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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How can i read .edf.seizures format in MATLAB?

I need to read chb01_03.edf.seizures file from CHB MIT database in MATLAB for seizure detection
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transfer function of a sampler in the s domain

I would like to modelize my whole system into the S-domain. This is a mixed system, there a numerical part (corrector, ADC, DAC) and an analogic part (plant transfer function, sensors, etc...). I know ...
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Problems computing the DFT of finite length sequence

I am having trouble finding the same answer as the solution manual for this sequence. The problem asks to compute the DFT of $$ x[n] = \begin{cases} 1 & \text{for even } n \in \{0\...
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What is impulse response in simple AWGN channel?

Assume a sender and receiver communicate through an AWGN channel. Let $x(t)$ be a transmitted signal and $y(t)$ be a received signal and $z(t)$ be the Gaussian noise. It is known that $y(t) = kx(t-\...
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Convolution of two sets

In my systems and signals course I had been asked a question about finding the convolution of two sets. I was given: \begin{align} x[n] &= \{3,2,1\}\\ h[n] &= \{1,-2,3\}\\ \text{Find}\quad ...
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How to correctly use sinc interpolation in Matlab?

What is the right way to use sinc interpolation for a given discrete signal $x[n]$? Following is the sinc interpolation formula: $$x(t) = \sum_{n=-\infty}^\infty x[n] \mathrm{sinc}\left(\frac{t-nT}{T}\...
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81 views

Autocorrelation function of a triangular wave

I am interested to find the analytical expression for the autocorrelation function of a signal that comprises triangular pulses. I have followed the derivation in "Statistical Theory of ...
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How to handle cross products in feedback loop?

I'm trying to simplify the following block diagram from to the following block diagram However, h(t), H(s) in time domain, has a cross product in it (gyroscopic torque). How can I represent the ...
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An example of a signal that neither have a $z$-transform nor a DTFT? [closed]

What is an example of a signal that do not have a $z$-transform or a DTFT? With explanation.
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Check vanishing moment property of db4 wavelets

I am reading the book "a primer on wavelets and their scientific applications" by James S. Walker. In chapter 3, Property I on page 46 says that if a signal $f$ is linear, then the $k$-level ...
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The effect of time increment $\Delta t$, frequency resolution $\Delta f$ and Gibbs phenomenon on the amplitude of the signal in the frequency domain?

Experiment: Vibration analysis (i.e.: major concern is on transfer function or frequency response). The input is an impulse (imagine as a knocking effect or knocking force), defined as a half sine ...
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In the context of DFT, Where Does the Nyquist Frequency Sample Belong In a Double Sided Frequency Spectrum (Positive / Negative Side)?

If we have an even number of data points $N$, after DFT in MATLAB, the output has the order: $$(\text{DC}, f_1, f_2, \ldots, f_{N/2-1}, f_\text{Nyq}, -f_{N/2-1}, -f_{N/2-2}, \ldots, -f_1)$$ For real ...
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Is Kalman Filter for LTV systems applicable on Hybrid systems?

As all of us know Kalman Filter is designed for LTV (Linear Time Variant) systems. But nobody in the literature applies that on Hybrid systems. In my opinion Linear Hybrid systems are a subset of ...
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Variance of AWGN in BFSK system

I am trying to compute the variance of AWGN in the system for finding the BER with $Q$ function. The PSD of the AWGN is $N_0/2$, my answer was $N_0T$ but it was incorrect. This is my calculation (...
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Calculating the output of a pole eigen signal in a difference equation

Let an IAR system be defined by the following difference equation: $$y[n]-\frac{1}{4} y[n-2]=x[n]+3x[n-1]$$ and an input signal $x[n]=(-0.5)^n$. The transfer function is defined as $H^z(z)=\frac{1+3z^{...
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Super Resolution in Frequency Domain Using Compressed Sensing

To be noted that I'm very new to this topic, I would like to understand the fundamentals of how to get Super Resolution in Frequency Domain estimation using the Compressed Sensing Model. I am also ...
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Difference between $\tt fft$ and $\tt dftmtx$ in MATLAB

I have the following MATLAB code: ...
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voltage current analysis in time

