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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21 views

Can largest-triangle-three-buckets downsampling method used with fourier transformed signal?

I've been reading on the largest-triangle-three-buckets downsampling method for downsampling. Though it was originally published in the thesis "Downsampling Time Series for Visual Representation&...
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11 views

How does the band pass wavelet act as a high pass filter in DWT

I am understanding that wavelets have a bandpass filter response due to their compact support, and when doing decomposition they are used as a high pass filter along with the scaling function as a low ...
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1answer
45 views

Fourier transform of the sampled signal

I want to calculate Fourier transform of the sampled signal in two ways. Let $$s(t) = \sum_{k = -\infty}^{\infty}\delta(t - kT)$$And $z(t) = x(t)s(t)$. So we have $$z(t) = \sum_{k = -\infty}^{\infty}x(...
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1answer
25 views

Some questions about the intuition of the DWT

Assuming a DWT of a signal of length 8 with Haar filter taps. At the lowest level, I end up with a3 and d3 both of length 1, d2 of length 2 and d1 of length 4 which is the same number of coefficients ...
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1answer
18 views

Matlab: xcorr: Having trouble when I try to calculate delay between two sinusoids

I have a problem when I try to use Matlab built-in function for cross-correlation 'xcorr'. Background: I created two sinusoids, one of them delayed in time. I choose center frequencies of these ...
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11 views

Output of LTI diagram with this question and is it stable

the input δ(t) and output of a LTI signal is shown below. 1- is this system casual? 2- is it stable? why? 3- draw the output of the system. Tnx in advance
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2answers
83 views

Ideal Lowpass Filters

I am a beginner to Digital Signal Processing. I took this course of DSP from Coursera in which I am stuck with this question. Since, I am new, please be descriptive. Any help will be appreciated. ...
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1answer
42 views

Calculating IIR Filter gain at given frequency

Let's consider an IIR filter with transfer function: $H(z)$. Given the sampling frequency $F_s$ how can I calculate gain at say $F$ ? When I was dealing with analog systems when I wanted to calculate ...
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30 views

How to convert ofdm symbol to signal?

Hello may I know how to convert ofdm symbol generated from ifft block to an OFDM signal for the purpose of transmitting it?
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3answers
57 views

How to improve the Kalman filter for tracking the periodic motion of a car?

I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad. Here is my situation. I have a ...
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1answer
30 views

How to construct Neyman Pearson statistic to detect discrete signal in AWGN with unknown location?

I have a discrete datastream of length $10^5$ samples. Somewhere embedded in it is a rectangular pulse of unknown amplitude (prior probability of data containing signal is 0.5) and width 100 samples. ...
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1answer
49 views

Can time-invariance be determined from a given a transfer function?

I've the following function. $$ G(z) = 2 + \frac{-1+5z^{-1}}{(1-0.5z^{-1})(1-z^{-1})}$$ Calculating it's inverse using $\mathcal Z$-Transform, I get the following function: $$g[n] = 2\delta[n] + 8u[n] ...
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Detecting complex signal within complex AWGN using Neyman Pearson statistic

I need to construct a Neyman Pearson statistic for detecting a complex signal with known amplitude and unknown phase in additive complex Gaussian noise. My hypotheses are: \begin{align} \mathcal{H}_0 &...
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2answers
66 views

1D DCT matlab code

I was writing MATLAB code to compute 1D DCT of sample y. On computing DCT for y=[0,1,2], code generates coefficient ...
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3answers
72 views

Meaning of sampling frequency?

Say there is a communication system, which can manage sampling frequency up to 4 MHz (given by software). Can the system be able to process signals with maximum frequency more than 2 MHz? Because ...
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1answer
40 views

Deriving of magnitude, phase response and impulse response of transfer function

I have a transfer function as $$H(z) = \frac{-0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z - 0.0625}{z^4}$$ I want to derive magnitude and phase response of this equation. can someone help me from here I ...
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30 views

How to plot poles, zeros and impulse response of a transfer function

I want to plot poles and zeros as well as impulse response of a transfer function that is given below: $$H(z) = -0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z -\frac{0.0625}{z^4}$$ For poles and zeros, I ...
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When are MLSE (with Viterbi algorithm) equalizer used in real life (only for equalization)?

The complexity of a MLSE decoder (with Viterbi Algorithm) is in the order of $M^L$, where $L$ is the length of the channel and $M$ is the order of modulation. My question is in what circonstances, it ...
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68 views

Separating/recovering base signal from two mixed signals, given phase information

I have collected two signals, $B_1(x)$ and $B_2(x)$. The signals start and end at the same $x$-values. Each signal $B_i(x)$ contains: a base signal $b(x)$, which is the same for both, and a signal, ...
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Are there any real world applications for complex-valued signals or impulse responses?

I was just curious... $$x[n] {\longrightarrow} \boxed{h[n]} {\longrightarrow} y[n]$$ I've never seen a real world filter where the coefficient of $h[n]$ were complex, or where $x[n]$ was a complex ...
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1answer
20 views

Having Problem about DownConversion

I hope, you are doing well. I want to ask question about baseband conversion. Background: I generated two AM signals in MATLAB, which one of them is shifted in time. I multiply the signals with $\cos(...
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1answer
26 views

what is the relationship between the reliability of a monte carlo test and the length of the samples tested and the number of errors found?

