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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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86 views

Estimating variance in arbitrary, periodic signal

I have a periodic signal $x[m], m \in [0;M-N+1]$ made of modulated templates $s[n],~ n \in [0;N-1],~ N \ll M = NK$ of finite energy and support (i.e. zero outside of its defined interval, which does ...
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43 views

Reconciling Continuous and Discrete Complex Domains

Having taken some courses in Systems and Stability dealing mostly with continuous time signals, I am accustomed to thinking about the Laplace and Fourier transforms dealing with complex and pure ...
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2answers
82 views

Is there a specific preferred order of operation on signals?

Basic Signal Operations Performed on dependent variables-- The periodicity of the signal is varied by modifying the horizontal axis values, while the amplitude or the strength remains constant. These ...
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1answer
59 views

What is the impulse response of SIMO channel and its equivalent in oversampling?

1- According to the below paragraph : Could someone explain, What mean M here? I mean when saying with Order M ? 2- On the other hand, When performing Fractional sampling, for example sampling ...
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0answers
94 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 ...
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1answer
136 views

How to convert DFT to DCT

I've been trying to find a fast 16 point dct2 and dct3 implementation, however I could only find it in literature expressed as mathematical equations, which honestly I couldn't understand. However I ...
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1answer
252 views

What is the noise whitening process?

I came across this process when working on OFDM in wireless communication. It's mentioned if we have two copies of a signal resulted from SIMO system (Single Rx Multiple Tx), we can process the noise ...
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1answer
19 views

How do you estimate necessary dynamic range?

Say I have a signal (1D in my case, but could be an image, etc.) that has been captured adequately on nice equipment with sufficient resolution and range to get all the details of the signal that are ...
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1answer
68 views

Band pass filter (digital resonance)

Q1:  Consider a discrete-time band-pass filter (BPF) that uses only two poles as $$ H(z) = G \frac{1}{\big(1-r \, e^{j \omega_0} z^{-1}\big)\big(1-r \, e^{-j \omega_0} z^{-1}\big)} $$ where this ...
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41 views

multiplying the received signal by carrier, in OFDM system

Sorry for this question, I'm still new in signal processing area. In OFDM system, let $x$ be the received signal, what do we call the process of multiplying the received signal $x$ by $e^{-j2\pi F_c ...
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1answer
132 views

What's the relation between the sampling rate and FFT size in OFDM

In OFDM system, Is there relationship between Sampling rate and FFT size? For example, if we downsample or oversample the received signal, Should we decrease or increase the FFT size accordingly? ...
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1answer
103 views

How to delay an audio signal by 1 microsecond? [duplicate]

I have an audio signal sampled at 44100Hz. I want to delay this signal by 1 microsecond (and maybe even less) for a steganographic purpose. Now if I delay it one sample, the corresponding time delay ...
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0answers
50 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 ...
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3answers
141 views

Are oversampling and downsampling the same thing?

According the books I have on DSP, is oversampling, sampling a signal at a much higher samplingrate then normally required, so to reduce the sample-rate (and increase the resolution of the signal) ...
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0answers
43 views

Can we sample the signal with any period as long as the Nyquist rate is respected

I have a question regarding the sampling rate. Suppose that we transmitted a signal $m(t)$ then at receiver side, we received the continuous signal $x(t)$, which is time varying and sampled with a ...
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28 views

How to extract desired frequencies from a spectrum using e.g. a Parzen window?

Disclaimer: I am a geophysicist working with time-domain data which needs to be converted to the frequency domain evaluated at a specific set of logarithmically-spaced frequencies. The textbooks I am ...
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1answer
67 views

Small shift in frequency in FFT

I'm trying to compare the estimation of the power spectral density (in this case of a fake cosine signal) by two different methods: 1st, MATLAB's fft function, and 2nd, a direct calculation from the ...
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1answer
155 views

Absolutely summable signals

Given an absolutely summable signal $x[n]$, the $z$-transform $X^z(z)$ is rational with a pole at $z=0.5$. Given the following the statements: $x[n]$ has a finite support in the time domain. $x[n]$ ...
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1answer
309 views

Why is the second half of the FFT negative frequencies

There are lots of questions here about what the negative frequencies in fft mean, but I'm confused on why the second half of the fft calculation is the correct calculation for a negative frequency. ...
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0answers
43 views

DSP book suggestions [duplicate]

I am very interested to know your thoughts on best DSP books available today. I know that the Discrete-Time Signal Processing of Alan Oppenheim is one of the bests ...
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24 views

Sound equalization : assumptions around the use of the transfer functions. Are they correct?

I'm trying to create a equalizer (in JAVA) and I made few assumptions but I'm not sure if I'm true or false about the use of the filters. Here is the list of the points I'd like to check. 1/ I'm ...
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2answers
77 views

Orthonormal Dictionaries for Band Limited Signals

If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
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1answer
62 views

What happens when the poles of this z-transform function are outside the ROC for a signal?

I am given a z-transform function for a signal $h[n]$. It's $H(z)=\frac{2z^2-0.75z}{(z-0.25)(z-0.5)}$. I am supposed to find $h[n]$ and check the stability of the system for these cases: a)ROC: $|...
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1answer
45 views

Meaning of a formula about transient frequency bins

I'm trying to understand the following formula in this paper: Sadly, the paper does not define most of the symbols it is using, so my guesses so far are: $T_{tr}$ refers to the sampling interval i....
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2answers
77 views

Understanding the conditions for recovering a discrete time signal through sampling

So, we had a very brief introduction to the Nyquist-Shannon sampling theorem (the discrete time version). While discussing this, we have seen that multiplying a discrete time signal $x[n]$ by an ...
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1answer
44 views

Auto-correlation of the sum of two generic signals

Be $x[n]$ and $y[n]$ two generic discrete-time signals. Given $s[n] = x[n] + y[n]$ I want to evaluate its autocorrelation $R_s[l]$. By definition (https://en.wikipedia.org/wiki/Cross-correlation): $$...
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1answer
258 views

How to perform this spectral decomposition in MATLAB?

