Questions tagged [discrete-signals]

A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.

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Oppenheim and Willsky Signals and Systems Solutions

Hi All: This list has been great for me as a beginner but I decided to work my way through Oppenheim and Willsky and Mahab "Signals and Systems" book since I still get sometimes confused by ...
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Adaptive Delta Modulation: Logic for step size control at receiver

I read that in adaptive delta modulation, we have a block for step size control (diagram below) which takes into account the one bit quantizer output in a feedback loop and modulates it, the intent ...
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K-Path sampling overall transfer function

I'm trying to derive the overall Z-transform for the K-path sampling system shown below. I numbered some of the equations that I'll reference. I don't think I understand going from equation 3 to ...
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Where did we get the DC term of the Accumulator from DTFT?

Define $y[n]:=\displaystyle\sum_{m=-\infty}^{n}x[m]$. The DTFT is found as follows: \begin{align*} y[n]&=\sum_{m=-\infty}^{n}x[m]\\ \\ &=\sum_{m=-\infty}^{n-1}x[m]+x[n]\\ \\ &=y[n-1]+x[n]\\...
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Eliminating drift generated from double integration of acceleration signal using Envelope Method

I'm trying to remove the drift generated upon the double integration of a noisy acceleration signal. But this question discusses only removing the drift upon single integration to generate velocity ...
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Waveform pattern detection in time series

I have some IMU data which I am using to detect activity patterns - walking, running etc. In order to differentiate one activity from another I need to do pattern matching in time series. Different ...
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40 views

how to find the frequency of the downsampled signal?

So, I am trying to solve this question. Consider the signal $x=cos((2π/3)n)$. The signal is downsampled by a factor of two. Indicate the frequency of the resulting output, normalized by $2\pi.$ (E.g., ...
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This is how my professor is finding the frequency response of an LTI system when given the impulse response. Is this wrong?

My DSP professor uses the freqz() function to find and plot the frequency response and I think it's wrong but I want to make sure before I point it out. Take this ...
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Calculate ACF in C++?

I would like to manually reproduce the method that authors of an article used in their research (DOI: 10.1038/s41598-017-02750-9 (Page 8. top)). It is mentioned as "ACF", so I wrote ...
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How do I implement a footstep recognition algorithm? One that recognizes the start and end points of each footstep?

I have some time series data captured from a person's footsteps/strides (specifically, a person on rollerblades). It came from an IMU sensor placed on a person's boot. Each data point captures ...
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Shift operators in graph signal processing (GSP)

A key element of Graph Signal Processing (GSP) is the shift operator, that describes how a signal changes when shifted on the graph. There exists many different proposals of shift operators. Several ...
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What is the advantage of using a Stepped Frequency waveform over FMCW?

What is the advantage of using a Stepped Frequency Waveform instead of a traditional linear FMCW ?
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Why is the range of frequency for discrete time Fourier transform $-\pi<\omega<\pi$? [duplicate]

In my class we are taught that the range for the frequency is $-\pi<\omega<\pi$ for discrete time Fourier transform, however for continuous time the limit is $-\infty<\omega<\infty$ why is ...
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question with chirped signal

I have some difficulty understanding the following question. I have written a code to plot continuous and discrete version of the chirped signal. ...
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Hypothesis testing with binary pattern

Let's say you have a sequence $\{x_i\}_{i = 1}^N$ of ones and zeros. You know that $P(x_i = 1) = \frac{1}{3}$. You want to test two hypotheses $H_0$: The sequence is $iid$ with $P(x_i = 1) \ \forall \ ...
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Different values when calculating signal's energy by hand vs MATLAB

Given the following signal: $$ x(n) = \left\{ \begin{array}{ll} u(0.01n-0.025)2.3704e^{(-0.287682n)}, & n\ge 0 \\ u(-(0.01n+0.025))2.3704e^{(0.287682n)}, & n< 0 \\ \end{array}...
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How to determine the number of multipath?

