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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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18 views

how for large lags k the r(k) co variance or Auto covariance is small ?

while a reding nonparametric method of spectral estimation -correlogram I encounter the following statement in Peter Stoica-spectral analysis of signal which I am not understanding. For most ...
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3answers
106 views

Detect the beginning of an increasing signal

After denoising and cleaning, I get amplitude signals like this (y-axis: dB): On bottom left of each of these 3 graphs, you can see a noise floor (nearly "horizontal line"). This noise floor ...
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3answers
157 views

How to calculate arbitrary phase shift in discrete signal?

When I have digital audio signal, represented in samples, I can easily phase-shift the signal by 180° by simply inverting the value of each sample. But what if I want to phase shift an arbitrary ...
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80 views

Why does bandpass performance break down at low frequencies? [duplicate]

I've got a basic bandpass filter design that works great at higher frequencies, but breaks down at around 150 Hz. Here's the MATLAB code: ...
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36 views

Model Based CoSAMP

I am currently studying compressive sensing, and am trying to implement algorithms. I successfully implemented CoSAMP, but then came across model-based CoSAMP. The algorithm looks very similar to me, ...
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2answers
61 views

How does sampling rate of $x[n]$ relate to sampling rate in frequency domain after DFT transformation?

I've got an analog signal $x(t)$ sampled at frequency $F_s$ to obtain samples: $$ x[n] = x(t) \bigg|_{t=n/F_s} $$ I transform this signal with DFT defined as: $$X[k] = \sum_{n=0}^{N-1}x[n]e^{-i2\pi ...
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56 views

How to catch the peaks from a signal [duplicate]

I am trying to get the peaks from a signal after I had applied FFT function. So I am trying to get only the high frequences along the signal, but with findpeaks I get alot of frequences that I dont ...
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1answer
41 views

Help generating coefficients for basic FIR LPF

I'm trying to generate coefficients for a FIR low pass filter to be used in an FPGA. I'm using python (scipy.signal) to attempt to do this, but am having trouble getting coefficients in a usable form....
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30 views

How do I draw convolution? [duplicate]

I know what is form for convolution but when I try to draw that I never get good answer. I think I don’t understand that good. How someone explain me with picture convolution of u[n]-u[n-5] and u[n+3]-...
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2answers
111 views

Calculating impulse response of system

Given is the illustrated circuit diagram of a linear, time-invariant, time-discrete system: How do I show that the total system has the impulse response $h[n] = aδ[n] + bδ [n - 1] + cδ [n - 2]$ and ...
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33 views

Sampling Process Question

This is what I know about the basic sampling process I am told that fbar(t) (i.e the sampled signal) is defined for all t. I don't understand that. If n is a finite integer (..,-3, -2, -1, 0, 1...), ...
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1answer
87 views

Is this two input discrete system linear? [closed]

Given two inputs $\: x_1[n]\: x_2[n]\:$Is the system $\:y[n]=x_1[n]\times x_2[n]\:$ linear ? My Approach: $(x_1\times x_2)[n]=S_1[n]\rightarrow Y_1[n]$ $(x_3\times x_4)[n]=S_2[n]\rightarrow Y_2[n]$ $...
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3answers
278 views

Distinguishing FIR and IIR from difference equation

Find the transfer function of the difference equation $$y_n = x_n + 1.2y_{n-1}$$ I fail to understand how one can distinguish between an FIR filter and an IIR filter by looking at the equation given ...
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51 views

How to denoise ECG signals like ECG-ID database?

I'm trying to implement an identification using ECG signals. I found ecgiddb and I'm trying to reproduce the results. In each single record of this database, there are two rows of data. The first ...
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1answer
228 views

Signals and systems book with linear algebra approach

I am currently taking a course on discrete-time signals and systems. I am using B. P. Lathi's Signal Processing and Linear Systems, which I don't like at all, as it doesn't draw any paralells to ...
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1answer
52 views

Can I apply CWT on a digital signal?

First, I am so sorry for my dumb and stupid question, I am very beginner with signals. Say that I have an ultrasonic sensor cabled to an ADC (Analog to Digital Converter). The ADC converts the analog ...
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128 views

EEG Signal Preprocessing BCI Competition

I have downloaded a dataset from BCI Competition III(Dataset 3a). I wish to classify the data into given 4 classes. The signal array is a time X channel matrix of some 900000 values sampled as 250 ...
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2answers
361 views

How exactly does 8PSK work on each I and Q leg?

