Questions tagged [continuous-signals]

A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum.

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14
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2answers
12k views

What are advantages of having higher sampling rate of a signal?

Being a non signal processing science student I have limited understanding of the concepts. I have a continuous periodic bearing faulty signal (with time amplitudes) which are sampled at $12\textrm{ ...
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12answers
32k views

Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original ...
17
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3answers
28k views

How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
10
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2answers
24k views

Deriving the Fourier transform of cosine and sine

In this answer, Jim Clay writes: ... use the fact that $\mathcal F\{\cos(x)\} = \frac{\delta(w - 1) + \delta(w + 1)}{2}$ ... The expression above is not too different from $\mathcal F\{{\cos(2\pi ...
4
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1answer
583 views

3D wiggle plot for an analytic signal: Heyser corkscrew/spiral

Just reading The Analytic Impulse, A. Duncan, 1988, I met the name "Heyser corkscrew" for the first time in my DSP life, for a 3D display of a cisoid or complex exponential $e^{i\omega }$ (often ...
0
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1answer
156 views

Confusion in CT Fourier Transform Proof

I am confused trying to understand the Proof of Fourier Transform from Oppenheim book Signals and Systems. I am pasting the equations directly from the book: $$\widetilde{x}(t)=\sum_{k=-\infty}^{+\...
7
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5answers
594 views

Inconsistency with the units of power spectral density and the definition the people often give

Perhaps someone can help me resolve something - this is my understanding: In deterministic signal analysis, for a signal $x(t)$ the signal energy is defined by $$E_{\textrm{s}} = \int^{+\infty}_{-\...
3
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4answers
371 views

Why do we have to rearrange a vector and shift the zero point to the first index, in preparation for an FFT?

I am trying to learn how to implement the FFT as a way to approximate the continuous-time Fourier transform, and as a "nice easy example" I have chosen to test it with a simple Gaussian pulse in the ...
1
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1answer
5k views

How to calculate the mean/center frequency of the spectrum?

Assume that the Fourier Transform of $x(t)$ is $X(j\omega)$. And I want to calculate the $\bar{\omega}$ which is the center freqency in the spectrum ( the highest). And a classmate tells me this ...
26
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2answers
4k views

Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
6
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3answers
1k views

Mathematically Inclined Signal and Systems / Signal Processing Book Recommendations

I'm an electronics engineering student with high inclination to analysis and pure mathematics. I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal ...
2
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1answer
20k views

What is the difference between continuous, discrete, analog and digital signal?

It's my first time studying DSP and I've faced a problem finding a convenient definition. Are the following definitions correct? And if so why there are some resources defining it in other terms such ...
4
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2answers
3k views

What is the intuition behind convolution? [duplicate]

I have been using convolution for finding outputs of various systems .I know how to use it.But I still don't know what does convolution exactly means? how one can define convolution ?
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1answer
849 views

Is convolution distributive over multiplication?

Is there any formula or expansion for $$a(t)*[b(t) \cdot c(t)]$$ $$a(t) \cdot[b(t)*c(t)]$$ where $*$ denotes the convolution? By expansion I mean something like $a(t)\cdot[b(t)+c(t)]=a(t)b(t)+a(t)...
5
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1answer
3k views

When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?

Heads up, this is for homework. I never took a signals and systems course, so I'm behind on this stuff. I want to compute the convolution of two rectangular regions. I know the standard equation ...
2
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1answer
586 views

How to analyse the sound of Motor

I have a motor, that I want to analyse, using its sound, so I can its 'character' I was using the the simple fft, and figured out, that it wouldn't help, so I tried the order analysis, at least I ...
1
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3answers
289 views

Help with obtaining the power spectral density of a simple continuous cosine (using both forms of the definition for PSD)

I am trying to go through a simple example to teach myself about Parseval's theorem and calculating power spectral density (PSD) in practice and would be very grateful if someone could check my ...
35
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6answers
55k views

The difference between convolution and cross-correlation from a signal-analysis point of view

I am trying to understand the difference between convolution to cross-correlation. I have read an understood This answer. I also understand the picture below. But, in terms of signal processing, (a ...
15
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2answers
12k views

Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ...
6
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3answers
13k views

For an LTI system, why does the Fourier transform of the impulse response give the frequency response?