I am looking at the transmembrane voltage of a neuron model and would like to investigate this in more detail. The applied current is divided into a deterministic and a noisy component - if I set the ...
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Discrete-time signals increase in frequency and period

I am studying Discrete-Time Signal Processing by Alan V. Oppenheim and Ronald W. Schafer. I am confused when it says periodic discrete signal oscillates more rapidly when its frequency is increased ...
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Circular Convolution as Cyclic Shift Operator

Given the following signal vectors: $$ γ=[ψ_0,0,ψ_1,0,ψ_2,0,…,ψ_{N-1},0]^T\in \mathbb{R}^{2N}, ϕ=[1,\frac{1}{2},0,…,0,\frac{1}{2}]^T \in \mathbb{R}^{2N}$$ I want to show that the convolution of $γ$ ...
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1answer
43 views

Is it possible to specify number of taps and cutoff frequency independently?

When specifying the properties of a moving average filter, is it possible to specify the number of taps and the cutoff frequency? My guess is no since taps (the number of samples in a moving average ...
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How to interpret frequency response of moving average system in discrete time signal processing?

Excerpt from Discrete Time Signal Processing by Alan Oppenheim: The text says this can be considered as an approximation of a Low Pass Filter. A low pass filter in continuous signal system is ...
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Aliasing below $f_s/2$

phi = exp(linspace(0, log(511), 1024)) - 1 x = cos(2 * pi * phi) Above will alias, despite peak instantaneous frequency evaluating to ...
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Detecting periodic components in discrete-time signals [closed]

I am looking for real data examples where it is of interest to detect the presence of a periodic component of some discrete-time signal when the period of the periodic component is not known. Suppose ...
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Evaluate expressions without computing DTFT

Let $X(\omega)$ be the DTFT of the sequence $x[n]$ given by: $$ x[n] = \{4, 2, -1, 5, -3, 1, -2, 4, 2\},\quad\text{for}\quad n \in [-6, 2] $$ I do want to compute $X(0)$ $X(\pi)$ $\displaystyle\int_{-...
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confusion related to finding inverse Z-Transform using Complex Integral Method

I am facing problems related to evaluation of inverse Z-Transform using Complex Integral Method; Consider $X(z)=\frac{z}{z-2} $ and $ROC: |z|>2$ then, $$x(n)= \frac{1}{2\pi j}\oint_c X(z) z^{n-1} \...
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Convert complex valued sinusoid to real valued sinusoid

This is the homework problem: convert $x[n]=je^{j\pi n/8}-je^{-j\pi n/8}$ to a real valued sinusoid. I understand that $\sin\theta=\dfrac{e^{j\theta}-e^{-j\theta}}{2j}$ In the solution, the answers ...
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1answer
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A basic question regarding frequency analysis of an EEG signal

Assume that an EEG signal is sampled at $f_s = 300$ Hz then a 10000-point segment of it is selected, called $x[n]$. The corresponding 10000-point DFT is then computed and called $X[k]$. Assume further ...
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DFT Signal DFT Length N , FFT

If We sample an Signal let say sine(2 * pi * f) with f=1Hz and a sampling Frequecy of Fs = 8Hz, is it right that the length of the data schoul be N = Fs/f or multiple of Fs/f like N= d*(Fs/f) with d=...
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53 views

Fourier coefficients of discrete difference of a square wave

I have a discrete square wave $f(t)$ where $t \in \mathbb{N}$, of amplitude $A$, period $T$ and duty cycle $1/T$ $$ f(t) = \left\{\begin{matrix} A, & \mathrm{if}\;t=Tn\\ 0, & \mathrm{if}\;t\...
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Converting Audacity Filter Curve EQ into transfer function and applying it to a signal via python

First of I am very new to Signal Processing and to python in general. I am trying to write a script where I would feed a voice recording into it, internally apply an eq and have the modified signal ...
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5answers
200 views

How is the DTFT of a periodic, sampled signal linked to the DFT?

I am trying to understand the connection between FT, DTFT and ultimately the DFT. But I am failing to link the DTFT to the DFT. This is how far I am getting: Say I have a function $f(t)$, and its ...
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2answers
82 views

Inaccurate phase returned by np.angle

I am generating 2 sine waves, first one has fundamental frequency = 50 Hz, amplitude=10, phase=0, the second one has fundamental frequency = 100 Hz, amplitude = 5 and phase = np.pi/6 (which is ...
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34 views

What is a “jump response” of a filter?

