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

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Autocorrelation of a $L$-point moving average system

The $L$-point moving system is: $$y[n]=\frac 1L\sum_{k=0}^{L-1}x[n-k]$$ $x[n]$ is a Bernoulli random signal with $\beta=0.5$ (equal probability) The autocorrelation of $x[n]$: $\psi_{xx}[m]=\delta[...
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30 views

Bode plot of discrete-time transfer function $H(z)$

$H(z)$ is the transfer function of a biquad filter as described here. I would like to plot the Bode plot of the magnitude response of $H(z)$. Scipy has a bode method (...
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1answer
32 views

DTFT and Inverse DTFT Homework Problem

I'm trying to solve this signals homework problem: So for part a, since multiplication in the time domain is convolution in the frequency domain, I just used a DTFT table, found the DTFT for $\left(...
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27 views

How can I implement a form of an autocorrelation of a signal?

Given a signal $x(t)$, how do I implement a form of autocorrelation function defined as $a(t,T) = x(t-T)x(t+T)$, where $T$ is an arbitrary constant? Ideally, the implementation should be fast, and ...
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49 views

Bandpass general equation to difference equation

I know this is a very basic question and I am coming out from a quarter of DSP. I want to create a function in Java which can taken in two parameters, either ...
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1answer
56 views

Is there a strategy for discrete control of a system with dynamics near sample rate?

I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to ...
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1answer
51 views

What can we understand when we increase the $N$-point DFT for a given signal?

I have an input sequence $$x(n)=\cos(0.48\pi n)+\cos(0.52\pi n).$$ I am determining its spectrum (amplitude of DFT values) based on the finite number of samples. For Example : Taking the first $10$ ...
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12 views

Discrete Wavelet Transform db4 [closed]

H, I want to know whether we can do Discrete wavelet transform dB4 in MSP430F5529? If yes what is the code to do it? Is any inbuilt function in C language to do the same?
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37 views

How is the energy of $x_1\cdot x_2$ related to the energies of $x_1$ and $x_2$?

Let's say first signal x1 = [1 2 3 4], second signal x2 = [0.08 0.77 0.77 0.08] (Hamming window), third signal ...
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2answers
246 views

Is my tranform the essence of DFT?

I'm someone just learning DSP, and want understand its essence. My transform is the simplest possible. Input signal is just one frequency: $256\textrm{ Hz}$. Sampling frequency is $2560\textrm{ ...
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1answer
37 views

A digital feedback network question

I saw the following digital network in a technical journal. I think the network's processing cannot be implemented because there is no delay element in the feedback path. How can we compute the "...
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34 views

Data reduction for a data collected from micro controller?

I have been given a project where I have to collect data reduce its size and send the data via bluetooth to some other storage. At first I thought it is simple data compression and used zlib and ...
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1answer
64 views

How is quadrature mixing done?

I've a Gaussian modulated signal whose quadrature and in phase components are separated. I'm multiplying these components with quadrature and in phase components of a signal of 10MHz frequency, ...
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1answer
48 views

Difference equation with complex zero

Let's assume I have the following transfer function: $$ H(z)=\frac{z-\left(\frac{1}{\sqrt{2}}+i \cdot \frac{1}{\sqrt{2}}\right)}{z} $$ It looks like a first order highpass-filter with a complex zero ...
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2answers
80 views

The mathematical interpretation of DFT [closed]

We have the DFT(matrix form) $X = Wx$ ($W$ is the Fourier basis matrix, $x$ is the original signal in time domain, $X$ is in the frequency domain). In mathematics, $x$ represents the coordinates of $...
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1answer
32 views

Classifying Discrete time filter

So let's say i have this frequency response of a digital filter: My question is how can i classify this type of filter ( low pass, high pass,...)?
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76 views

Method of reconstructing a band-limited signal from discrete samples

I understand current cell phones use digital communications. Given that this industry brings in billions of dollars each year, there is much incentive to get the best performance possible. So what ...
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1answer
17 views

Relating phase shift to the ROL/ROR operations

Is phase-shifting in continuous-time analogous to the rotate-left (ROL) and rotate-right (ROR) operations in discrete-time?
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1answer
15 views

Stability of the summation function

Stability of the below function was asked. $$ T(x[n]) = \sum_{k=n_0}^n x[n] $$ I understand that $x[n]$ shouldn't exceed $M$ value. $x[n]\le M$. I mean, we are looking for if the input is bounded, ...
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1answer
33 views

Simple discrete time transformation $x[(n-1)^2]$

If I want to do the following transform $$x[(n-1)^2]$$ I have thought about substituting each value of $n$ in $x[n]$ according to $x[(n-1)^2]$ i.e at $n=0, x[0]=1$ to put it in $x[(n-1)^2]$ $x[(...
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2answers
42 views

Very simple question about signal periodicity

$$x[n] = u[n]+u[-n]$$ Is it periodic or not? My answer is $$u[n] = {1 , n\geqslant0}$$ $$u[-n] = {1 , n\leqslant0}$$ which means that the signal $x[n]$ is always equal to $1$ from $-\...
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Inverse Discrete Wavelet Transform - partial reconstruction

I'm pretending to approximate a time series/vector usind dwt , with haar filter, in R. I can apply the full ...
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25 views

How to implement PLL blocks in MATLAB

I want to implement a PLL in MATLAB with individual components as Phase Detector, LPF and VCO. My problem is in implementing the LPF. I have determined the values of the pole and zero for the Laplace ...
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1answer
27 views

Adaptive Piecewise Constant Approximation (APCA) with wavelets/DWT

I am trying to approximate a vector or a time series, in order to have as little changes as possible. To do so, I pretend to apply the Adaptive piecewise constant approximation (APCA) algorithm. ...
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61 views