I know that for a given system, the Fourier transform of its impulse response gives its frequency response. I want to find where this property comes from, but haven't been able to find if it's a ...
4
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1answer
2k views

$2\pi$ periodicity of discrete-time Fourier transform

In my signals and systems course, we have learned that the discrete-time Fourier transform is $2\pi$ periodic, but the continuous-time Fourier transform is not periodic in general. For reference, we ...
2
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1answer
12k views

Proof of time-invariance of continuous-time system

I have a system with the following input/output relation: $$ y(t)=x(-t) $$ and I want to prove (not graphically/draw) that its not TI (time invariant). I tried to write down $y(t-T)$ and compare ...
4
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4answers
13k views

About Fourier transform of periodic signal

In Fourier transform for periodic signal, I checked different books and I found a different explanation in each book. Let's take the explanation in Signals and Systems by Rajeshwari & Rao: The ...
9
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3answers
1k views

Fourier Transform Identities

We know the below, $$ \mathscr{F}\big\{x(t)\big\}=X(f) \tag{1} $$ $$ \mathscr{F}\big\{x(-t)\big\}=X(-f) \tag{2} $$ $$ \mathscr{F}\big\{x^*(t)\big\}=X^*(-f) \tag{3} $$ Now, if for some signal $$ x(-...
2
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2answers
627 views

Linear Constant Coefficient Differential Equations: Zero-Input and Zero-State responses

The solution to a linear constant coefficient differential equation of the form $$\sum_{k = 0}^{N} a_k y^{(k)} (t) = \sum_{k = 0}^{M} b_k x^{(k)} (t)$$ can be written as $y(t) = y_{ZI} (t) + y_{ZS} (t)...
2
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1answer
172 views

Time invariance of a System

I have this small question about the time invariance of a system. Which is: If the current output is multiplied by the current input (see both are variables) will the system be time variant or time ...
2
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3answers
241 views

Sampling Theorem and Signals Explained to a Mathematician

Let $f:\left(-\frac T2,\frac T2\right)\to\mathbb{R}$ for some $T>0$. The Fourier coefficients of $f$ are $$\left\{\begin{matrix}a_0&=&\displaystyle\frac 1T\int_{-T/2}^{T/2}g(t)\;dt\\a_k&...
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1answer
1k views

Sampling signal after root raised cosine

I am generating series of 1 and 0. then pulse shaped them with root raised cosine and after than deciding to do match filtering and recovering the bits however it turns out that I am not getting the ...
0
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3answers
1k views

Is the system represented by the equation $y(t) = x(2t)$ time invariant?

I came across this problem in the text book Signals and Systems - Oppenheim (Example-1.16). To solve this, I followed the following algorithm (described in the book earlier for a separate problem): $...
0
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1answer
6k views

Convert normalized frequency to real frequency in AR model

Let us suppose that we have modeled signal using AR model, and suppose we have following model: I used spectral estimation function from MATLAB pyulear Now ...
9
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1answer
2k views

Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

I have been studying signals and systems lately and I have came across the following claim: The uniform sampling of a periodic continuous-time signal may not be periodic! Can someone please ...
3
votes
1answer
968 views

Sinusoid with increasing frequency

How would you describe this signal? It's like a sinusoid but as if its frequency was constantly increasing: could you write down a mathematical description? Thanks. And no, this is not homework...
2
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1answer
197 views

Detect signals degree of imbalance

I have got this question: let's suppose that I have three signals, representative of the same variable, but taken on three different component of a same device; in my case, three load signals, ...
2
votes
3answers
2k views

Why cosine is not an eigen signal?

