Questions tagged [discrete-signals]

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

260 questions with no upvoted or accepted answers
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7
votes
3answers
8k views

First order low pass filter

I am trying to better understand the first-order low pass filter: Summary: Per wikipedia, a first order low pass filter yields the following in discrete time: $$ \frac{Y(s)}{U(s)}= \frac{\omega_{c}}...
6
votes
0answers
170 views

EWMA based differential that is strictly positive on strictly increasing irregular time series?

Let's say I have a time series $ \{t_i, x_i\} $ where the $x_i$ are strictly increasing and the $t_i$ are not regularly spaced. I can define a differential operator as $$ \Delta_i = \frac{x_i-x_{i-1}...
5
votes
0answers
162 views

Distribution of the output of AWGN channel

$$\mathbf{Y}=\mathbf{X}+\mathbf{W}$$ $\mathbf{X}$ is input, an $n$-dimension equiprobable vector in a finite subset of complex space $\mathcal{A}^n \subset \mathbb{C}^n$ with norm $\sqrt{\rho n}$ (...
5
votes
2answers
184 views

Regression vector size for prediction, reconstruction and filtration with adaptive filters

I am working with adaptive filters and similar adaptive models (mainly with gradient adaptation) for a few years. I and my colleagues always struggle to find out the correct size of regression vector. ...
5
votes
1answer
227 views

Is there a strategy for discrete control of a system with dynamics near sample rate?

I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to ...
4
votes
0answers
3k views

Verifying MFCC Final Result

I have created a Octave code for MFCC calculation for speech recognition, which takes a wav file as input and then gives the MFCC as the output. But the final results are a bit confusing, so I am ...
4
votes
0answers
107 views

Capacity of channels with pilots?

Question is about "channel capacity" http://en.wikipedia.org/wiki/Channel_capacity I guess it is pretty elementary for experts, however I have not seen it discussed in e.g. Proakis book or Tse "...
4
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0answers
146 views

Discrete-time model of 2-user CDMA system, recovered information at receiver using polarity detection?

I have discrete-time model of 2-user CDMA system with: $b_1=-1, b_2=+1, \alpha_1, \alpha_2, s_1, s_2$ and $n$ white noise. What are the recovered infromation bits for user 1 and user 2 respectively ...
3
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0answers
32 views

NLMS algorithm for a MISO structure

I am trying to implement an NLMS algorithm for a multi-input single-output(MISO) structure. We take a reference signal x, then we made a new set of P input signals from it as follows: x_op (k) = x(k)...
3
votes
1answer
58 views

Potential issues arising from too stable discretization

When numerically simulating a system, usually some kind of discretization is necessary, obtained by some kind of z-transform, such as, for instance, the bilinear transform $s\mapsto \frac{2}{\triangle ...
3
votes
1answer
111 views

Use samples of Fourier transform as DFT?

Consider the LTI system given by: $H(z) = 1 - \frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$ Let $x[n] = (\frac{1}{2})^nu[n]$ be the input to the system. We want to find the output for $n = 0,1,...,N_a$, using ...
3
votes
2answers
625 views

Determine if two signals are the same?

I'm pretty new to signal processing. My data is the $(x,y,z)$ acceleration of someone walking with a smartphone in his/her pocket. Goal Given two signals, determine if it's from the same person ...
3
votes
0answers
1k views

4th order cumulant of signal

I'm trying to implement some code for watermarking on audio based on a scientific paper. I'm stuck in the part of the pseudo code where they calculate the fourth order cumulant of the approximation ...
3
votes
0answers
160 views

understanding discrete wavelets

I was reading section 4.3.3 from chapter 4 of "A Wavelet Tour of Signal Processing", "...Let $\bar{f}(t)$ be a continuous time signal defined over $[0,1]$. Let $f[n]$ be the discrete signal obtained ...
3
votes
1answer
623 views

How can I detect peaks and regions of highest variance in a 1D signal?