DFT of a continuous quasi-periodic signal

If I have a continuous quasi-periodic signal and I want to do a DFT of signal then what could be appropriate length of continuous signal that I should consider for sampling? I want to do DFT of the ...
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1answer
39 views

Wavelet transform in MATLAB

Suppose I have a wave with $20 \textrm{ kHz}$, $100 \textrm{ kHz}$ and $300 \textrm{ kHz}$. Sampling frequency used is $1000 \textrm{ kHz}$. I apply the discrete wavelet transform on the wave like <...
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1answer
52 views

Implementing Welch's method for Power Spectral Density

I want to implement Welch's method for PSD calculation in MATLAB. I do not want to use built in MATLAB cpsd function, such that I can change the FFT implementation ...
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1answer
37 views

MATLAB and sampling rate

I have a question about sammpling rate in MATLAB. I read a .wav file using audioread(). It give me sampled data called ...
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1answer
19 views

How is the matrix $\mathbf R_x$ not Toeplitz in case of a signal missing one term?

I am solving a question that says if we have sequence $x(n)$ of a signal missing one term then we have to find autocorrelation matrix $R_x$ as follows: $$R_x = E\{\mathbf {xx^H}\}$$ Now if I take $...
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1answer
25 views

Difference in following random proccess

Let just say I understand the first process that is white noise, Process 1: If $x(n)$ is a Gaussian random variable and a process is formed from a sequence of $x(n)$ and all random variables ...
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18 views

concerning the usable frequency band of signal

The spectrum amplitude of the response of instruments is generally trapezoid-shaped, with a flat portion in the middle and decaying at higher and lower frequencies. By deconvolving with the ...
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2answers
35 views

Measuring amplitude of a spectral component

I'm trying to measure the amplitude of a spectral component in a signal. The component's frequency is always known beforehand. I take a given number of samples, apply the flattop window to reduce ...
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1answer
49 views

Envelop detection with low sample rate?

I have a signal up to $3\textrm{ MHz}$. The ADC that sample it has a rate of $1.5\mu s$. So a full $T$ of the signal is $0.3\mu s$, and I can only sample each $1.5\mu s$. It sounds not enough, but I ...
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2answers
142 views

Features of a non-periodic signal for comparison

I am looking for comparing a signal (256 / 512 point discrete | non-periodic ) (obtained after extracting some features from the captured image) with a database of around 5000 signals (256 /512 point ...
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1answer
34 views

Problems calculating Z-transform

I am trying to solve a class exercise in which I am given the following, in Laplace domain: $$G(s)=\dfrac{e^{-Ts}}{s+3}$$ $$H(s)=\dfrac{1}{s}$$ And I need to calculate $\dfrac{C(z)}{R(z)}$, which is ...
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1answer
42 views

Output a sine wave from samples-limits?

Using a micro-processor of 48MHz, I am trying to output a sine wave from the DAC (digital to analog ), and I am not sure if my ...
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1answer
25 views

Behaviour of the poles in transfer function $H(s)$, given system properties

If a linear system is causal and its impulse response is an energy signal. What's the behaviour of the poles of $s$-domain transfer function $H(s)$?
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27 views

Unique signal extraction from a cumulated signal

I'd like to start off by saying that I am not very experienced at signal processing, so I apologise in advance if I do not explain everything properly the first time. I would like to analyse the ...
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2answers
34 views

A question about the concept of the time

$\delta[n+1]$ equals to one only $n+1 = 0$ ? If the 1. is true, so what does a signal $x[n+1] $ stand for? Is this signal causal or anticausal? I mean, if 1. is true, $n = -1$, so is this signal ...
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1answer
43 views

Real Time Goertzel Algorithm

Why is Goertzel Algorithm considered a block algorithm? Given that my input is bounded, couldn't I just run it forever (taking every sample that comes out after some length N) given a big enough word ...
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26 views

Simple sample and reconstruction code - MATLAB

I am trying to go from theory to code. I take x (let say 16KHz is continuous time) then I sample it in 2Khz So I do ...
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19 views

Is adding zeros part of the Hermitian Symmetry process?

I have been reading about DMT/OFDM and every source I find defines their system differently. I simply want to know if zero insertion is part of the Hermitian symmetry process that produces real OFDM ...
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1answer
46 views

Why does Fourier zero-fill interpolation pad the middle frequencies?

In this: http://dspguru.com/dsp/howtos/how-to-interpolate-in-time-domain-by-zero-padding-in-frequency-domain the author says that we can interpolate a signal by zero-padding the middle frequencies in ...
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69 views

what is nyquist rate of $h(t)\cdot h(t)$ and $h(t)\circledast h(t)$

Let's say we have $h_c(t)$ as a continuous-time signal with bandwidth $B$ and we would like to sample it. To be able to reconstruct it correctly, the sampling rate must be greater than $2B$. Now ...
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15 views

How can i plot the power spectrum in terms of time history representation of a signal?

I have a signal and How to plot the power spectrum in terms of time history representation as shown in the below figure in MATLAB. and also i would like to plot the spectrogram as shown in the ...
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41 views

Filter Design near Nyquist frequency (complex curve fitting)

I'm fitting IIR filters to a complex transfer function with Matlab's invfreqz.m. My fitting results are very good, but when I come very close to the Nyquist frequency the phase response runs to 0 and ...
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312 views

What really means stationary and non-stationary?

I really struggle to find out what really means stationary signal. There are some nice definitions in textbooks and wikipedia. But what that means in practice? To understand what is it, please answer ...