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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Sampling Theorem: How to know the value between two samples of a Signal

According to Sampling theorem, in order to reconstruct a signal we need to sample it at the rate => twice the highest frequency component of that signal. (provided signal is band limited). Let's say, ...
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0answers
20 views

How to calculate the step response and transfer function

The output system is: $x(t)$ -->(S)--> $y(t) = \int_{-\infty}^{t}x(\tau) d\tau$ I am still not sure whether my work is correct, please some one advise me. I know that a step response is the ...
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1answer
23 views

Memorylessness of simple delay system

As usual, $y(t)$ is the output signal of a system, and $x(t)$ is the input signal. I'm wondering whether or not a certain system has memory. It's easy for me to see that the system $y(t) = ...
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1answer
26 views

Proof of a CTFT property

How do I prove that the absolute value of CTFT of a positive continuous time signal is less than or equal to its value at central frequency(0)?
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3answers
36 views

Does the hold part in sample and hold turns the signal from discrete to continuous?

I am trying to link sample and hold to discrete and continuous time domain. Could someone please confirm: When sampling but not holding for "an extended" period of time, you have discrete samples. ...
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2answers
52 views

Complex signal transform

I must strengthen my knowledge in the mathematical properties of signals, and would like to know the following thing: if I have a complex signal, written in magnitude and phase, it's like if I have ...
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0answers
49 views

Output of an LTI System With Given Frequency Response?

I will have my final exam this week. While I was studing for it I coudn't solve this problem. I think that I should work more about Fourier Transforms. I m thinking that the solution can be obtain by ...
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2answers
78 views

how to generate a smooth sine wave with time varying frequency in matlab

I'm currently designing a knock sensor for my FSAE team's car and I'd like to be able to test various software strategies with a fairly realistic signal (at least more realistic than a couple sine ...
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1answer
53 views

How can I approximate a signal

I have a signal as the below figure. I am looking for some schemes to approximate the signal. I have found some ways for that task: Using basis function (polynomial) to approximate the signal ...
3
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2answers
60 views

Is the book wrong? — How to sketch frequency response obtained from H(z)?

This question is directly related to digital signal processing, so I am asking here. How to sketch frequency response obtained from $H(z)$? I'm adding an example and its solution below. I did not ...
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1answer
42 views

Advantages of Splines in Compressed sensing

I am working in compressed sensing, basically in ECG reconstruction Normally we were using biorthogonal wavelets for reconstruction. Someone advised me to use exponential spline basis instead of ...
2
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1answer
51 views

reducing MIPS in detecting tones

Currently our software is detecting tones using FFT and checking if there is only a single peak in frequency spectrum. Our software needs to know what kind of input it is before taking action. So we ...
5
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4answers
369 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 thepicture below. But, in terms of signal processing, (a ...
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0answers
8 views

extended unwrap(), locating sawtooth peaks (weight of pass-through silo vs time)

Given is a recorded saw-tooth-like signal. (It's a weight of a bulk solid silo, continuosly and slowly emptied almost all the time, and quickly filled from time to time - without interrupting ...
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1answer
24 views

What is concurrent Signal?

I have come across with the term 'concurrent signal'. What does this type of signal means? What are it's importance?
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0answers
16 views

Obtaining SNR from SINR - 802.15.4

In the 802.15.4 standard, the following equation is used to calculate the BER: $$BER = 0.5 e^{-SINR/2} $$ I would however for my simulations like to avoid using SINR but rather SNR. I would like to ...
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0answers
31 views

Remove microphone rustle / clothing rustle from raw audio data

Thank in advance for the help. I have several GB's of raw audio data that I have collected as part of a research study. This audio is divided up into individual samples approximately 30 seconds in ...
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1answer
23 views

How do I use MATLAB to obtain a continuous state equation from a transfer function and ode45 to solve it?

I have the following transfer function that I am trying to model in MATLAB with some additional unity white noise: $$G(s)=\frac{1}{s^3 + \beta s^2}$$ I used the following to obtain the ...
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1answer
25 views

Power of periodic signal

Given a signal $s(t) = e^{j(t+\pi)}$, I conclude that the signal is periodic with period $T=2\pi$, so its power should be $$P = \frac{1}{T}\int_{-T/2}^{T/2}|s(t)|^2dt= ...
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0answers
37 views

converting higher order transfer function in s-domanin to the cascaded biquad transfer functions, also in s-domain

I'm trying to convert a transfer function (tf) in s-domain (num: b17*s**18 + b16*s**17 + ... + b0, den= s**20 + a18*s**19 + ... a0) to cascade of the biquad ...
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1answer
16 views

Why ignores constant when applying integral into differential-equation.?

I studied how to draw 'Direct-form I' and 'Direct-form II' from differential equation. The book taught me like this: $$\mbox{Give equation: }{a_0}{y(t)}+{a_1}{y'(t)}+{a_2}{y''(t)} = ...
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2answers
91 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 Alan Oppenheim. "The ...
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1answer
100 views

properties of System

I am studying Signals and Systems. Anyone, please help me to answer the problems. $y(t)=dx(t)/dt$ is time invariant: True or False ? $h(t)$ is the impulse response of an LTI system. If $h(t)$ is ...
2
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1answer
58 views

Using superposition and time invariance to find RL circuit response

I am confusing reading book by Chaparro (Signal System with Matlab) in example 2.7. He give a question, a RL circuit with unit-step source $ v(t) = u(t) $ will result response, $$ i(t) = (1- e^{-t}) ...
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1answer
41 views

Making sense of the delay formula between two sensors in an antenna array?