I am working on making a modulator in VHDL and am implementing 8PSK. Currently, I have BPSK and QPSK looking good, and I have verified the spectrums. However, now that I am moving to 8PSK, I am stuck ...
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0answers
18 views

Find which groups of ants are coexisted in the location from their signal profiles using NMF

I try to solve biological problem to tell which groups of ants are co-existed at this location by their sounds in specific time frame. My chosen framework is Non-negative Matrix Factorisation (NMF) ...
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2answers
94 views

Method for finding the best non-increasing approximation function of a given signal

I have a discrete-time signal (with noise) and I want to determine the best non-increasing function that represents it. Of course it would be useful if the obtained function were defined in terms of ...
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2answers
238 views

Autocorrelation of discrete signal $\sin{2\pi fn}$

Determine the autocorrelation $r_{xx}[m]$ of the discrete signal $$x[n] = (\sin2\pi fn).$$ where $n$ and $m$ are integers. Using the definition I get $$\begin{align} r_{xx}[m] &= \...
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144 views

How to read .wav file to n array [duplicate]

Can anyone provide a solution to move the value on a .wav signal into an array in C# or C++? I want to process the signal. Thank you.
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1answer
56 views

Some doubts in the matlab code of computing Wigner distribution

I found that a discrete form of the Wigner distribution was $$WD(n,k) = \sum_{m = -N/2}^{N/2}f(n+m)f^*(n-m)e^{-j\frac{2\pi}{N+1}2mk}$$ where $f(n)$ is the signal and time limited within $|n|\le N/2$. ...
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1answer
45 views

Show that $S[n]= \frac1M \sum e^{\frac{2\pi l n}M}$ for $l = 0$ to $M - 1$

I am learning about image processing. Currently, I am reading about upsampling and down sampling. Here is some background what I am reading: I was wondering if someone show me a proof of how ...
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2answers
296 views

How to extract features of individual spikes in non-negative signal?

I have data of non-negative (in the sense there's no signal below baseline) spiking waveforms, which are in the form of a 1D array of numbers: Spikes that cross some threshold are considered real ...
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2answers
60 views

MLE formulation — confusion regarding the terms in the equation (Part1)

If $v \sim CN(0,2\sigma^2_v)$ is a circularly complex Gaussian random variable which acts as the measurement noise in this model $$y_n = x_n + v_n \tag{1} $$ where $x \sim CN(0,2\sigma^2)$, then is ...
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3answers
250 views

Reducing noise from the same frequency band as signal

Sorry for the vague question (as I'm not even quite sure what I want to do is possible), just asking for some general direction to take my research. For a brief description, my signal resembles ...
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0answers
19 views

How to fit a constant acceleration model given a set of x,y,t point with nonuniform timestamp?

I have a bunch a point $(x,y,t)$ in 2D $(x,y)$ with their sampled timestamp t. assuming acceleration do not change. How can I estimate a model $(x^*, y^*, vx^*, vy^*, ax^*, ay^*)$ where $(x^*,y^*)$ ...
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0answers
250 views

multiplication of two signals with phases

I need to multiply two discrete signals in the following form $$(a(t)+i b(t))\exp{(i \phi(t))},$$ where $a(t)$, $b(t)$ and $\phi(t)$ are real smooth discrete functions along $t$. I need to obtain the ...
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1answer
197 views

Is the sum of white noise and shifted white noise white noise again?

Let $W[k]$ be a stationary white noise with variance = 1 Question: Is $X[k] = W[k] + c \cdot W[k-1]$ white noise? $c$ is a real number.
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31 views

Sourse separation from known underdetermined mixing matrix

How to recover uncorrelated N sources from given N-1 signals and known mixing matrix M, (e.g. 9x8 matrix)? If I just use pseudo-inverse matrix M+, my source estimates are correlated with each other ...
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1answer
74 views

Channel Capacity - is this only for discrete/digital signals?

