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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33
votes
6answers
51k views

The difference between convolution and cross-correlation from a signal-analysis point of view

I am trying to understand the difference between convolution to cross-correlation. I have read an understood This answer. I also understand the picture below. But, in terms of signal processing, (a ...
26
votes
2answers
4k views

Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
22
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5answers
125k views

Difference between discrete time fourier transform and discrete fourier transform

I have read many articles about DTFT and DFT but am not able to discern the difference between the two except for a few visible things like DTFT goes till infinity while DFT is only till N-1. Can ...
19
votes
3answers
35k views

What is the difference between linear and non-linear filters?

How a mean filter is called as linear filter and a median filter is called as non linear filter? I understand how a mean and median filter operates, but I was not able to relate with the term linear ...
19
votes
2answers
21k views

Stationary vs non-stationary signals?

There are nice technical definitions in textbooks and wikipedia, but I'm having a hard time understanding what differentiates stationary and non-stationary signals in practice? Which of the following ...
17
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8answers
5k views

Is there an algorithm to compute the phase for a single frequecy?

If you have a function $f(t)=A \cdot \sin(\omega t+\phi)$, and reference sin wave $\sin(\omega x)$ what would be a fast algorithm to compute $\phi$? I was looking at Goertzel algorithm, but it doesn'...
17
votes
1answer
24k views

Help calculating / understanding the MFCCs: Mel-Frequency Cepstrum Coefficients

I've been reading bits and pieces online but I just can't piece it all together. I have some background knowledge of signals / DSP stuff which should be enough prerequisites for this. I'm interested ...
16
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8answers
4k views

DSP or signal/image/data processing jokes

Some other StackExchange/StackOverflow sites are entertained with a certain level of humor or fun. What is your favorite “data analysis” cartoon? is particularly worth mentioning (IMHO) this xkcd ...
16
votes
1answer
861 views

Is wavelet analysis useful for 1D signals?

Wavelets seem to be very useful for image processing. Assuming that I'm only ever going to study signals of time, i.e. 1D signals, should I still take a course in wavelet analysis? Are they applicable ...
15
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5answers
12k views

What are the problems with designing an FIR filter using FFT?

I'm trying to get an understanding of the relationship between an FIR filter designed from "first principles" using a filter kernel with convolution, and a filter designed in one of two ways using FFT ...
15
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3answers
5k views

Why convolution is required, or what is the philosophy behind convolution?

I am working in digital image restoration field. I have read all things about convolution, that, for an LTI system, if we know its impulse response, then we can find its output by just using ...
15
votes
1answer
8k views

Getting loudness of a track with RMS

I'm trying to calculate the loudness of an audio track I have stored in a buffer. The buffer contains PCM data of the signal and I want to get how 'loud' it is by using Root Mean Squared. I assume I ...
15
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2answers
666 views

Where did Arnold Tustin first introduce the bilinear transform?

It's well known that the bilinear transform is also known as Tustin's Method. As far as I know, Arnold Tustin really did introduce the idea into the control systems literature, so the name isn't just ...
14
votes
2answers
11k views

What are advantages of having higher sampling rate of a signal?

Being a non signal processing science student I have limited understanding of the concepts. I have a continuous periodic bearing faulty signal (with time amplitudes) which are sampled at $12\textrm{ ...
14
votes
2answers
11k views

Using continuous verses discrete wavelet transform in digital applications

I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or ...
12
votes
7answers
4k views

Obtain a signal's peak value if it's frequency lies between two bin centers

Please suppose the following: The frequency of a signal's fundamental has been estimated using FFT and some frequency estimation methods and is lying between two bin centers The sampling frequency is ...
12
votes
1answer
4k views

Relationship between DCT and PCA

I have a basic implementation knowledge of the 2D 8x8 DCT used in image & video compression. Whilst reading about Principle Component Analysis, I can see a lot of similarity, albeit PCA is clearly ...
12
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3answers
5k views

How to detect “fast” changes in signal processing

I'm working on a project where we measure the solderability of components. The measured signal is noisy. We need to process the signal in real time so that we are able to recognize the change that ...
11
votes
9answers
613 views

Where is the flaw in this derivation of the DTFT of the unit step sequence $u[n]$?

This question is related to this other question of mine where I ask for derivations of the discrete-time Fourier transform (DTFT) of the unit step sequence $u[n]$. During my search for derivations I ...
11
votes
4answers
71k views

What is meant by 20 dB signal-to-noise ratio?

I'm reading a paper in which a discrete signal $$x(n) = s(n) + w(n)$$ is considered. $s(n)$ is a known, deterministic series, and $w(n)$ is white noise with zero mean. The authors write that ...
11
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4answers
51k views

Difference between Digital signal and Discrete signal

I have just started studying Digital Signal Processing. Can someone explain what is the difference between a Discrete Signal and a Digital Signal in simple words? Thanks in advance !
11
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2answers
13k views

How to compute dBFS?

I asked myself how to compute dBFS (dB full scale) from a value of sample between 1 and -1? and in general?
11
votes
1answer
218 views

Quantitative Comparison of Scaled, Delayed and Warped Signals

The following question is detailed in 1D, with time as the ordinal variable. Similar questions could apply in other dimensions. In several signal processing techniques, such as blind source ...
10
votes
7answers
11k views

Why Does the DFT Assume the Transformed Signal Is Periodic?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur). Now, if you look at ...
10
votes
3answers
1k views

Is there a way to obtain the impulse response of a discrete system by just knowing it's response to the discrete unit step function?