Given a filter $X(z)$ I want to find $G(z)$ such that it is stable, causal and minimum-phase, and it accomplishes that $$X(z)=K_0G(z)G^*(1/z^*)$$ where $K_0\in\mathbb{R}$. Of course, $G^*(1/z^*)$ ...
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85 views

State Space conversion of Sinusoidal model

i would like to learn how to convert sinusoidal model into state space form which has following equation our model consist of sum of periodic components with additive of white noise, given by ...
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1answer
218 views

Relation between the DTFT and CTFT in sampling- sample period isn't as the impulse train period

I will quote an answer of Matt L. from this post (I didn't comment there because I can't) If you have a continuous-time signal $x(t)$, then the two signals you're talking about are $$\begin{...
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1answer
67 views

How do I plot the square of the amplitude response?

I have calculated the transfer function of an FIR filter $$ y[n] = x[n] + α · x[n − R] $$ This is what I have $$ H(z) = 1 + αz^{-R} $$ Now I should plot the square of the amplitude response. So I ...
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Is there a criterion that says at what point you can distinguish 2 partially overlapping Lorentzian peaks?

If you have 2 Lorentzian peaks that partially overlap and you have some frequency resolution df (your points in frequency space are separated by df) and both Lorentzian peaks have FWHM $\Gamma$ is ...
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183 views

Detection of Troughs and Notches in a PPG Signal

I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below... I'm having problem in finding the troughs and dicrotic notch for ...
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1answer
42 views

FFT for distance-limited sum of pairwise products

I have a sequence of fixed length $N$ input arrays ($x_0$, $x_1$, ..., $x_{n-1}$), and my goal is to compute output arrays as such: $$d_{00}[l] = \sum_{i = 0}^{N - l} x_0[i]x_0[i + l]$$ $$d_{01}[l] = ...
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1answer
110 views

What's the relationship between the parameters of this noise generator and the gaussian curve it produces in the frequency domain?

This algorithm produces a sequence $y$ having a magnitude spectrum that resembles a normal distribution, peaking at frequency $\omega$: $$b[n]=(1-\sigma)b[n-1]+\frac{\sigma}{\omega} C$$ $$p[n]=p[n-1]+...
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1answer
52 views

Harmonics in Quantal Histogram

I'm studying what I believe to be a system that produces a (noisy) quantal response (i.e. there should be a minimum increment of response). To do this, I've plotted a histogram of some ~6000 amplitude ...
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1answer
73 views

How to choose the right segment length for a given signal?

Im working on plotting the power spectral density of a random time series measured. I know the target spectrum.The idea is check the measurement vis-a-vis the target spectrum. However, I get slightly ...
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0answers
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Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
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23 views

Correctly finding Bands(pulses) in a discrete signal

I'm trying to find a way to detect bands in a signal so that I can assign a metric to that band based off of width and amplitude. An example of the signal can be seen below, where the signal is in red,...
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3answers
919 views

Power of a Discrete time signal

I was learning on power of signal and i went through different formula in internet . I get different results when i go through internet . But in other site average power is written as I dont know ...
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2answers
126 views

Isolate High Variance vs Low Variance Sections of Signals

I have the following one-dimensional signals: The goal is to identify the sections with smaller variances compared to the rest (For Python, that is to get their index value in the array). In the ...
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1answer
44 views

Measure 3-D length using smart-phone's accelerometer

I'm wondering if we can measure 3-D length only by our smart-phone's accelerometer. And we all know these low cost IMUs are not accurate. You can model accelerometer's error this way: $$ a = f*a' + g ...
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1answer
119 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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1answer
77 views

Remove Frequency Range

I got a signal and I would like to remove a specific frequency range. I am a frequency noob, so I will explain it by images: I have a frequency filter (butter bandpass): I have a signal and it's ...
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1answer
57 views

How to make series circle shift invariant

I have a series of numbers. They may be integer, floating, or ...
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1answer
69 views

what is the periodicity of $e^{j\omega n}$ when $\omega=0$?

what is the periodicity of $e^{j\omega n}$ when $\omega=0$? I think it is $N=1$. But signals and systems book by Oppenheim and Willsky page no.28, mentions it as undefined. I can understand this for ...
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0answers
111 views

Graph signal processing

What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
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2answers
61 views

x(t) and x(-t) are flipped (left to right) signals of each other

$x(t)$ and $x(-t)$ are flipped (left to right) signals of each other. but $x(2t-3)$ and $x(-2t+3)$ do not share that kind of relation as I thought incorrectly. Can some one comment on this? Is ...
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2answers
400 views

Are discrete systems defined by LCCDE always LTI?

Suppose a discrete-time system is defined by linear constant-coefficient difference equation $$\sum_{k=0}^{N} a_k y[n-k] = \sum_{k=0}^{M} b_k x[n-k]$$ where at least two different coefficients $a_i,...
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1answer
112 views

Gaussian Equivalent of Convolving an Image 50 Times with a Box Filter

I have a image that I'm convolving 50 times with a box filter, and I like to replace this with a single gaussian filter. Because both box filter and gaussian filter are separable I can just study the ...
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1answer
266 views

How can I transform a time signal into a third octave spectrum?

I try to make a third-octave spectrum from a time signal and I have some troubles with the algorithm. I'm not an expert in signal processing so I don't know what is wrong. Here what my algorithm ...