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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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9 views

Plane Settings of the Matched $z$-transform Method

I've come across that the matched $z$-transform maps poles of the $s$-plane design to locations in the $z$-plane. My question is, what is the $s$-plane and what does this mean? I'm aware that the ...
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1answer
34 views

ADC and Matched Filtering

A basic theorem in communications is the matched filter maximizes the SNR at sampling. I'm a little confused on how this relates to discrete time systems and sampling rate. Normally if you sample at ...
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1answer
23 views

Time Setting of $z$ and Laplace Transforms

I'm aware that the z-transform and the Laplace Transform have an analogous relationship but I want to be doubly-sure that the z-transform only works in discrete-time and that the Laplace transform ...
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1answer
17 views

Differences in moving window rms due to sampling rate

I have a 10 second recorded signal band pass filtered from 100-500 Hz. The original sampling rate is 10 kS. Now I run a moving window RMS with a window length: 10 ms on the signal (10/1000 * sampling ...
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28 views

PLL carrier recovery: intermediate versus baseband

When looking at carrier recovery, a PLL is often applied to correct the frequency offset between the local oscillator and the transmitter after down conversion. I'm wondering what happens to the PLL ...
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6 views

How to match resolution of two or more signals

I have received the following 4 time-series signals and wanted to do some data analytics using these. Although the sampling is the same for all of these signals, 2 samples per second, problem is that ...
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0answers
17 views

IFFT, negative frequencies and noncausal impulse

When using the IFFT to compute an approximation to the IDTFT, frequency range is 0 to 2$\pi$ versus $-\pi$ to $\pi$. This produces a different impulse sequence(causal I think). How do you calculate ...
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2answers
24 views

Does a phase rotation introduce a delay?

Suppose I have 2 complex time series, $x_1$ and $x_2$. If I measure the delay between $x_1$ and $x_2$, I get $t$. If I make $x_2 = x_2 e^{-j 2 \pi 10}$, and measure the delay between $x_1$ and $x_2$...
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1answer
16 views

Equivalence of difference equation with system of difference equations

I have this system and tried to write down its difference equation as follows $$ y[n] = b_0v[n] + b_1v[n-1]\\ v[n] = x[n] - a_1v[n-1] $$ I was asked to prove that the system can be ...
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2answers
27 views

Confused in difference between sequence versus signal?

I am learning basics of signals and systems with MATLAB If i create a vector in matlab such that x=[ 2 5 10 20], will it be considered a sequence or a signal? As ...
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0answers
37 views

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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1answer
25 views

what is the output of MFCCs?

I had calculated 13 MFCCs coefficients of a speech signal and i got output in the form numerical vectors please see below figure. My confusion whether it is in time domain or frequency domain. suppose ...
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1answer
25 views

Downsampling by block averaging

Many spectroscopic detectors used to study light absorbance as a function of time. These detectors cab sample data at 160 to 250 Hz. There is an option of choosing lower sampling rates such 80, 40, 20,...
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2answers
42 views

Contradiction while using the convolution sum for a non-LTI system

In a recent quiz, we were given the following problem: The cascaded LTI systems $\mathcal{T}_1$ and $\mathcal{T}_2$ respectively have impulse responses $h_1[n]=\delta[n+3]$ and $h_2[n]=\delta[5−n]$....
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1answer
34 views

Matlab FFT not producing symmetric spectrum

I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset. ...
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0answers
10 views

Punctured Turbo Code Decoding: Convergence Issue

I have been trying to create a basic BCJR decoder for a rate (1/2) punctured turbo code. The puncturing is simple, the encoder alternatively selects between the parity bits generated by the two ...
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2answers
55 views

Convolution of Two Impulse Signals

I have encountered convolution of two different impulse signals. ...
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0answers
29 views

how can I know this system is Time invarient?

y(t) = 0 (t<0); x(t) + x(t-2) (t>=0); y(t) = 0 (x(t) < 0); x(t) - x(t-2) (x(t) >= 0); y[n] = x[n] (n>=1)...
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0answers
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Frequency warping while creating filter coefficients

If I have an audio signal at 16kHz with frequencies band-limited to 8kHz. I want to low-pass filter this signal such that fc=4000Hz. Meaning when I reconstruct the signal I do not want any content ...
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1answer
26 views

Please help me understand this paper about Discrete Wavelet Transform!

