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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73 views

Find another cosine y(t), whose frequency is as close as possible to that of x(t),

I am going to be straight forward and say this is one of the problem sheets and I am stuck on one of the questions. I already know the answer as I have been given them but I am trying to work ...
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1answer
282 views

Variance of the Discrete Gabor Transform for practical implementation

When we design a discrete Gabor filter for a 1D signal, how do we determine the variance of the filter, depending on the time step of the signal? Is there any empirical theorem/result that we should ...
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173 views

how to detect the center frequency of a QRS complex in an ECG signal?

i want to design a filter that can effectively detect the QRS complex in ECG signal(whose Fs=360Hz) and reduce high frequency noise components. i want to know as to how the center frequency is ...
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2k views

Is $\delta(n) = u(n) - u(n-1)$?

In my text book, Digital Signal Processing, Principles, Algorithms, and Applications by John Proakis, it asks the question to show how $\delta(n) = u(n) - u(n-1)$. I can understand how this is true ...
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0answers
299 views

Complex Demodulation (CDM) and Fixed Frequency Complex Demodulation (FFCDM)

I do not quite understand the difference between the CDM and FFCDM. How can I implement CDM in a program?
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1answer
686 views

Apply band pass filter (BPF) before calculating the power of a signal (PSD)?

From my understanding PSD tries to give a good estimation on the power each frequency attributes to the overall signal power. If I am only interested in a frequency range $(\omega_0 \leq \omega \leq ...
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1answer
695 views

Finding linear convolution of two time series

PROBLEM Two real, causal time series $$f_k = a^k \quad \text{and} \quad g_k = b^k$$ where $a \neq b$, $|a| < 1$, and $|b| < 1$, are given for $k = 0,1,2,...$ Find the linear convolution $h_n$...
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1answer
700 views

window for short time fourier transform

When we implement the 1D-short time fourier transform, the formula is as such: $$ Sf[m,l]=\sum_{n=0}^{N-1}f[n]g[n-m]\exp\left(\frac{-i2\pi l n}{N}\right). $$ the window $g$ used is normally ...
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2answers
7k views

Determine whether a signal is periodic or not and get fundamental period

Here is my signal Cos(n/2)*cos(pi*n/4) cos(n/2) has period 4pi and cos(pi*n/4) has period 8 Now, the question is will the signal be periodic for fundamental ...
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20 views

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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36 views

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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14 views

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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1answer
22 views

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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0answers
43 views

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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37 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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24 views

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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35 views

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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22 views

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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51 views

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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2answers
50 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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27 views

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
68 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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18 views

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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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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26 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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20 views

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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31 views

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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36 views

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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1answer
69 views

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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3answers
62 views

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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1answer
52 views

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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1answer
40 views

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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1answer
34 views

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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1answer
58 views

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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45 views

modified LMS algorithm

Suppose am given the modified LMS Algorithm below: $W\left(n+1\right)\:=\:\alpha W\left(n\right)+2\mu e\left(n\right)X\left(n\right)$ Where: $\mu$ is the step size $e$ is the error signal at the ...
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1answer
32 views

Formant analysis LPC (Matlab)

I wanted to do formant analysis using MATLAB and did everything according to the following tutorial: https://de.mathworks.com/help/signal/ug/formant-estimation-with-lpc-coefficients.html I have speech ...
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29 views

How to get coefficient of the discrete fourier Series from the fourier transform

Given $X(v)$ the Discrete Fourier transform of a discrete periodic signal $x(n)$, it's possible to arrive to the $c_k$ of the Fourier series $$x(n)=\sum_{k=0}^{n-1} c_k \exp(2\pi i k t) $$ directly?
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31 views

How to subtract echoed signal from mixture of voice and echo signal?

I am working on an echo removal project. So far, I have successfully identified the far-end signal of length 21 ms at a sampling rate of 48000Hz whose echo is present in my near-end signal of 21ms. I ...
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0answers
27 views

Finding arbitrary/random repetitive patterns in signals (both self and across two signals)

I am trying to figure out a direction for my research. I need to find random repetitive patterns between two signals and on each individual signal. I have read about FFT and time series-motif ...
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0answers
47 views

How to design filter for a stochastic process (signal)?

The given stochastic $y[n]$ is composed of two signals, $s[n]$ which is the desired signal, and $\epsilon[n]$ is the noise which is a zero-mean weak-sense stationary signal. The desired signal is a ...
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28 views

decomposition of a function to piecewise functions

Is the next answer correct: $$a\left(z\right)=\sum _{\left\{k\right\}U\left\{k'\right\}:f_k\le \:z,\:z\:\in R,\:f_{k'}\ge z\:;\:z\ge 0}1-\frac{f_k}{z},\:b\left(z\right)=\sum _{\left\{k\right\}:f_k>...
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1answer
47 views

How to find average and power of a signal

I need to find the average and the power of this signal: $$x(n)=\sum_{k=1}^{\infty}2^{-k}e^{j2{\pi}kn}$$ The problem is that the summation starts at 1 and not at 0, and a part of that how can I find ...
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41 views

N, N-Discrete fourier transform

What is $N$,N-point Discrete fourier transform? Is it different from 2D Fourier transform? and how to compute $N$, N-point Discrete Fourier Transform of a given laplacian filter kernel? say for a ...
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40 views

What types of distributions (except the Gaussian) that follow for random jitter in a correlated signal?

For the simple case, let's consider the correlated signal $s$ with jitter (without noise) as follows: \begin{align} s(t, \theta_i) = \cos(2\pi f (t + \epsilon_t) + \phi + \theta_i), ~~ i=0,1, ... \end{...
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0answers
14 views

How to make 2 finger rake receiver to counter intersymbol inferference?

I have to transmit Walsh sequence (spreading codes) modulated with 8 psk with a channel impaired by intersymbol interferences, fast fading . Suppose i have a stream of data for instance 1 0 1 1, 0 0 0 ...
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0answers
21 views

Identifying sounds patterns from wav file

I have an audio recording stored as a .wav file. My goal is to identify exact sounds patters from it using Python. The problem I'm facing is there's a clear "ting" sound in the audio file, ...
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1answer
36 views

Lower bound of weighted average of sequence

Can anyone prove that $$\mathrm{avg}\left(\frac {a_i}{\left(1+a_i\right)^2}\right) \ge \frac{\mathrm {avg}({a_i})}{\left(1+\mathrm{avg}{(a_i)}\right)^2}$$ for a sequence of positive valued elements $...
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49 views

DWT and FFT on a very low frequency signals

I am trying to extract features from a very low frequency signal of $0.1$ HZ and less than $100$ samples. Is it advisable to use FFT and DWT on this signal?
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1answer
26 views

Impulse invariance vs. DT representation of a CT system: Where is the inconsistency?

Suppose you have a continuous-time (CT) system $h_c(t)$, bandlimited to $B$. Your goal is to represent the system as a discrete-time (DT) system $h[n]$, sampled at $f_s \leq 2 B$. Clearly $h[n]$ won't ...
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37 views

MAP Estimation Problem for Frequency Band Occupancy Calculation

Consider designing a wireless communication system. Your communication link is not iso- lated in the environment, there are other similar devices trying to communicate in the same general frequency ...

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