{C_2} \cdot \frac{3 \sqrt{3}}{4}$ for two pulse‐train Fourier coefficients

What is the probability distribution of the DFT of a real Gaussian white noise random vector?

When can product of cosine signals be written as sum of cosine signals? [duplicate]

Fourier Transforms of functions of polynomial growth multiplied with Ш

What would be the equivalent filter coefficients of sine and cosine of a signal

Representations of unit step function in terms of impulse function---discrete versus continuous time

Generating and Interpreting the Allan Variance Sigma-Tau Diagram

On a mathematical definition of a pulse shape

How can I find a nice expression for this series?

Why in an LTI convolution $\int L\{ x(\tau) \delta(t - \tau)\} \ d\tau$ does $L$ still “see” $t$ as its variable, not $\tau$?

Kalman Filter with correlated measurement noise derivation

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