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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1answer
90 views

Deriving statistics of band limited Random Noise

The question is: Consider a continuous random number with a Gaussian distribution of mean $\mu$ and variance $\sigma$ . The RV is measured from time $t=-\infty$ to $t=\infty$. This time domain signal ...
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1answer
3k views

How to add two signals?

If x(t) is the curve shown in the image how can I find (x(2t)+x(2t+2))? I know how to find the individual terms but don't know how to add them! And how can I express my answer in terms of the unit ...
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3answers
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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 ...
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1answer
33 views

Plotting the spectrum of a continuous sinusoid function

I am just learning about spectrums and I am a little confused. I have given a simple example and where I get stuck. Plot the spectrum of $x(t) = 5\cos\left(800\pi t + \frac{3 \pi}{7}\right)$. So ...
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1answer
1k views

Convolution by differentiation property of convolution

This is the question when i am trying to do it by the deravative property of convolution https://en.wikipedia.org/wiki/Convolution#Differentiation like this Actual answer should come like this $...
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1answer
54 views

Time Delay Margin

I have a question regarding the time delay margin. I know the definition of time delay margin now I want to know that for the stability of the system is it good to have large time delay margin or ...
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5answers
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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 ...
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1answer
160 views

Public datasets of signals

Is there a public database where I can find or anyone can provide me real signals. I'm looking specifically for pairs of natural signals (e.g. from Sensor networks) to test some cross-correlation and ...
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2answers
92 views

What is the type of these signals?

I want to do some DSP and Machine learning experiments on Electrical and Acoustic signals, but, due to some language setbacks, I didn't know how to call the type of my signal, what I use to google now,...
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1answer
115 views

Multi-taper Coherence, With Tapers=1

I had a question regarding multi-taper estimated coherence. It appears when the number of tapers is set to 1, all coherency values, per frequency, are always 1. It's obvious solving for autospectra $...
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1answer
265 views

Time variance of $y(t)=x(2t)$

At first I had trouble proving the time variance for this as I would do the usual mistake as in question Is the system represented by the equation $y(t) = x(2t)$ time invariant?. The solution has ...
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3answers
709 views

Precision measurement of sine wave amplitude with ADC

I want to measure amplitude of a sine wave input precisely with a limited resolution ADC. As an example suppose that I have $1\textrm{ MHz}$ pure sine wave input to the $320\textrm{ Msps}$ $10$-bit ...
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1answer
406 views

Understanding the relation between instantaneous frequency and phase of a sinusoid

Sorry for a basic question but I really wanted to understand the relation between the instantaneous frequency and instantaneous phase of a sinusoid. We know that we can get the the instantaneous ...
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1answer
31 views

measuring how much signal corrupted by passing from a medium [closed]

I am looking for a measure to report how much a signal has corrupted by passing a medium. Suppose we have a signal 2Hz and amplitude ...
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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(-...
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2answers
557 views

Understanding the definition of mean/autocorrelation

I was studying about the definitions of mean, expected value and autocorrelation. I wanted to verify my understanding the evaluation of mean, expected value and autocorrelation. At the same time to ...
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1answer
40 views

Finding a change in a signal

I am looking to some C algorithm(for MCU), where I have these signals : First graph you can see that there is an event in the middle and it goes back to normal, second and third there is some event ...
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1answer
731 views

QAM Constellation Construction - Basic 4/8 QAM

I wanted to know how to construct the set of amplitudes/phase for QAM modulation. I saw that a QAM signal can be represented as: $$ s_m(t)=A_{mi}g(t)\cos(2\pi f_c t)-A_{mq}g(t)\sin(2\pi f_c t) $$ ...
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1answer
697 views

Fourier Transform of a signal using direct integration and properties

Am trying to compute the Fourier Transform of a function using the properties of the Fourier Transform once and checking my answer using direct integration. My problem is that am not getting the same ...
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1answer
141 views

What is the optimal Wiener-filter for this purpose?

Suppose I want to measure something with a sensor which in response to $u(t)$ produces an output signal in form of $v_{out}(t) = (1-e^{-t/ \tau})u(t)$, where $u(t)$ is the Heaviside-function and $\tau=...
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1answer
100 views

Quantization of analog sound signals

I am using Librosa to detect pitch in a guitar audio signal. I have very little background in signal processing, and I was quite confused with the distinction between analog - digital signals and ...
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1answer
81 views

Learner level information on Kalman filtering for different input kinds

I am learning Kalman filters and have seen example on data as state varaibles that have real values / numeric. However, in digital communication the information is in digital - bits. So, can Kalman ...
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1answer
503 views

What are two different continuous-time signals when sampled at $10\textrm{ Hz}$ would produce the sequence $x(n)=\cos(n\pi/8)$?

The answer is: $\cos(1250\pi t)$ and $\cos(21250\pi t)$ I’m not able to verify. My understanding is that when you periodically increase $t$ by $1/10$ ($10$ here is the frequency, so $1/10$ is ...
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0answers
29 views

For extracting the characteristics of the signal what minimum duration should be considered?

Being non signal processing student I have a limited understanding of concepts. I have a continuous periodic bearing faulty signal of 10 seconds duration sampled at 12 kHz. So I have 120,000 ...
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0answers
176 views

z-transform of $2^k$

It seems that you can decompose it as such: $f(n) = a^n u(n) + a^{-n} u(-n-1)$ But I already have issue here, is it basically saying that $ u(n) + u(-n-1) = 1$? this is the plot of u(n) and u(-...
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2answers
2k views

Laplace transform of product of signal and impulse train

I'm reading 'Discrete Time Control Systems' book by Ogata and came across a few statements (specifically, (3-1) and (3-2)) which I have not been able to understand. It is said that any continuous ...
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2answers
10k 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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2answers
1k views

How to remove spike from the data series?