I know how to determine if a filter is FIR or IIR, but I don't understand the question. What is a "jump response"?
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Sampling interval $T$ as a multiplier in digital processing of a continuous-time signals

[from: Discrete-Time Signal Processing, Oppenheim and Schafer, p.224] Q: Why do we have $T$ as multiplier in $TY_a(j\Omega)$ in Eq.155?
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Why not use the same “standard” exponentials for both continuous and discrete time

In continuous time the standard exponential signal is usually defined as $$ e^{st}, \quad\text{with}\quad s = \sigma+j \omega $$ In discrete time the standard exponential signal is usually defined as ...
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In pulse code modulation what is pulse word represent?

we study lot of things in PCM we do sampling quantization encoding etc but we never come across pulse so what is pulse word represent in PCM
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Impulse response of forward difference cascaded with one sample delay

Below is the excerpt from Discrete Time Signal Processing by Alan Oppenheim. I don't get how $(\delta[n+1] - \delta[n]) * \delta[n-1])$ becomes $\delta[n] - \delta[n-1]$. The convolution sum operator ...
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1answer
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Discrete Fourier transform of a finite length signal which saturates at non-zero value

I am performing spectral analysis of a finite length signal that saturates to a non-zero value. The signal ($s(t)$) can, practically, be write as $s(t) = f(t) \big(1-H(t-t_0)\big) $, where $t_0$ is ...
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Is this piecewise-defined system time-invariant?

\begin{equation} G_c \qquad y[n] = \begin{cases} u[n] & \text{if} & n<0\\ 2u[n] & \text{if} & n\ge 0 \end{cases} \end{equation} I found this question in ...
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1answer
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Interpolated FIR filter (from Oppenheim and Schafer's Discrete-Time Signal Processing, 3rd ed)

[from Discrete-time Signal Processing by Oppenheim and Schafer, 3rd ed., p.196] Two questions: In this context, the filter with system function represented by Eq. (103) is called an interpolated FIR ...
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1answer
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Discrete-time Fourier transform of $a^{|n|} u[n]$

I have a problem calculating the DTFT of this pair: Could anyone tell me why the DTFT for $a^{|n|} u[n]$ is different from $a^{n} u[n]$'s?
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Prove that a specific auto-correlation function is even

Background (from digital signal processing): The $\delta$ function is defined as below: $$\delta[n]=\begin{cases} 1 \quad \mbox{if} \hspace{.4em} n=0\\ 0 \quad \mbox{o.w.} \end{cases}$$ In an LTI (...
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Transform lowpass filter to highpass filter, what happened to unit sample response and difference equation?

I know that multiple a lowpass filter signal by $(-1)^n$ can transform it to a highpass filter. $$ s_{hp}[n]=(-1)^n s_{lp}[n] $$ But exactly what happened to the unit sample response and difference ...
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If a time-series has odd number of samples does it have no energy at Nyquist frequency?

Suppose I have real time series A with n samples and time-spacing dt and I want to analyze ...
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Problem with applying elliptic filter to ecg signal

I'm currently working on an article for ECG classification which it says that it has used elliptic bandpass filter with 0.5Hz and 50Hz critical frequencies to eliminate base-line and interference etc. ...
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1answer
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How can you perform echo cancellation on features of audio signals?

I am working on a project that takes some features of audio signals and classify them with a neural network. However, the audio signals are added with their own echo with the environment. What would ...
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Why do we need DFT when we already have DTFT?

We already have DTFT so why do we need DFT? Please don't write DTFT is used for discrete, aperiodic signal which transfers in the frequency domain to periodic and continuous, but in DFT is discrete ...
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1answer
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The shift-invariance operator

I am reading the paper "Algebraic Signal Processing Theory: Foundation and 1-D Time". In page one, the first paragraph of second column, I did not get why shift invariance forces the ...
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Filtering Angular Measurements

I am trying to apply a filter to reduce noise in angular measurements. Since the data comes with noise, the filter needs to be able to handle measurements that are not smoothly progressing; for ...

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