I am trying to understand this paper says. I have found this paragraph to be vague: (a) Preprocessing Stage. The first step in this stage was to apply the Discrete Wavelet Transform (DWT). This ...
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3answers
537 views

Compress a signal by storing signal diff instead of actual samples - is there such a thing?

I am working with EMG signals sampled at 2kHz and 16 bits, and noticed that they "look smooth", that is, the signals are differentiable, and if I apply a "diff" function (...
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1answer
44 views

Time delay estimation between two complex signals(IQ)

I need to time align two complex signals. The two signals obtained were at different RF frequency before digitisation. So,I have two complex signals(IQ) and I need to do delay estimation and apply ...
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2answers
35 views

What exactly is captured in a Sample of the Nyquist-Theorem variety?

I'm new to DSP and was thinking of sampling in the traditional music creation way, in that you capture a sound and play it back, warp it, etc., but when I thought about the Nyquist theorem, I realized ...
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0answers
23 views

Chirp resolution as a function of bandwidth

My question concerns about the Chirp resolution during the crosscorrelation as a function of the sampling rate and available bandwidth. Suppose at a transmitter a chirp signal is transmitted (ranging ...
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1answer
35 views

DTFT frequency range

$$X(e^{j\omega}) = \sum_{n=-\infty}^\infty x[n] e^{-j\omega n} $$ The frequency term $\omega$ in DTFT is normalized as $\omega = \frac{\Omega}{f_\mathrm{s}}$ $\Omega= 2 \pi f$ is the angular ...
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2answers
159 views

Removing step-function like noise from signal, knowing when the step functions occur

So I currently have a system which is fit for very short time measurements. Whenever a measurement is long, however, there is a need to continuously update the reference, which, each time, will ...
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0answers
40 views

What is the error rate in compressed sensing?

Let $x \in \mathbb{R}^n$ be a $k$-sparse vector. Given $A \in \mathbb{R}^{m \times n}$, we have a measurement vector $y$ given by $$y=Ax$$ Let $\hat{x}$ be defined as follows $$\hat{x}:=\arg\min_{z\...
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2answers
78 views

Doppler Shifting A Chirp Signal

So I have a digital linear chirp signal: $$ x[n] = \sqrt{\frac{2}{N}} \cdot \cos\Big( 2 \pi \frac{f_{0}}{f_{s}}n + \pi \frac{B}{N} n^{2}\Big) $$ Where $f_{0}$ is the initial frequency, $f_{s}$ is ...
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1answer
25 views

Discrete-time, second-order section, direct-form II filter

I found dfilt.df2sos in Matlab and trying to figure it out how do I do that in Python? Is there any function that works similarly with the Matlab function? I also ...
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0answers
24 views

How to calculate Continuous Wavelet Transform (CWT) for specific frequency range in Python?

I am new to this topic pardon if I ask stupid questions. My first question what is a scale and how to convert it into a frequency? Secondly, I want to get cwt of a signal, but I want to have the ...
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1answer
47 views

Classifying and filtering out noise from zero crossings

Note: I know absolutely nothing about zero crossings nor signal processing in general. However, I am doing programming exercises that require them. I've searched around but I cannot understand most of ...
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0answers
33 views

Find output from a system with x(n) = u(n)

I've started learning signal processing and I'm trying to understand this exercise: Assume an LTI system, described by the difference equation: $$y(n) - y(n-1) - 6y(n-2) = x(n-1)$$ Q: Find ...
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1answer
26 views

How to get descrete fourier tarnsfom [closed]

Could anyone explain me please how to produce descrete fourier transform of such signal? There are no anymore information besides the picture in this task.
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1answer
44 views

Reconstructing a signal from FFT by adding individual signal components

I'm attempting to reconstruct a signal from the DFT of the signal. I tried to do it by extracting the individual sinusoids and adding them up, but the answer I get is incorrect. ...
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1answer
73 views

Moving average filter for sound in MATLAB

y[n] = b0x[n] +b1x[n-1] I have this MA filter in matlab as following ...
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1answer
39 views

What is used to initialise difference equations that require data from the output?

