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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35
votes
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 ...
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 $A(s)$ ...
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? ...
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 ...
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{ ...
12
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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 ...
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 ...
10
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5answers
5k views

Why do linear systems show sinusoidal fidelity?

I am looking for a proof for sinusoidal fidelity. In DSP we study a lot about linear systems. Linear systems are homogenous and additive. One more condition it satisifies is that if a signal is a sine ...
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(-...
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 ...
9
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3answers
23k views

Alias frequency Formula

I'm taking a multimedia systems class in my MSc Computer Science, and I'm having some trouble understanding the formula for the alias frequency - this could stem from my misunderstanding of the alias ...
8
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2answers
246 views

Does the inverse-CTFT exist for a dirac delta?

Does the inverse continuous time Fourier transform exist for a Dirac delta (A single causal/non-causal spike)?
7
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5answers
596 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}_{-\...
7
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7answers
663 views

Intuition behind commutativity of convolution in LTI systems

Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system? If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
7
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2answers
894 views

determine two signals with a scale factor

Suppose I have 2 signals from function $f_1(x)$ and $f_2(x)$, respectively, and assume the sampling rate is above Nyquist frequency, so we can restore the underlying functions $f_1(x)$ and $f_2(x)$. ...
7
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1answer
4k views

eigen values and eigen vectors of signal

What does the Eigen values and Eigen vector of a signal or function represent? What is its physical significance? I know about basis vectors of a signal which constitute the orthogonal planes where ...
7
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1answer
257 views

Why would I want to define a modulation index for each tone (DSB-FC)?

So the exercise is basically a signal $f(t)$ that is going to modulate the carrier $A\cos(\omega_ct)$ using a modulation index of $m=1$. I have to find $A$ and the power of the modulated signal: $$ f(...
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 ...
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 ...
6
votes
2answers
495 views

why total energy of a finite duration continuous signal becomes infinite after sampling

If I have a continuous-time energy signal and multiply it with an impulse train, the frequency domain representation has infinite replicas. The total energy if we sum them up becomes infinite. What ...
6
votes
1answer
323 views

How to derive $r(t) = c(t) \circledast \frac{1}{2} h_b(t, \tau)$?

Consider a linear time-variant channel. The transmitted signal is $x(t)$, the channel impulse response is $h(t, \tau)$, and the received signal is $y(t)$. Then $$ y(t) = \int_{-\infty}^\infty x(\tau) ...
5
votes
6answers
2k views

What is the first derivative of Dirac delta function?

Could you please help me in a simple way, what is the first derivative of a Dirac delta function? I found this answer: The informal answer is a positive Delta function immediately followed by a ...
5
votes
5answers
3k views

Effects of linear interpolation of a time series on its frequency spectrum

Situation In order to synchonisize different time series i have to apply linear interpolation on them. After the interpolation and synchronization the signal is transferred into its frequency domain ...
5
votes
3answers
2k views

What is the opposite of sampling called?

We call the conversion from a continuous time signal $f(t)$ to a discrete time signal $f_s[k]$ "sampling". Is there a name for the reverse operation, i.e. creating a continuous time signal from a ...
5
votes
2answers
7k views

How does shift and scaling inside of a function affect its Fourier Transform?

The properties aren't entirely clear to me, sorry for the basic question. I know the Fourier Transform of one function. Say, $\text{rect}(x,y) \Leftrightarrow \frac{\sin \pi u}{\pi u} \frac{\sin \...
5
votes
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 ...
5
votes
4answers
1k views

Continuous Time Signal and Discrete Time Signal - Connection Between Periodicity and Discretness

I know that all periodic continuous time signal have discrete spectral representations, but are all discrete spectral representations periodic in continuous time? Also, can all periodic signals be ...
5
votes
1answer
831 views

Correct method for drawing waveforms

I need to draw waveforms for biometric data like ECG and EEG signals. When I have more samples than pixels at the X-axis, I need to draw a vertical line between the MIN and MAX sample-value for that ...
4
votes
4answers
999 views

Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
4
votes
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 ...
4
votes
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 ?
4
votes
2answers
120 views

Are there any advantages oversampling?

Are there any advantages of undersampling or oversampling in signal processing point of view?
4
votes
2answers
4k views

Detecting outliers/noise from sensor data

I am trying to detect outliers/noise as indicated on the diagram below from sensor data. Can anyone advice how to go about it? I can only do this in python, so are there libraries in python that I can ...
4
votes
2answers
4k views

Main differences to take into account between continuous and discrete time signals

I started studying DSP and the first things that came out were the differences between continuous and discrete time signals. So, I was wondering if I understood well these concepts before I keep going ...
4
votes
3answers
799 views

How to Prove a System Is Invertible?

what i know is that for a system to be invertibel it should be one-one , but I am confused that if i am given a transfer function of a LTI system how can I prove or verify if it is invertible. ...
4
votes
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 ...
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....
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
2answers
990 views

Example of an LTI system with complex impulse response

In general, I know that the impulse response $h(t)$ of an LTI system can be complex. However, all of physically realizable, useful systems I've come across have purely real impulse responses. I did a ...
4
votes
1answer
308 views

Signal Processing using Fourier Transform

So I'm trying to understand how MRI machines work. I understand all the concepts of it, the parts, what they do, how the machine works, etc. The part I'm having trouble with is the fourier transform ...
4
votes
1answer
523 views

Bridging CTFT and DTFT for a cosine

I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT. For example if I take a basic example: $$\begin{aligned} x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
4
votes
2answers
1k views

What should the amplitude be when plotting 1-sided Amplitude Spectrum?

I have a continuous signal x(t) such that $x(t)=12cos(6\pi t)+6cos(24\pi t)+3cos(30 \pi t)$ and is asked to sketch a 1-sided Amplitude Spectrum of the signal x(t) if sampled above the minimum ...
4
votes
1answer
640 views

What techniques are available for correcting constellation rotation due to phase ambiguity?

In order for a receiver to recover a baseband signal, it needs a carrier signal equivalent to that used by the transmitter for upconverting the original baseband signal. Unless pilot tones are used, a ...
4
votes
3answers
960 views

Periodicity of the discrete-time Fourier Transform

The DTFT of a sequence $x[n]$ can be written as $$X(e^{j\omega}) = \sum_{n = -\infty}^{\infty} x[n] e^{-j\omega n}.$$ Is the smallest (fundamental) period in frequency of the DTFT always $2\pi$? Or ...
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
2answers
8k views

What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: ...
4
votes
2answers
2k views

Deriving the integration property of the Fourier Transform

I want to derive the property of the Fourier Transform that states that if $X(j\omega) = \mathcal{F} (x(t))$ then $$\mathcal{F} \left( \int_{-\infty}^{t} x(\tau) \mathrm{d} \tau \right) = \frac{1}{j\...
4
votes
1answer
585 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 ...
4
votes
3answers
873 views

creating a seamless signal / loop using interpolation

I'm trying to create a seamless loop using a "non-periodic" signal using interpolation to smooth out the beginning and the end but I'm still getting a click at the beginning when it loops and I listen ...
4
votes
2answers
963 views

Continuous-time mathematical formula for deconvolution filters

I have an elementary function $p:\mathbb{R}^2\rightarrow\mathbb{R}$ which (locally) represents an image. It's a polynomial, and its the result of the following 2D convolution: $$p=f\star G\star \...

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