In the image above, there is a formula for the delay of a signal at a given sensor 'i' in an antenna array. I don't understand how they arrived at that formula. Each antenna array element is ...
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1answer
79 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: ...
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0answers
81 views

Proof of Properties of Fourier series in CT

I feel problem in understanding the proof of Fourier series properties Time scaling $$b_k = \frac{1}{T}\int_{T}x(t)e^{jk\omega_0t}dt$$ $a$ - scaling factor $$ = ...
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3answers
72 views

magnitude and phase Fourier coefficients

While solving Fourier series coefficients in example, i found couple of things which confuse me. How the minus sign changes to plus sign $a_1= 1-\frac{1}{2j} = 1+\frac{1}{2}j$? After plotting the ...
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1answer
90 views

Mathematical model of a signal in Compressive Sampling

Currently I am reading a paper on Compressive Sampling, and trying to understand each and every parts of it. When I came across the mathematical model of the signal in paper, I got confused. I have ...
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1answer
81 views

Proof for determining Fourier coefficients

While determining Fourier coefficients we have this equation $$\int^{T}_{0} x(t) e^{-jn\omega_0t} dt = \sum^{+\infty}_{k\ =\ -\infty} a_k [\int^{T}_{0} e^{j(k-n)\omega_0t}dt]$$ I want to ask that how ...
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1answer
36 views

Value of $A_k$ in Fourier series

Fourier series in continuous time domain while representing $a_k$ in rectangular form $$ a_k = B_k + jC_k$$ But when using the value of $a_k$ in the main equation: $$ x(t) = a_0 + ...
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1answer
31 views

Fourier Series Proof

I want to ask Question about the Fourier series in continuous time domain while reading a book signals and systems Alan Oppenheim. I have confusion in understanding the statement on page 189 of its ...
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1answer
39 views

Fourier series in continous time domain

I want to ask Question about the Fourier series in continuous time domain. I am following signal and systems 2nd Edition by Alan Oppenheim. I have confusion in understanding the statement that ...
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1answer
99 views

Question on sketching the amplitude spectrum of signals

I can't seem to understand the sketches of the amplitude spectrums provided in my tutorial solutions. For this part , I understand that X(f) is basically sampling (T/Tp)sinc(Tf). But from what I ...
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1answer
34 views

Working out integration of basic signal functions

As the title suggests , I'm having problems working out the integration of some basic signal functions. Shown below are the questions and my workings. For some reason I'm just unable to get the ...
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1answer
53 views

How to seperate 3 sinusoidal signal of same frequency and phase but different amplitude? [closed]

The wireless encrypted communication works as sending the message signal (sinosoidal) along with 2 dummy signals(sinosoidal) of same frequencies same phase but different amplitudes(assume no ...
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2answers
77 views

Algorithm for testing input sound for multiple expected notes?

** originally I asked this question on stack exchange and was pointed to dsp.stackexchange ** I need to determine when the correct musical notes (from a piano) such as in a chord are being played. ...
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1answer
54 views

Denoising / thresholding via wavelets

When I apply differerent thresholding, wavelet denosing functions to non stationary time series which has been detrended via Loess regression and demean it. I expect that when this processed series ...
0
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1answer
49 views

Can you explain about the following formulas? in Signals and System

In my textbook, any signals could be expressed like the following formula. $x(t)=\displaystyle\frac{a_0}{2}+\displaystyle\sum_{n=1}^{\infty}[a_n\cos(2{\pi}nft)+b_n\sin(2{\pi}nft)]$ I understand that ...
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0answers
28 views

Time and phase estimation in OQPSK using ML criterion

Let me first make an introduction to the problem by stating some intermediate results: An OQPSK signal has the general form: $$\\\tilde{s}(t)=\sum\limits_{i}\tilde{a}_i ...
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1answer
20 views

Transform a continuous time differential equation of a Low Pass Filter to discrete time

Assuming I have a linear differential equation of first order low pass filter: $$RC*y(t)'+y(t) = x(t) $$ And Assuming i know now that the input x(t) is being sampled at a rate of $T_s$ how can now ...
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0answers
92 views

Signal reconstruction in FMCW radar

I am doing fmcw radar simulation. I have an output of mixer and from that I want to reconstruct the amplitude and phase of the signal. Therefore, I am taking hilbert transform and by the ...
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3answers
108 views

How do u prove that a cosine signal with irrational period and another cosine signal with a rational period are orthogonal?

For example, $\cos(4t)$ and $\cos(4\pi t)$ sum is aperiodic. Hence it is said that these two signals are orthogonal over infinite limits? But how to prove this? Normal integration of product of the ...
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2answers
74 views

Properties of a custom wavelet family for continuous wavelet transform

First of, I'm new to signal processing. I have a signal which is a linear composition of several basis signals, whereas the same basis signal can occur several times, that is translated, but not ...
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2answers
61 views

How can one put information within a signal waveform and make it to traverse through different kind of medium? [closed]

This is a soft question. There are different types of signals like analog ,discrete or digital one. But my question is how can one put information within a signal waveform and make it to traverse ...
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0answers
6 views

Discrete dataset into to continous dataset?

I am trying to perform system identification on a system.The input i am going to provide is sinewaves with different frequencies. I sampled a sine wave with 100 Hz which is used a input for the ...
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0answers
51 views

Closed-form responses for 2nd-order all-pass filter

Here is a Laplace transform for a 2nd-order all-pass filter: $$ f(s) = \frac{s^2 - \frac{\omega_0}{Q}s + \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2} $$ The equation and a nice visualization ...
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1answer
121 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 ...
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1answer
53 views

Properties of Stochastic Processes [closed]

I have a basic question about stochastic processes: When some informations such as wss, uncorraleted sampled, white about random signal (say x[n]) are given, what do we exactly have? For example ...
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2answers
63 views

why fourier series gives lower amplitude for max value of signal

I want to approximate below signal using fourier series on Matlab. My code is below ...