Given some difference equation for a filter like $y[k] = ax[k] + bx[k-1]+ cy[k-1]$, how would you initialize it? Since it needs an old output value (feedback) to calculate the new output value, it ...
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1answer
20 views

Double check z-transform ROC of $a^nu[n]$

For the z-transform ROC of signal $a^nu[n]$, it has been computed to be $|z|>a$. For example (as I have found on Wikipedia), the signal $(\frac{1}{2})^nu[n]$'s ROC will be $|z|>\frac{1}{2}$, as ...
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1answer
38 views

Plotting the Phase Response

I would appreciate it very much if someone would be able to provide some clarity on plotting phase responses. For instance, given that the frequency response of a filter can be written as H(exp(j*&...
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0answers
20 views

Impulse response of discrete time system

I am learning about discrete systems and in this derivation something struck me as quite odd. Solving for $A_0$ in this equation seems dubious as it ignored all other values of $n$. For example, at $n=...
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1answer
41 views

How to find lattice coefficients of all pole IIR filter with filter coefficient $k_m$ is 1?

Given the following system function $$ H(z) =\frac{1}{1+\frac{2}{3}z^{-1}+\frac{5}{8}z^{-2}+\frac{2}{3}z^{-3}+z^{-4}} \tag{1} $$ We have to draw lattice structure for above system function The ...
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1answer
40 views

Finding period of a square wave with varying sampling frequency

I have a square wave (0-1.8V) with a varying sampling frequency (from a circuit simulator). It is also not a perfect square wave (the high and low signal could be very close to but not precisely zero ...
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1answer
40 views

Discrete Time Convolution Example

How did we get this final answer in example in fig attached. I understand that delta(n) is a DT unit impulse where it is 1 at n = 0 and zero elsewhere. I understand that u[n] is a unit-step where it ...
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2answers
50 views

Significance of modular arithmetic in DFT?

In what ways does modular arithmetic plays a part in DFT? Why is it a so integral part of DFT?
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2answers
52 views

Periodicity of sum of discrete signals

In my lecture slides for school and from this website here "The sum $z[n] = x[n] + y[n]$ of periodic signals $x[n]$ with fundamental period $N1$, and $y[n]$ with fundamental period $N2$ is periodic ...
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1answer
37 views

Help me understand the stages involved in filtering a signal using Discrete Fourier Transform

I have a series of discrete values measured from a sensor. I want to filter the frequencies coming from this sequence of values. Then, if I understood the process correctly this is what I do: I ...
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1answer
16 views

Defining bound on input signal to test accumulator for BIBO stability

For an accumulator, defined as shown in the image below, why would I define $B_x=1$? $u[n]$ is defined at zero so my (possibly misguided intuition) is telling me that I'd choose $B_x = 0$ to not ...
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0answers
27 views

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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1answer
24 views

For discrete wavelet transforms, is redundancy needed to ensure perfect reconstruction?

So I was using pywt and I noticed that in the padding mode documentation they explain the following: DWT performed for these extension modes is slightly ...
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0answers
36 views

Please explain Multiplication property in Z transform?

I am having problem visualizing contour any example will be great help. As far as as where I need it I was trying to find Z transform of a contracted signal by first multiplication by impulse train.
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2answers
46 views

How to select the sampling frequency when the input signal frequency is not known

I am trying to observe the noise produced by UPS present in our lab, under no load (a normal running condition when its power is on). As I don't know its frequency range, I have randomly chosen 4 ...