I'm not a signal processing person at all so hopefully I'm not asking an obvious question (if I am, I'd appreciate any resources that would help give more context). I have a 1D vector where the ...
3
votes
0answers
7k views

Simulink continuous to discrete question

I'm new to Matlab/Simulink and would like to convert the continuous system below to discrete for eventual conversion to C code. Matlab has a c2d function, but I don't know how to apply it to a ...
3
votes
0answers
295 views

Wavelet computation with filter bank - differing results

I'm trying to get a grip on Wavelets. I've read "Wavelets, Their Friends, and What They Can Do for You" which lead me to an implementation of the discrete DWT with filter banks. Basically, I'm using ...
3
votes
0answers
142 views

Interpretation of a periodogram: the effect of window sizes

I am specifically working on a categorical time series of best n number of parallel threads (for n=1..16) for a multicore workstation. I constructed the Walsh-Fourier periodogram for size 2^10 and 2^...
3
votes
0answers
791 views

calculate root mean square, ratio of power, constant false alarm, … of a signal

I am new to Digital Signal Processing, and am reading a paper. I don't know how they can extract some features from signal, like root mean square (RMS), Constant False Alarm Rate - CFAR, Mean Value ...
3
votes
0answers
60 views

How to analyze a pattern of discrete events belonging to a 24 hour and ~90 minute cycle?

I'm a sleep researcher and since last december I've been collecting data on mydreaming and awakening in the middle of the night. Dreaming occurs within a well-known 80-120 minute "cycles", with ...
3
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0answers
106 views

Finding the output for an input sequence

So I think I have the answer I just want to make sure I'm doing things correctly. Let a be in the open unit disk, $F_s > 0$, and $0<f_0 < \frac{F_s}{2}$. Let $h[n]=0$ for $n < 0$ and $h[...
2
votes
1answer
23 views

Zero State and Zero Input Responses from Steady State Response

Let a linear, time-invariant, causal discrete linear system be described by the following difference equation: $$y[n] = 0.9y[n-1] + 0.1x[n]$$ Assuming that $y[-1]=2$ and $x[n]=20\cos(\Omega n)u[n]$, ...
2
votes
0answers
39 views

How do 2D DCT basis functions interact to produce 8x8 JPEG tiles?

This section is a bit of an intro. If you want to skip directly to where the problem is explicitly outlined, skip to the bottom of this post. Please note that I'm not hip with mathematical lingo, so ...
2
votes
0answers
19 views

Is it possible to create a causal filter with a positively-sloped phase response?

I am currently prototyping a set of noise-cancelling headphones that utilize active EQ to modify the noise-cancelling signal, allowing the user to modify the frequencies that they hear or don't hear. ...
2
votes
0answers
41 views

Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?

Let $$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$ Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure what will the frequency domain for $Y(\nu)$ look like for a ...
2
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0answers
48 views

Explicit formulation of the role of eigenvectors of the matrix of a linear time-invariant filter

At this point in a lecture by MIT Professor Strang the idea of gaining insight into a filter by studying its eigenvectors is introduced. The idea is clear with the example chosen in the lecture: an ...
2
votes
1answer
142 views

How does a digital filter work?

To introduce my situation: I'm developing a digital synthesizer in a form of a C++ library, working with low level APIs like WASAPI, ASIO, ALSA etc. It's probably not very practical and I'm mostly "...
2
votes
0answers
107 views

Why is channel estimation done after synchronization and why does it work?

I am interested in Software Defined Radio communications where almost all processing is pushed to the digital domain. I'm wondering why is channel estimation done after frequency and phase ...
2
votes
0answers
52 views

How can I extract the 2 polyphase components of a signal after sampling at the half of sampling rate

Suppose I have a continuous signal x(t), which was sampled using sampling function s(t) whose sampling rate is Ts.How can I sample the continuous signal by Ts/2 instead of Ts in order to get two ...
2
votes
1answer
145 views

Estimate smartphone accelerometer bias

I was planning to develop Android / iOS applications that enable users to measure 3D length using their smartphones. According to this question, you need to know at least the time-varying bias that ...
2
votes
0answers
117 views

What is the correct way to do Short term Fourier transform and extract the phase information from local sections of a signal?

I took a triangular voltage signal and taking it's time derivative I obtained the current through a pure capacitor. Then I took different portion of voltage and current signals, took their Fourier ...
2
votes
0answers
312 views

How to eliminate matched filter background?