In a multipath propagation environment if we take the time index of reach channel tap by the integer multiples of sampling periods, assume the RMS delay spread $ \sigma_{tau} $ and maximum excess ...
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Unit impulse response of a cascade interconnection of three discrete-time systems

I am nearly at the end of finishing a problem in my textbook but I couldn't understand something in the answer; I did everything to the point I found the overall response of the system in terms of $...
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32 views

Calculate impulse response when output contributes in input

I have an exercise in which I need to find the impulse response for this given system: $$y(n)=\frac{1}{2}y(n−1)+x(n−1)+x(n)$$ As per my knowledge, I need to find the homogenous solution. My homogenous ...
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How to simulate a continuous signal passing through a capacitor (simple coupling capacitor)

the differential equation for the current flowing through a serial capacitor (see for example https://www.allaboutcircuits.com/textbook/direct-current/chpt-13/capacitors-and-calculus/) indicates that ...
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Computing Discrete Convolution in terms of unit step function

Consider : $$ x[n]:=\begin{cases} 1&\text{if $3\leq n\leq 8$}\\ 0&\text{if otherwise} \end{cases} \quad\text{and}\quad h[n]:=\begin{cases} 1&\text{if $4\leq n \leq 15$}\\ 0&\text{if ...
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Confused about shifting convolutions

We know that for two signals $x[n]$ and $h[n]$ such that : $$ y_{1}[n]=(x*h)[n]=\sum_{k=-\infty}^{\infty}x[k]h[n-k]=\sum_{k=-\infty}^{\infty}h[k]x[n-k] $$ We can deduce that :$$y_{2}[n]=x[n+2]*h[n]=y_{...
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Calculate the power of a discrete-time signal

We got this question in our test :- $$S(t) = 5\cos(10πt - π/2) + 6\sin(15πt)\cos(15πt)$$ My Solution :- $$S(t) = 5\cos(10πt - π/2) + 3\sin(30πt)\qquad \textrm{[Using $\sin(2A) = 2\sin(A)\cos(A)$]}$$...
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36 views

Unit impulse response $h[n]$ of a discrete time system with multiple characteristic roots 0

I am trying to obtain the unit impulse response of a system in the form: $$y[n+N]+...+a_{N-1}y[n+1]+a_{N}y[n]=b_0x[n+N]+...+b_{N-1}x[n+1]+b_{N}x[n]$$ $$Q[E]y[n]=P[E]x[n]$$ (where E is the unit advance ...
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There appears to be a contradiction with the recurrence solutiom

Consider the equation : $$ y[n]-\frac{1}{2}y[n-1]=x[n] $$ where $x[n]:=\left(\frac{1}{3}\right)^{n}u[n]$. First, I founded the homogenous solution $y_{h}:=A\frac{1}{2^{n}}$ $$ y_{h}[n]=\frac{1}{2^{n}}...
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Is the expansion of this expression correct?

\begin{align*} &(\delta[n]+\delta[n-1])*(\delta[n]+\delta[n-1])\\ \\ =\;&\delta[n]*\delta[n]+2(\delta[n]*\delta[n-1])+\delta[n-1]*\delta[n-1]\\ \\ =\;&(\delta[n]+2(\delta[n]*\delta[n-1])+\...
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33 views

Where is the mistake in the convolution?

Let : $$ x[n]=\begin{cases} 1&\text{if $0\leq n\leq 4$}\\ \\ 0&\text{if otherwise} \end{cases} \qquad \text{and} \qquad h[n]=\begin{cases} \alpha^{n}&\text{if $0\leq n\leq 6$}\\ \\ 0&\...
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Discrete Convolution of two piecewise sequences having this specific form

Assume I have the following two sequences : $$ x[n]=\begin{cases} \alpha&\text{if $a\leq n\leq b$}\\ \\ \tag{1} 0&\text{if otherwise} \end{cases} \qquad \text{and} \qquad h[n]=\begin{cases} \...
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ADC sampling rate and signal bandwidth for FHSS

If i am correct; for a radio receiver the ADC sample rate will have to be higher than at least twice the BW of the data (disregarding sparse sampling techniques). So for frequency hopping spread ...
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understanding the result of the simulation of In-phase and quadrature part BPSK signal

I am a student and working on a hardware implementation of a transceiver and going to check an algorithm of time recovery that includes symbol synchronization and sampling clock synchronization. The ...
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53 views

Impulse Response of real coefficient, LTI System

I'm trying to obtain the impulse response $h[n]$ of a system whose frequency response is $H(e^{j\omega})=R(\omega)e^{-25j\omega}$. I believed that $h[n]=h[n-25]$, would be the correct answer, however ...
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45 views

Circular wrapping of an asymmetric function (in DFT calculations)

Convoluting a signal (using discrete FT) for a given interval [a, b] with a Gaussian can be done by circular wrapping as shown in Numerical Recipes. I found a shortcut for circular wrapping so that ...
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36 views

Convolution of discrete signals using convolution sum

I want to perform the convolution of the following discrete signals: $$h[n]=u[n-2] $$ and $$x[n] = (0.5)^nu[n+2]$$. That's what I've done so far: $$\sum_{k=-\infty}^{\infty} (0.5)^ku[k+2]*u[n-2-k]$$ ...
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How to create/find a dereverberation filter?