In continuous time it was possible; $$ u(t){\longrightarrow} \boxed{\quad\textrm{system}\quad} {\longrightarrow} y(t)\implies \delta(t)=\frac{du(t)}{dt}{\longrightarrow}\boxed{\quad\textrm{system}\...
10
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2answers
3k views

Discrete-time Fourier Transform of the unit step sequence $u[n]$

From text books we know that the DTFT of $u[n]$ is given by $$U(\omega)=\pi\delta(\omega)+\frac{1}{1-e^{-j\omega}},\qquad -\pi\le\omega <\pi\tag{1}$$ However, I haven't seen a DSP textbook that ...
10
votes
1answer
745 views

How can I automatically classify peaks of signals measured at different positions?

I have microphones measuring sound over time at many different positions in space. The sounds being recorded all originate from the same position in space but due to the different paths from the ...
10
votes
1answer
1k views

What is the difference between normalized peak of correlation, versus peak of correlation divided by its average?

Given a template, and a signal, the question arises as to how similar the signal is to the template. Traditionally a simple correlation approach is used, whereby the template and a signal are cross-...
9
votes
1answer
2k views

Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

I have been studying signals and systems lately and I have came across the following claim: The uniform sampling of a periodic continuous-time signal may not be periodic! Can someone please ...
9
votes
3answers
3k views

Shift a signal by fraction of a sample

I have a signal with a sample time of 0.5 micro seconds and I would like to shift this signal by a fraction of the sample time, say by 3 nano seconds. I have read a few online resources about ...
9
votes
3answers
19k views

Discrete Fourier transform symmetry

I was reading the chapter on discrete Fourier transforms in Lyons' book -- Understanding Digital Signal Processing -- and could not understand the last paragraph about symmetry. There’s an ...
9
votes
1answer
3k views

Scalogram (and related nomenclatures) for DWT?

My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing ...
9
votes
1answer
2k views

How can I decompose a signal into square waves?

I am dealing with signals that are a superposition of different square waves with different amplitudes and phases. Normally, one would decompose a signal into sine waves with help of the Fourier ...
9
votes
1answer
9k views

How does the $\mathcal Z$-transform's “region of convergence” work?

I'm a novice in DSP and I have few doubts regarding the $\mathcal Z$-transform and its region of convergence (ROC). I know what a $\mathcal Z$-transform is. But I'm having trouble with understanding ...
8
votes
5answers
2k views

Why Do I Get This Crackling Noise on Zeroing out the High Frequencies?

I recently started playing with the Fourier transform (after spending a few weeks learning about the mathematics behind it). I decided to try hacking together a low-pass filter on the following sound ...
8
votes
1answer
4k views

Audio normalization

I have a recording in pcm format and I want to do some simple analysis. I have some questions about what is normalization. As far I understand it is to get all the amplitudes between a range i.e. [-1,...
8
votes
1answer
5k views

Questions about discrete signal energy calculation

I'm looking at the definition of signal energy (e.g. Wikipedia, cnx.org). For discrete signals, it's defined like the following, where $x(n)$ holds the signal: $ Energy = \sum_{n=-\infty}^{\infty} |...
8
votes
1answer
173 views

Open access signal processing journal?

Signal processing is Elsevier, so it's not open access, and IEEE Transactions on Signal Processing is also not open access. I was wondering if there's any decent journal on par with those that's open ...
8
votes
3answers
2k views

What is the effect of aliasing on the magnitude of the autocorrelation?

I've a question about the effect of aliasing on the magnitude of autocorrelations. From a simulation in MATLAB, I don't see any effect of aliasing or any need to anti-alias filter when I take the ...
8
votes
1answer
2k views

Apply wavelet transform to analyse EEG signal

I would like to apply The Morlet wavelet transform to analyse my EEG signals. I have many short signals each is only 1 min long. and they all recorded in 30Hz. I have Two questions: In the Morlet ...
8
votes
3answers
12k 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}}...
7
votes
3answers
8k views

Demonstrating the effect of aliasing

How does the signal look when we don't use the Nyquist rate to remove aliasing from a signal during sampling? Let's suppose the signal is sinusoidal, with a frequency of 500 Hz and an amplitude ...
7
votes
3answers
7k views

What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
7
votes
3answers
11k views

What are high frequencies and low frequencies in a signal?

I'm new to signal processing. I'm plotting a signal in the time-domain in matlab. I don't understand which parts of the signal are high frequencies and low frequencies, can someone explain what a high ...
7
votes
3answers
3k views

can't find out the period of my signal

I've a noisy signal, which is the sound of motor with a constant speed, so the sound "should" be periodic, I know that there is a way to use the autocorrelation function to get the period,I did it, ...
7
votes
2answers
2k views

How can output sequence be equal to the sum of copies of the impulse response, scaled and time-shifted signals?

I am sorry, this is a very basic question. But i am having hard time understanding is how it is possible. I know impulse response is the output of the system when impulse sequence is given as input ...
7
votes
7answers
609 views

Intuition behind commutativity of convolution in LTI systems

Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system? If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
7
votes
2answers
3k views

MOD-N Circular Convolution

How to find MOD-2 Circular convolution for the two sequences $h =[-1,3,-2,1]$ and $x = [1,-1,-2,1,3,2,1,2]$. I know the answer is $7$ $0$ from matlab but I don't know how to find it graphicly or ...
7
votes
2answers
857 views

determine two signals with a scale factor

Suppose I have 2 signals from function $f_1(x)$ and $f_2(x)$, respectively, and assume the sampling rate is above Nyquist frequency, so we can restore the underlying functions $f_1(x)$ and $f_2(x)$. ...
7
votes
5answers
5k views

What are some methods for detecting a sinusoid in noise?

I'm looking for a broad classification on the kinds of techniques available. Something I can use to begin a literature survey. Some details: should be feasible for real-time implementation. Binary ...

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