# 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 ...
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(...