The question My goal is to detect an unknown frequency $f_1$ with a mixer and a matched filter. My simulation shows (below) that I correctly identify the 50 kHz external signal - but it also ...
2
votes
0answers
73 views

Distinguish between chords and single notes

I am implementing a pitch detection system where I detect pitch in single notes (guitar). I recently found this library, that detects chords in an audio signal. When there are chords in the signal, ...
2
votes
0answers
133 views

Constructing $X(\omega/2)$ from the FFT of $x[n]$

Let $X(\omega)$ be the Discrete Time Fourier Transform (DTFT) of $x[n]$, I want to construct $X(\omega/2)$. Precisely, I use FFT function to compute the samples of $X(\omega)$ in one period, say $[0,...
2
votes
0answers
237 views

1/f noise generation

Recently I was reading a paper about the pink noise generation. But I don't have any background of this field. I am confused with some part in the paper. First, the Voss's algorithm generated a ...
2
votes
0answers
136 views

Optimal method to calculate Fractional Fourier for Chirp signals

There are several method exist in the literature to calculate fractional Fourier transform. My interest is in chirp signals and want to find time delay estimation using fractional Fourier transform (...
2
votes
0answers
79 views

Why does filtering the same discrete dataset while choosing different sampling rates yield different results?

If I have a two-dimensional discrete dataset (one space, one time), and I create subsets of this dataset by "sampling" (although the original dataset isn't continuous) it at different rates, should I ...
2
votes
0answers
46 views

Why doesn't the mel-scale use the twelth-root of 2 instead of a biased sample listener?

For the mel frequency spectrum, which is used extensively in audio-processing, the technique uses subjects to identify pitches of uniform distance from one another. Isn't this distance just the 12-th ...
2
votes
0answers
60 views

Is there an exact solution for this re-sampling problem?

I want to know if there is an exact solution for the following problem and how to approach solving it: I have a discrete-time signal where the Nyquist theorem is satisfied: $r_k = \sum_i a_i^{(1)}h^{...
2
votes
0answers
676 views

Extracting the phase of a jittering sine wave using python

The background: I conducted an experiment where I rotated an object (with three-fold symmetry) many times and recorded the projection of the object. I should be able to tomographically reconstruct ...
2
votes
0answers
283 views

DC offset removal from tetra signal

Hey I want to remove DC offset from tetra signal captured as inphase and quadrature phase samples(I and Q samples). I and and Q samples are 16 bit signed values. I tried averaging 2000 I and Q samples ...
2
votes
0answers
338 views

Kalman Filter: continuous state space, discrete observations

This is just an idea. How can we model the kalman filter to get the state representation in continuous space when the observations to the system are actually from the discrete space. The discrete ...
2
votes
0answers
386 views

How to model/estimate channel in discrete time with different sampling time?

I want to estimate a channel based on LTE 3GPP EVA with given power delay profile (set of average power and delay of channel taps). ...
2
votes
0answers
114 views

Voice sample prediction scheme

I have some telephone voice audio with occasional "blips" in the audio. The blips appear to come from an IP link buried in the PSTN (this is a conceptual explanation, so don't worry about things like ...
2
votes
2answers
94 views

Signals - question due to sampling

I don't have an idea how to start it. Help pls :) $$m = z(t) + \frac{\operatorname{Sa}(t-T)}{4}$$ We have some signal $z(t)=\left(\operatorname{Sa}(\frac{t}{T})\right)^2$. How often the m signal ...
1
vote
0answers
43 views

Position Kalman Filter fails to track a constant-acceleration path

I'm trying to build a discrete Kalman Filter that fuses accelerometer (acceleration) and GPS (position, velocity) measurements. However, I'm finding that my filter can't properly track a constant-...
1
vote
1answer
29 views

Measuring group delay through a linear phase filter

I'm having a difficult time wrapping my head around a phase/ group delay problem and it corresponding to where you start sampling so I built up a system to test some of these issues. The system passes ...
1
vote
1answer
26 views

Is fft2 in MATLAB unitary? Some differences happen

I meet a problem when implementing fft2 in MATLAB. The question is I try to simulate the realistic measurements $Y = |FCXF^H|^2$ - the intensity of Fourier domain of object $X$, where $F$ denotes ...
1
vote
0answers
21 views

MFCC parameters for gunshot recognition

I'm writing a gunshot detector software. I'm using this article as reference:https://arxiv.org/ftp/arxiv/papers/1706/1706.08759.pdf. For now, my software is able to recognize an impulsive sound. Now, ...
1
vote
0answers
21 views

Frequency warping while creating filter coefficients

If I have an audio signal at 16kHz with frequencies band-limited to 8kHz. I want to low-pass filter this signal such that fc=4000Hz. Meaning when I reconstruct the signal I do not want any content ...