Signal Processing

Questions tagged [discrete-signals]

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

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$H(e^{j\omega})$ represented with a limited no of samples

I have a low pass filter defined as: $$ H_{lp}(e^{j\omega})=\left\{ \begin{aligned} &1 &|\omega|>\omega_c \\ &0 &\omega_c<|\omega|<\pi \end{aligned} \right. $$ and the ...
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Kay Statistical Signal Processing Estimation Theory Example 7.14

Example 7.14 from Kay Estimation Theory A common WSS random process has the ACF $$r_{xx}[k]= \begin{cases} 1+b[1]^{2}+b[2]^{2} & \text{k = 0}\\ b[1] +b[1]b[2] & \text{k=1}\\ ...
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How to remove or smooth the comb filter effect in real time audio signal mixing?

I have been working on a project where I have to mix multiple audio signals of the same source coming from different slave smartphones on one master smartphone in a distributed way. Now I have aligned ...
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How to rectify acceleration vibration signal?

I have acceleration vibration signal containing 2500 data points. What I need to do is rectifying the signal becomes no negative values but still has same mean and standard deviation as the original ...
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Efficient Method to match vector time series where the vector entries may not line up

Asking here because I couldn’t find or didn’t have the right words to search for the answers online. Also sorry for no examples—gotta maintain my NDA for work. I have two N-dimensional vector time ...
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525 views

What is the definition of a "Symbol"

I’m looking for the simplest, precise definition of a Symbol e.g. The symbols found within a signal The signal has a N symbols per second I'm following this tutorial. The fellow defines the term ...
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2answers
78 views

Encode bits in timing of signal

If you had two computers with two atomic clocks you could measure the time between signals at $10^{-16}\,\text{s}$. Can the time between signal pulses be used to encode additional bits of information ...
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52 views

Periodic signal detection algorithms?

I am currently working on pulsar signal periodicity detection. Most of the literature which i studied used traditional FFT (Fast Fourier Transform) or (Epoch Folding) techniques to find the ...
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1answer
58 views

Prove Convolution Property for DFT using duality

If $x_1[n]$ and $x_2[n]$ are finite length sequences of length $N$ $$\mathcal{DFT}(x_1[n] \circledast x_2[n]) = X_1[k]X_2[k]$$ where $X_1[k]$ and $X_2[k]$ are the DFTs of$x_1[n]$ and $x_2[n]$, ...
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Prove Discrete Time Fourier Series Multiplication property

Note: This is not a homework problem. I'm just stalled at a point because I think I might be interpreting the duality property incorrectly. If $x_1[n]$ and $x_2[n]$ are periodic with period N, then if ...
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How to effectively stationarise non-periodic wave signals?

I am pre-processing a non-periodic signal for further implementation of autoregressive modelling on the signal. The signal is shown in the following figure. However, when I applied the Augmented ...
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2answers
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Design of all pass filter with desired phase response

I want to design an all pass filter with a desired phase response in MATLAB. But in MATLAB, all pass filters are designed either by specifying the all pass filter coefficients or from a transfer ...
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1answer
32 views

n independent, normal, random variable distribution

There is 2 time-series signal and we have to compare the distribution of them. I have heard there is a theory that says for n independent, normal, random variables of a series with many members, the ...
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Split Electroencephalogram data into interictal and preictal segments

I like to build a classifier to predict EEG seizures for my undergraduate work. I read that researchers tackle this as a binary classifier: interictal (normal behavior of the brain) vs preictal (...
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1answer
36 views

On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies

It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
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Sampling frequency after aggregations

I have accelerometer signal, which is preprocessed by the actigraph on-device. Original sampling rate is 32 Hz, but activity count is summed for every minute, so I have a signal with 1 measurement per ...
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Introductory DSP Texts [duplicate]

I have an interview for a communication theory position and part of the interview requires basic knowledge of signal processing. What are good introductory texts that cover the basics of signal ...
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3answers
71 views

Why does the term "discrete" usually appear near the term "digital?"

