# Questions tagged [theory]

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### Are complex exponentials the only eigenfunction for arbitrary LTI systems?

After reading a few posts, like this. I know that arbitrary LTI systems always have complex exponential eigenfunctions. And that for specific LTI systems you can also have other types of ...
1 vote
47 views

### What is the effect of multiplication on the value of discontinuities?

I see that the values of a distribution at discontinuities are essentialy equal to the mean of the right-hand and left-hand limit values when dealing with distributions in relation to the Fourier ...
19 views

### In Bluetooth Low Energy, why are Enhanced Data Rate packets only 3 Mb/s?

In the "Introduction tu Bluetooth Device Testing" document ( https://download.ni.com/evaluation/rf/intro_to_bluetooth_test.pdf ), the modulations for Bluetooth Classic are said to be a ...
420 views

### Why is the reference pressure for dB SPL 20uPa?

The article here says that This 20-micropascal reference was selected because it was the quietest sound pressure level that a group of normal hearing test subjects could detect. which makes me think ...
64 views

### FMCW Transmit Signal and Fly-back Effect

I am studying a thesis about nonlinearities in the transmit signal and it mentions the following: The first 2,500 samples, which correspond to the Tmax of each of each sweep period and are affected ... 66 views

### how to tune and demo

How does one go about tunning your fm demod algorithm to a given carrier frequency. Consider the following algorithms that are present in this website: DSP Tricks: Frequency demodulation algorithms ...
1 vote
143 views

### Power Spectral Density and Wiener–Khinchin theorem for 2 different stochastic processes

I know the famous Wiener-Khinchin theorem for stationary random processes: the Fourier transform of the autocorrelation function of a stationary random process is equal to the Power Spectral Density ...
98 views

### Shortened linear codes

I've been working on my linear code assignment in my coding theory course and I have encountered a problem I would like to get help with. the question is described below. I will try to expalin what I ...
3k views

### Qualitative Explanation of Fourier Transform

I am reading the book Fundamentals of Music Processing by M.Muller and I am close to understanding the idea behind the decomposition of a signal into basic frequencies, and would appreciate some help ...
890 views

### Are all exponential functions eigensignals of LTI systems?

I know that complex exponential functions are eigensignals to LTI systems. Do these include real exponential functions? E.g. $2^t, e^t, ...$ Thanks for the help!
1 vote
507 views

### How is time used in this autocorrelation expression?

There are two papers I'm working through that explain applications of autocorrelation. The first - by Monti - is quite clear to me: It runs a sum over the time axis. The second one by Brown makes no ...
269 views

### Multiplying signals in discrete-time vs continuous-time

Given two discrete-time signals $a[n]$, $b[n]$ and its product $c[n]=a[n] b[n]$. The ideally interpolated, continuous-time version of $c[n]$ is \begin{align} c_1(t)&=\sum_{n=-\infty}^{\infty} a[n] ...
1 vote
235 views

### Validity of applying Heaviside function for signal processing applications

I wasn't sure if this question was more suitable for math.stackexchange, but I suspect it's more-so a signal processing question (albeit, a theoretical one) than a mathematical one. I am currently ...
1 vote
392 views

### How does Overlap-Add work for IIR filter?

So let's say I'm trying to implement something like an LPC vocoder. I analyse a speech signal by breaking it up in small chunks and determining their LPC coefficients, which are by design, the ...
474 views

### Is there any new scientific capability to build non-causal filters in real world?

According to this post: In discrete-time systems, causality is a requirement only when processing (filtering) signals in real time; i.e. when the index nn corresponds to a physical time n×Tsn×...
3k views

### Derivation of Nyquist Frequency and Sampling Theorem [closed]

I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
13k views

### Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
2k views

### LTI system and initial conditions

I suspect this is rather obvious once explained; I must be misunderstanding something. From reading various answers here (such as this one), I understand that an LTI system must have zero output for ...
1 vote
100 views

136 views

### Discrepancy when calculating LTI system output using inverse z-Transform

I'm given a difference equation, $y[n]-0.4y[n-1]=x[n]$, and asked to find the natural response $y_n[n]$, forced response $y_f[n]$ and complete response $y[n]$ if $x[n]=4 (0.25)^nu[n]$ and $y=0$. ...
1k views

### BIBO stability and input at system's pole

My understanding of BIBO stability is that if a bounded input is applied to a discrete-time, linear, time-invariant BIBO system, the output will also be bounded. A sufficient condition for this is ...
457 views

### Output of a discrete-time LTI system different form than input?

This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question ...
1 vote