The units of channel capacity is bits/second. Does this mean this only refers to discrete/digital signals? Is channel capacity analogous to bandwidth in case of an analog signal transmission?
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1answer
89 views

Problem understanding steps towards defining the convolution sum

I have a problem understanding the reasoning behind a step that was taken to characterize a LTI system. So, we were told the following: For each integer $k$, we have the following function: $$ \...
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0answers
24 views

frequency signatures of musical instruments in an audio file

How can an audio signal be analyzed to identify the instruments in it? Let's say the audio contains drums and a guitar. The element that distinguishes these (or any) instruments is its timbre. Can ...
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35 views
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1answer
50 views

Impulse Invariant mapping [closed]

Can someone help me to better understand the Impulse Invariant mapping? : $$h[n] = T \cdot h(nT)$$ I don't understand why the discrete-time impulse response, $h[n]$, is taken from the sampled ...
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17 views

how to sweep OSNR

I have an optical sept-up ... Laser source+16QAM signal -> IQ modulator -> LO+EDFA+coherent receiver. I would like to get BER vs OSNR in the experiment. Can anyone help me please how I can sweep BER ...
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225 views

Prove that the system is time variant or time invariant

Prove that following system is time variant or time invariant: $$y[n-1]-y[n-2]=x[n]+x[n-1]$$ My answer : Delaying the input by $k$ that means $$Y[n,k]=T\{x[n-k]\}$$ Hence, $$y[n-k-1]-y[n-k-2]=x[n-k]...
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1answer
47 views

Finding number of independent samples using autocorrelation

I have a pressure signal (y) with 512000 samples and with a sampling frequency ...
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2answers
276 views

Why edge sharpening produces high frequency?

I have a low-resolution image in which the high frequencies are missing. When I apply an edge sharpening filter some of the missed high frequency is recovered. I am wondering why this edge sharpening ...
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1answer
94 views

Amplitude problem by puting 5 FIR in a row

I'm trying to use 5 FIR in a row to improve the S/N ratio on my signal, but I have some difficulties doing it. In fact I have 2 signals, let's call them sig_I and sig_Q. I want to apply my 5 filter ...
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1answer
49 views

How does the assumption that symbols are equi-probable hold

If I draw a number uniformly between zero and one, what is the probability that they are equal? Mathematically, it should be zero but I don't recall why? Can somebody please help in explaining why the ...
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2answers
193 views

Autocorrelation of a Shifted Sequence

Suppose I have a sequence $x[k]$ with $\mathcal{Z}$-transform $$ X(z) = x_{0} + x_{1}z^{-1} + x_{2}z^{-2} + \ldots + x_{N-1}z^{N-1}$$ I know that for real-valued $x[k]$ the $\mathcal{Z}$-transform ...
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0answers
49 views

Voltage auto- and cross-spectrum

If I want to get the voltage auto- and cross-spectrum, can I use the reference shown below? What does the factor 1/2 in the second part equation mean? I already have the FFT of my V1 and V2 and I ...
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1answer
42 views

Clarification on Discrete-time convolution and signal shifting

What are $y_1[n]=x_1[n]*h[n]$ and $y_2[n]=x_2[n]*h[n]$? $$x_1[n]=(0.1)^nu[n],\quad x_2[n]=(0.2)^n,\quad h[n]=(0.3)^nu[n]$$ I am confused about how to calculate $y_{1}[n]$. The formula for discrete ...
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1answer
55 views

Is this a power signal?

$x[n]=\sin(\pi n)$ Since this is a discrete signal, and n can take only values like ...,1,2,3 ... the value of the power is getting zero, and since it gets zero does it mean that it's not a power ...
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0answers
22 views

Average delay in skewed cross-correlation function with phase lag zero, plus example

I am calculating the cross-correlation function (CCF) between two digital signals in the following way: $$CCF(τ) = r(M(t),N(t+τ))$$ where $r$ is the Pearson correlation, $M$ and $N$ are two signals, ...
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1answer
179 views

Algorithm for identifying beat grid in music with non-constant tempo

Are there any algorithms for automatically fitting a beat grid to a song (tempo matching) when the song has a slowly changing tempo or BPM? The output would be a vector of onsets. Here's a picture ...
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1answer
144 views

Time scaling of discrete-time sequences and the DTFT

In the second edition of Signals and Systems by Alan Oppenheim, he discusses the DTFT of a "time-expanded" sequence that is effectively a slowed down version of the original sequence and can be ...
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1answer
290 views

How to sketch the following discrete time signal $\sum_{k=0}^{n} \delta[n-k]$?

I tried to solve it like in the picture but It feels so wrong though.