Are these terms just parallel words? If not, why is it that when one reads about the first then one is very likely to come across the second? In such case, what would be a nice example to explain the ...
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1answer
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How to alleviate the edging effect of the Hilbert transform?

I am trying to use Hilbert transform to extract the envelope of a residual signal. After implementing the Hilbert transform, I find that envelope jumps very high at its boundaries. May I ask the ...
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4answers
99 views

Why does twice the sampling rate (Nyquist Theorem) seem inadequate?

I was told in my electronics course that "to reproduce a wave, we need to sample it at least twice every period." If I take this to be literally true, then a sine wave with only 2-3 samples ...
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2answers
66 views

Are signals modeled either digitally or analogously or can signals modeled as both?

Are signals modeled either digitally or analogously or can signals modeled as both?
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62 views

Subspace decomposition

While reading the paper "Perturbation analysis for subspace decomposition with applications in subspace-based algorithms" by Zhengyuan Xu, I came across the decomposition technique called ...
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Plotting the difference in magnitude and phase between two signals using specgram

I have two synthesised audio signals that I've convolved with impulse responses from a multi-channel microphone and I'm wanting to plot the difference in phase and magnitude using matplotlib's ...
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76 views

Symmetries of discrete analytic signals

Defining "analytic" as $x_a[n]$, where $X_a[k] = \text{DFT}(x_a[n])$, and $$ X_a[k < 0] = 0, \tag{1} \label{1} $$ what time-domain properties, such as symmetry or norm, are guaranteed for ...
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45 views

How to measure smoothness of a signal

Lets say I have two signals with a different number of data points - a step function and a smooth spline as you can see below. What is mathematical operation I can use to quantify the "smoothness&...
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1answer
27 views

FInd the amplitude function to a system

I'm studying a course in signal analysis and have come across an exercise where I find the analytical part a bit tricky. I am to find the amplitude function $|H( f )|$ for a system with the impulse ...
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Properties of the Frequency Domain to Ensure a Periodic Inverse Discrete Fourier Transform

I've been working on a project to send data via sound waves. The way I've carried this out is by encoding the data in pulses in the frequency domain, and then creating a unique sound wave containing ...
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2answers
169 views

What is the sampling rate for the continuous unit step signal?

I would like to know how I can find the sampling rate for the continuous-time signal: u(t) - u(t-2014), where u(t) is the continuous unit step function can be uniquely recovered from its sample.
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Recovering from exponential discrete-time signals

The spectrum of the discrete-time signal $x(n)=e^{-2n}$ is sampled at frequencies $2\pi\frac{k}{2014}$ for $k=0,1,\ldots,2013$. Can the signal $x(n)$ be uniquely recovered from these 2014 samples? ...
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1answer
39 views

Fourier transform of an aperiodic discrete-time signal

I have a signal of the form $x^{*}(-n+2)$. To derive the signal's Fourier transform I use The following properties of DFT: $x^{*}(n)=X^{*}(-\omega)$ and $x(n-k) = e^{-j\omega k}X(\omega)$ so the ...
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1answer
73 views

Symmetries of analyticity / zero self-correlation

I seek to understand symmetry properties of analytic sequences, without referring to frequency domain: what criteria must a complex sequence $x[n]$ satisfy to be analytic? Framed alternatively, such a ...
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1answer
68 views

Which of the following sampling methods can be used to sample x(t) such that this signal can be uniquely recovered from its samples?

Assuming that a continuous-time $x(t)$ having its frequency content in the frequency band $1612\leq|F|\leq2015(Hz)$ is sampled with the sampling rate $Fs=806$ samples per second. Which of the ...
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1answer
34 views

What does not happen if we limit the duration of this sequences to 2014 samples?

