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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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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29 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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27 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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28 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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23 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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53 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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Finding similarity between two audio signal spoken by two different person

I have one master.wav file of 14 seconds and another child.wav file of 221 seconds divided into total 207 chunks each of 14 seconds. Now i want to compare each child chunks with master file and want ...
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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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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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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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59 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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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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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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203 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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Finding natural frequency from vibration analyzer data

I was asked to find the natural frequency from a waveshape obtained from vibration analyzer, and I performed an FFT and told that the peak represents the natural frequency. Now I am called as an ...
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3answers
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how to compute the signal passing from the low pass filter?

I am currently trying to solve this question. Let $x[n]=\cos(\frac{\pi}{2}n)$ and $h[n]=\frac{1}{5}\text{sinc}(\frac{n}{5})$. Compute the convolution $y[n]=x[n]∗h[n],$ and write the value of $y[5].$ ...
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Is there a way to describe the pattern of a signal as a numeric value?

I've been digging a little into signal processing and I just started a networks and telecommunications class at college. We saw there are different encode techniques Amplitude, Frequency and Phase ...
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How could I approach determining if this 2D system represented as a 2D summation formula is linear?

I have a given 2D system: $$y(m,n) = \sum_{k_1=-\infty}^{m} \sum_{k_2=-\infty}^{n} x(k_1,k_2)$$ My usual approach to determining if a system is linear is to test if it is homogeneous and additive. ...
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Finding the discrete time Fourier series for signal

I think I did everything correctly here, but I must be missing something still. We have the following signal: My approach: We are told that the signal has period $N = 4$ We know $$Y[k] = \frac{1}{N}\...
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Why do we use compression for discrete siganls?

Time compression/expansion (also called dilation) maps the input discrete signal $x$ to the output discrete signal $y$ as given by : $$ y[n]=x[\alpha n] $$ When $\alpha>1$, the signal experiences ...
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What is “filter periodization”?

A library defines periodize_filter_fourier, which is an equi-spaced averaging formulated by $$ v_f[k] = \sum_{i=0}^{\text{n_periods}-1} h_f[i\cdot N + k], $$ where $v_f$ is periodization of $h_f$, $N=\...
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How do you reduce $H\left(e^{j\frac{\pi}{2}}\right)$ further according to a textbook solution

I want to know how I could get from the first line to the second. I've been trying to figure it out for a while with no luck. Thank you in advance! \begin{align} H\left(e^{j0.5\pi}\right) &= \frac{...
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Matlab group delay not corresponding to reality

I studying effects of digital filters group delay (IIR). In Matlab there is a function grpdelay which allows for particular frequency get a value of delay in samples But after filter applying and ...
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52 views

Continuous vs. Discrete Fourier Transform for representing a physical phenomenon

This question is related to the differences between discrete and continuous Fourier Transform equations. Although I've found some good explanations about the difference in this forum, I cannot see how ...
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1answer
39 views

Finding the discrete time fourier coefficients to this problem

I'm trying to find the fourier series to this discrete time signal. $$x_1[n] =\begin{cases} +\frac72&\text{if }0\le n \le 4\\ -\frac72&\text{if }5\le n \le 9 \end{cases}$$ My approach: We see ...
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41 views

Convergence of a finite series on MATLAB

If I have output values of a signal $y$ (or series) stored in a $1\times N$ matrix, where $N$ is finite. Is there any MATLAB code or function I can use to determine if the signal converges or diverges?...
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29 views

Represent DFT coefficients with respect to Continuous time-Fourier series coefficients

Does anyone know how to represent the Discrete Fourier transform (DFT) coefficient, $X[k]$, with respect to the Continuous time-Fourier series (CT-FT) coefficient, $X_k$? I come to the conclusion as $...
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Phase shift of discrete cosine transform (DCT)

The most common type of discrete cosine transform (DCT-II) is defined as \begin{align} X_k&=\sum_{n=0}^{N-1}x_n\cdot \cos\left(\frac{\pi}{N}\left(n+\frac{1}{2}\right)\cdot k\right)&\text{where ...
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Why is FFT-based convolution efficient only for signals of large size?

According to the documentation of scipy.signal.fftconvolve This is generally much faster than convolve for large arrays (n > ~500), but can be slower when only ...
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3answers
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gaussian window for designing filters in DSP

I understand that we do not use rectangular window as a window in filter design because of the ringing/gibbs artifacts due to the sidelobes of the resulting sinc function in the time domain. ...
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The difference between tensorflow stft and scipy stft

I'm trying to wrap my head around stft, and checking the docs, tf.signal.stft and ...
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1answer
49 views

Is it possible to add some kind of noise to a non stationary (having unit root) signals to make them stationary?

I am working on time-series signals for which I need to fit a model (like MVAR) that could describe the process satisfactorily. However, my signal has a unit root and is highly non-stationary because ...
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34 views

Relation between continuous time transfer function and sampled approximation

Suppose I have some continuous time system and associated transfer function: $$ y(n)=x(n)+x(n-1)$$ $$ H(j \omega) = 1+e^{j \omega (-T_s)} $$ Now suppose I create a discrete-time approximation of this ...
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Approximate using DFT phase shifting property

I have a discrete signal $x(n)$ having $N$ samples with DFT $X(n)$. Here $N$ is large say $N=600$. Let the samples of $x(n)$ be, $x(n) = \big[x(0), x(1), x(2), ..., x(N-1)\big]$. But if suppose ...
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64 views

Particular Solution to Difference Equation

I have a system given by $$y[n] - \frac{1}{4} y[n-1] - \frac{1}{8} y[n-2] =3x[n] $$ I want to solve for $y[n]$ for $x[n]=(\frac{1}{2})^nu[n]$. The complementary solution evaluates to $[k_1(\frac{1}{2})...
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25 views

Impulse Response for an Anti Causal Linear Shift Invariant System

I have a system given by $$y[n] - \frac{1}{4} y[n-1] - \frac{1}{8} y[n-2] =3x[n] $$ I'm asked to determine the impulse response of both an anti-causal and a causal Linear Shift Invariant System ...
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Is it important to learn to find de period of the sum fo two DT signals?

The fundamental period (N) of the sum of two DT signals could be the LCM of the fundamental periods. However, this is not always the case. I would like to know wether, during engineering design or ...
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1answer
59 views

Finding SNR for a portion complex signal

I'm a software engineer that has been given the task of calculating the SNR of a communications signal that is represented by an array of complex numbers. I'm not quite sure how to proceed. Here's ...
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34 views

What is the difference between Goertzel algorithm and cross correlation in time

Im reading https://en.wikipedia.org/wiki/Goertzel_algorithm, when we want to discover the amplitude of a some frequency in a given signal what is the difference between applying Goertzel algorithm and ...
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58 views

The optimal estimator using FIR Wiener filter

The received signal $y(n)$ is defined as $$y(n) = h(n)*x(n) +v(n)$$ where $h(n)$ is unknown impulse response and $v(n)$ is a white Gaussian noise. The value of $x(n)$ for $n=1, ..., 32$ are given. The ...
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105 views

What is the purpose of wrapping the negative times of a response function in discrete convolution?

I am trying to rationalize a figure given in the Numerical Recipes in C in the section of Fourier based convolution and deconvolution. The authors show the example of a continuous convolution with a ...
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25 views

Generating data with given Auto and Cross Correlations

I have two discrete vectors $\mathbf{x}_1$ and $\mathbf{x}_2$, and I'm trying to generate more data $\mathbf{f}_1$ and $\mathbf{f}_2$ that has some basics properties of $\mathbf{x}_1$ and $\mathbf{x}...

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