# 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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### 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 $\sqrt{\rho n}$ (...
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. ...
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 ...
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### 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 ...
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 "...
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 ...
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### 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)...
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### 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 $x[n]=20\cos(\Omega n)u[n]$, ...
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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 "...
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 ...
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 ...
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 ...
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### 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 ...
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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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 ...
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### 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). ...
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 ...
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### 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 ...
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### 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-...
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### 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 ...
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### 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 ...