I am confused with this multiple-choice question: Assuming that $x(n) = e^{-2n}u(n)$, what does not happen if we limit the duration of this sequences to 2014 samples? A. The signal power leaks out ...
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2answers
42 views

Parseval's Theorem for Time Domain Data with DC

I have read several times that the variance for time domain data with a zero mean is equal to the integral of the power spectral density divided by N. From wikipedia, the discrete form of Parseval's ...
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41 views

Remove Noise from Discrete Signal with given Noise Model

I am interested in finding the true signal $p \in \mathbb{R}^D$ of an observed discrete signal $t \in \mathbb{Z}_{+}^D$. I know that each observed $t_{i}$ with $1 \leq i \leq D$ is the result of a ...
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1answer
82 views

How to Frequency Modulate an Audio Signal

I've started to learn about FM and I followed this guide to FM a sine wave. I have managed to do it and here is the result: And the code: ...
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1answer
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Microphone Data Comparison for breathing data... best way to compare two files?

I am currently trying to compare the amplitude vs time data between two different microphone readings (.wav files of inhales and exhales) and detect which reading produced a louder sound, on average. ...
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2answers
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How does the scale of a wavelet relate to the Fourier frequency (or period) under CWT?

I noticed that there are many ways to relate the scale factor of wavelets to some characteristic frequency, such as the peak frequency, the central instantaneous frequency, and so on(plz see section 2....
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1answer
124 views

Representing a digital ramp function in terms of unit step function

I am following a DSP course by Prof. Datta Roy which is available on you-tube. I have a concern on one of the ways he represents a digital ramp function in-terms of digital step functions. The digital ...
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1answer
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How do I confirm that range cell migration correction was done correctly? Is there a way to check this graphically without looking at the signal data?

I am implementing the Range Doppler Algorithm for a Synthetic Aperture Radar project and I am at the step where I must perform Range Cell Migration Correction. This step involves creating a sinc ...
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31 views

Peak detection in noisy waveforms

I have a set of 1-dimensional time-series, a subset of which contain either one or two peaks, and the remainder of which are pure noise. I've smoothed these data by ...
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Resources for practicing numericals related to digital signal processing?

What are some good resources related to DSP that has solved numericals? For instance, solved numericals related to the problems like these-: https://drive.google.com/file/d/1EC7-...
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1answer
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Different mathematical signal models for different applications

I am looking for some interesting and physically meaningful applications of different signal models. I am currently working with complex analytic signal model given below, but I couldn't come up with ...
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2answers
76 views

Create a time signal with a known magnitude response

I am trying to construct a time signal that needs to have a known magnitude response. The idea is to apply in Matlab/Octave an IFFT directly to the desired magnitude response: this corresponds to ...
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1answer
32 views

Is a continuous time aperiodic signal discrete in the time domain?

This is a statement I have read from a textbook: Whenever we have periodic signals continuous or discrete time the frequency domain is discrete and time domain is continuous. Whenever we have ...
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1answer
44 views

Phase offset analysis in real trsnsmitted signal

Assume we are transmitting a real signal $x(t)$ through a channel $h$ in passband as : $y(t) = x(t)cos(2πf_c t + ∅) * h(t)$ = $Re(x(t)e^{j2πf_c t})*h(t)$ where $f_c$ is the carrier frequency and $t$...
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1answer
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Is single integral inverse CWT possible with real-valued wavelets?

Where the CWT in the title refers to the continuous wavelet transform. Torrence1998 proposed a reconstruction formula as shown below Obviously, Eq.(11) is a single integral. However, Torrence1998 ...
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1answer
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How to find a system without an input $x[n]$ is linear or non linear

The question is this: $$ y[n] = \cos\left(\frac{5\pi}{8}n + \frac{\pi}{4}\right)$$ This is what my teacher said when I asked him for help-: In any system, inputs are not given, then we have to assume ...
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3answers
107 views

How is a constellation diagram constructed in practice?

I am simulating some optical signals in Matlab as they pass through a waveguide, get amplified, mixed with noises, etc. For the record, I am a theoretical physicist, not an engineer nor an ...
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1answer
24 views

Inverse discrete Fourier transform or inverse Fourier transform of composite function?

I collected spectrometric data which produced a graph with the intensity of each frequency of light. What more do I need to perform an inverse fourier transform of this data? Should I attempt an ...

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