I want to find the coefficients of dereverberation filter in MATLAB. How to do that? I have found the coefficients of reverberation filter: ...
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26 views

understanding echo cancellation model

so, here is a very simple model. The CCDE is given, but I was trying to derive it on my own and now I am stuck. first of all, the reverse y[n] when goes through the delayed system, it turns to y[n-M]....
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77 views

How to handle a logarithmic term in Kalman filter?

I am trying to implement a Kalman filter for an echo pulse detection application as similar to this paper. (an open source version is here (pg 16)) The measurement variable is $h(x,t)=A_0 (\dfrac{t-\...
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29 views

Variance Due to white noise input

I have the problem below. It sounds simple but for some reason I have been stuck on it for a long time and don't know what am doing wrong. Am trying to solve this using correlations. So we all know ...
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3answers
39 views

Summation limits in DFT

Assume a discrete time signal $(x_n)$ is given. Some texts define the DFT as $$ X[k] = \sum_{n=-N}^N x_n\exp\left(\frac{-2\pi j k n}{N}\right) $$ while others define it as $$X[k] = \sum_{n=0}^{N-1} ...
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SPL dB to voltage conversion misunderstanding

base on these links: https://electronics.stackexchange.com/questions/96205/how-to-convert-volts-to-db-spl https://electronics.stackexchange.com/questions/302833/convert-digital-and-analog-values-to-...
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49 views

how to find frequency response of microphone

hello I want to find the frequency response of a microphone. I give the input signal to my speaker and it produces a specific SPL with specific frequency. on the other side, I read the microphone ...
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simulink discrete integrator block problem

I am testing the Simulink discrete integrator block as shown in the picture below. The simulation is fixed step with $T_s = 1e-5$ and the cosine wave block setting and the scope display is also shown ...
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Help with filter stability, ROC and output of a system

I am trying to solve these two questions, but I am stuck with the filter stability and ROC. Hope somebody could help me with it. According to what I understand, the third option is correct. Fourth ...
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67 views

Kalman filter with multiple sensors

I have been reading more about EKF and I am a bit confused on how you handle predictions with multiple sensors. Ex, I have IMU, GPS, Odom and Stereo Camera. Each can be used to predict location, how ...
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What are some practical examples of complex signals? [duplicate]

I am aware that complex discrete-time signals are of the form: $$ x(n) = a(n) \cdot e^{j\omega n T} $$ However, I have not yet worked with complex signals, only real ones. What are some practical ...
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DTFT Pairs confusion

When I am in the DT Fourier Domain, and I want to come back to the time domain, which pair do I use? Asking because both pairs have the exact same "form" in the Fourier domain, and that is ...
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How to calculate the magnitude of frequency response from Pole zero plot

I have checked the theory to calculate the magnitude of frequency response from the pole-zero plot from the previous posts. As far as I understand(and I hope I am correct), the magnitude can be ...
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34 views

How do I find the Energy Density Function of $g(t)$ if i am not given an input or impulse response?

$$g(t)=\frac{12a}{t^2+a^2}$$ I need to find the Energy Density Function of the signal, but everywhere I look has an input and an impulse response. Does anyone know how to solve this. Would I just take ...
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43 views

Frequency modulation: which algorithm for discrete signals (Java, Swift, etc.)

I'm writing an audio app in Swift - and one task consists in frequency modulation of a given signal (microphone input or sound file) - thus I'm iterating through all frames of a buffer like ...
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What is the physical significance of statistical quantities like mean, variance, skewness and kurtosis of a digital signal?

I understood the mathematical meanings of the mean, variance, skewness and kurtosis. But when we calculate these quantities for a signal (say a digital audio signal), what physical meaning do they ...
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205 views

Difficulty with a Fourier Transform

What would be the best way to take the Fourier transform of $$ f(t)\cdot \cos\big(\pi(t-1)\big) $$ I'm aware that when you take the Fourier Transform of $\cos(kt)$ you get two impulse at the location ...

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