I am getting load cell reading from my adc ADS1231 every 100 ms or say at 10Hz i.e. 10 samples per seconds. I have obtained the readings as shown in the image. As you can see i am getting spike on ...
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1answer
70 views

$n\textrm{ Hz}$ waveform sampled at $m\textrm{ Hz}$ per second

Here is an example of plotting a square wave given in SciPy Documentation A $5\textrm{ Hz}$ waveform sampled at $500\textrm{ Hz}$ for 1 second: ...
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0answers
62 views

need help about DFT? [closed]

I am trying to get the answer from some of my questions: ...
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1answer
592 views

How to Do Convolution a 2D Signal (Image) and Result of Convolution of Two 1D Filters?

Assume a 2-D signal (i.e., some image). Load image and assume it to be signal x. Next assume that instead of having a 2-D filter you have two one D filters $$f_1[n] =\begin{bmatrix}0.25 && 0....
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2answers
4k 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 ...
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1answer
62 views

What function to apply to a signal to expose its burstiness (i.e., make the burst part more evident than the non-bursty part)

I am working on some signals one of which I have attached below: What can I do (i.e. functions that I can apply to this signal) to get something like the signal below: Note how one can draw a line ...
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1answer
1k views

Determining if the given system is LTI

Problem Given the compound system below, with the input $x(t)=\operatorname{sinc(t)}$, the output of A is $y(t)=\operatorname{sinc(2t)}$ and the output of B is $z(t)=\operatorname{sinc(t)}$, ...
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1answer
55 views

Best averaging to convert 50Hz Chi data to one hour averages?

I have a $50\text{Hz}$ data set of temperature variance destruction or $\chi$ in the ocean for 365 days and hence is too bulky to handle. I want to convert it to hourly averages. Simple question: How ...
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1answer
49 views

How to differentiate the product signal $f(t)\theta(t)$, where $\theta(t)$ is Heaviside's unit step function?

What is the derivative (in the engineer's sense) of the causal function $f(t)\theta(t)$, where $\theta$ is the Heaviside unit step function? I've seen the formula $f'(t)\theta(t)+f(0)\delta(t)$, ...
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2answers
90 views

How will the signal $\sum_{n=-\infty}^\infty \Delta (t-n)u_{-1}(t-n)$ look like?

How will the signal $\sum_{n=-\infty}^\infty \Delta (t-n)u_{-1}(t-n)$ look like? I understand that $\sum_{n=-\infty}^\infty \Delta (t-n)$ is a periodic signal with period $1$, where the triangular ...
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1answer
3k views

conversion of 1d signal to 2d signal for CNN operation

I have a 1D signal data sampled at 25kHz and I want to modify in to 2D signal so as to modify it as the input to ConvolutionalNets as they work only on 2 dimensional data. What are possible ways to ...
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1answer
598 views

RMS of absolute-valued sinusoid

A signal $x(t)=|\sin(2π(1000)t)|$ ($|x|$ is the absolute value function) is fed to an ideal low-pass filter with cutoff frequency of 1500Hz to produce an output $y(t)$, what is the RMS voltage of $y(t)...
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3answers
762 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): $...
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1answer
831 views

Combining 2 sinusoids of equal amplitude with different frequencies into 1 new “wave”

This question is about combining 2 sinusoids with frequencies $\omega_1$ and $\omega_2$ into 1 "wave shape", where the frequency linearly changes from $\omega_1$ to $\omega_2$, and where the wave ...
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1answer
60 views

Confused about the period of a discretised time-series

I have managed to confuse myself about the periods of discretised time series. It is all rather embarrassing. This is one period extracted from my continuous signal (radians on y, time on x): To ...
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1answer
369 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 ...
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2answers
559 views

why human voice is band limited while it's time limited?

According to Wikipedia, time-limited signals can not be band-limited and vice versa. Also we know that human voice is band-limited and has frequencies from $50\textrm{ Hz}$ to $4\textrm{ kHz}$. So ...
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1answer
285 views

Combining Bandpass filters on 1D signal to obtain better SNR?

I have a signal which I'm trying to extract information from (specifically, features to recognize using DTW). Parts of it have very clear and unique features which are unfortunately only sometimes ...
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1answer
88 views

Find the center of positive plateaus of rectangular function

If I have a rectangular function with irregular positive parts, is there a clever way of finding the center of each positive "plateau"? The application is, that I threshold a continuous function and ...
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2answers
101 views

Signal and system convolution

In the convolution equation $y(n)=x(n)\circledast h(n)$ if two things are given like $y(n)$ and $x(n)$ then how can find the $h(n)$?
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3answers
4k views

Why DTFT coefficients are periodic and why continuous Fourier transform coefficients are not periodic?

As I understand, when the input signal is discrete in time and we want to find the coefficients of Fourier transform, DTFT is used and the coefficients in frequency domain are periodic, but I can't ...
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1answer
2k views

What is the Fourier transform of a multiplied cosine signal with rect?

I tried to find the Fourier transform for this signal, but I have some doubt about the result: $$g(t) = \cos\left(\pi\Delta{f}t\right) \text{rect}\left(\frac{t-\frac T2}{T}\right)$$ My calculation ...
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1answer
577 views

What is the total impulse response in a system with feedback interconnection?

Let's assume that we have a system with a typical feedback interconnection where the output is given by the following equation: $$y(t) = \left(x(t) - z(t)\right) \star h_{1}(t) \tag{1} $$ where: $$z(...