According to this website: If the output of a system has the same type as its input signal, then the input signal is referred to as the eigen function of the system. but in this question it is ...
2
votes
1answer
1k views

PSD of a sum of two stationary real signals

I have 4 signals ($w_1(t),w_2(t),u_1(t),u_2(t)$ of which I know the power spectral densities (PSDs) $S_{w_1,w_1}(\omega),S_{w_2,w_2}(\omega),S_{u_1,u_1}(\omega),S_{u_2,u_2}(\omega)$ and the cross PSD $...
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2answers
6k views

Energy of Sinc function

How to find energy of sinc function $x(t) = \frac{\sin \pi t}{\pi t}$ with out the help of Fourier transform or Parseval's theorem?
0
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2answers
5k views

Understanding the frequency domain [duplicate]

I'm trying to understand what frequency domain is. I found general explanations on the Internet, for example: frequency-domain graph shows how much of the signal lies within each given frequency band ...
-3
votes
1answer
545 views

Ideal BandPass Filter

Let suppose x(t)=$\sum\limits_{k=-∞}^∞ R(t-kT)$ $R(t) = \begin{cases}1 &[0,2T] \\ 0 & \text{otherwise} \end{cases}$ x(t) is the input to an ideal bandpass filter with $\text{BandWidth} = \...
4
votes
2answers
90 views

Continuous vs discrete signal energy

I am looking to calculate the signal energy of real, sampled acoustic data. According to this source, the energy of a continuous signal is: $$\tag{1}\hspace{1cm} E_x = \int_{-\infty}^{+\infty}|x(t)|^...
4
votes
1answer
336 views

“chirp” with arbitrary period

Say you have a linear chirp, which is a bit like a sinusoid with a gradually increasing period, but instead of the linearly increasing period, could you pick an arbitrary value, like the red line in ...
4
votes
1answer
3k views

Filter coefficients for colored noise Voss Algorithm

If I use a generic filter for generating colored noise like pink,brown,white then how do I modify this statement and how do I know what are the coefficients to be used in AR model for different noise....
3
votes
6answers
409 views

Design a LTI system which returns DC value of the input signal

Suppose that $h(t)$ is the impulse response of LTI system. The input signal $x(t)$ is periodic with period $T$. Determine $h(t)$ so that the output signal $y(t)$ only be the DC component of $x(t)$. Is ...
3
votes
1answer
241 views

Is it possible to simplify the convolution integral if the functions are non-zero in disjoint areas? [duplicate]

Possible Duplicate: When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start? I have a function $f(x,y)$ and $h(x,y)$. $f(x,y)$ has a ...
3
votes
1answer
2k views

Analog signal can be discrete time?

I am new to this site and field too.I always thought analog is continuous and digital signal is discrete. I read this today and got confused about analog signal Analog can be continuous time(CT) ...
2
votes
4answers
232 views

Very basic question about how we define frequency in signal processing

When talking about general periodic continuous-time signals for which $$x(t + T_0) = x(t)$$ where $T_0$ is the fundamental period we define the fundamental frequency $\omega_0$ as $\omega_0 = 2\pi/T_0$...
2
votes
2answers
226 views

How can I generate a sine and cosine function using an exponential function?

I have been trying to generate sine and cosine sampled graphs by a given sampling frequency. ...
2
votes
1answer
6k views

Additive but not homogeneous continuous system?

I am trying to find an example of a continuous system that is homogeneous, but not additive. So far, the only example I could find was an example from this page, which describes system as $y(t) = \...
1
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1answer
48 views

explanation of Hybrid systems?

I want to study Detailed explanation of hybrid systems?Which incorporate both continuous and discrete time signals & systems? for example In which a continuous-time input signal is transformed ...
1
vote
1answer
490 views

Recommended signal processing books? [duplicate]

I am learning about signals in school but I found it very hard. Can someone help me by giving some references about any books? We are studying Fourier transform, signal power, filters, digital and ...
1
vote
1answer
64 views

Discrete and Continuous Signals

I am new to the signals area and have been reading through a lot and have some questions. Suppose I have a saved audio file on my computer, .wav file. I can view the time domain of the signal by ...