Considering this setup, single tone transmission over a channel impaired by AWGN, doppler spread, and inter symbols interference. We are to compute the BER as a function of the SNR. We want to find ...
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1answer
17 views

deconvolving a 1d signal using a lookup table of “PSFs”?

assuming I measure a signal that has different PSFs per position in time. for example: ...
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1answer
43 views

What the disadvantages of up-sampling

Let's say we have a signal $x[n]$ upsampled at the transmitter by $4$ and then downsampled at the receiver by $4$ too. As known, the performance will be much better compared with transmitting the ...
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2answers
62 views

Showing error energy goes to zero

Let $$\hat{x}[k] = \frac{1}{2\pi}\int_{-W}^{W}X(e^{j\omega})e^{j\omega k}d\omega,\label{ift}\tag1$$ where $$X(e^{j\omega}) = \sum_{n=-\infty}^{+\infty} x[n]e^{-j\omega n}\label{dft}\tag2$$ Also, $$d[k]...
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2answers
55 views

Coefficient Scaling of IIR filter to obtain unity gain response

I am designing a 2nd order IIR digital filter : My tf equation with coefficients is ...
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1answer
28 views

How to apply band-pass filter and get the filtered back from frequency to time domain in python?

I know this is basic for signal processing, but, I am not sure what is wrong about my approach. I have a signal that behaves as damped sine signal with a sampling frequency of 5076Hz and 15,000 number ...
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1answer
73 views

Duality in the discrete-time Fourier series

Suppose $g[n]$ is periodic with fundamental period $N$ and $f[k]$ being its Fourier coefficients i.e. $$ f[k] = \frac{1}{N}\sum_{n=<N>}g[n]e^{-j\frac{2\pi}{N}nk}$$ In more convenient notation $$...
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1answer
39 views

Confusion regarding notation/symbol?

I was reading circular convolution topic from Digital Signal Processing Using Matlab 3rd Ed,by Proakis. I came across a strange term/symbol; I have highlighted it in attached snapshot I have also ...
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23 views

Filtering out symmetric noise from an oscilloscope reading

I have a signal that looks like this: The data is readings from two oscilloscope channels, one color coded blue, the other color coded orange. I would like to filter out the supply noise (all the ...
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1answer
32 views

Conjugate symmetry of the DFT of real-valued sequences

I have read about Fourier transformation that real signals are "mirrored" in the real and negative halves of the Fourier transform because of the nature of the Fourier transform. For ...
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1answer
29 views

Understanding index transformation in derivation of Fourier transform for sampling rate reduction

Was going over some notes regarding deriving fourier transform equation for Sampling Rate Reduction. Reference to Notes from below link https://ocw.mit.edu/courses/electrical-engineering-and-computer-...
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1answer
27 views

How are these two discrete time signals equal?

How are these two signals equal? What I have tried: $ x[n] = (-3)(-2)(-2)^{n-1}u[n] + (-2)^{n-1}u[n] $ I am not sure how this leads to the answer.
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1answer
37 views

Convolution that outputs a unit impulse

Im thinking whether any convolutional operation can output a unit impulse, an example to further explain: where a convolution between system $h[n]$ and unknown system $g[n]$ would output $\delta[n]$. ...
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13 views

scipy.signal.deconvolve not working, Blind deconvolution in python

I am trying to deconvolve my original signal with a given wavelet (Ricker wavelet). But scipy.signal.deconvolve is not giving any output to the signal. Impulse signal can be generated by below code. ...
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2answers
55 views

Z transform of finite signals

I was trying to solve the Z-transform for u[n] - u[n-N], where u[n] means discrete unit step function, and N is some finite integer. I solved this using 2 methods. ...
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1answer
11 views

A question about the Commutativity Property in discrete signals block diagrams

According to the Commutativity Property of block diagrams, we can place b0 at the entrance or at the exit of the block diagram, it wouldn't matter. My question is, if we placed it at the entrance, we ...
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28 views

How to make noise power estimation on a single tone transmission?

Suppose we have a single tone transmission over a Single Input, Single Output (SISO) channel impaired by Inter-symbol Interference and Additive White Gaussian Noise (AWGN). How to compute the noise ...
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1answer
14 views

Frequency response of discrete PT1 in MATLAB

I want to calculate the frequency response of a discrete PT1 system with T=T1 and K=1. (the code is at the bottom of the question) To validate the magnitude response, I want to use an sinusoidal input ...
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1answer
54 views

Stationarity, discrete-translation operator, and the power spectral density matrix

Let $\mathbf{T}$ be the translation operator/matrix in discrete-time domain which can be written as $\mathbf{T} = \mathbf{\Phi} \mathbf{P} \mathbf{\Phi}^*$ where $\mathbf{P} = \exp(-i Diag([w_0, w_1, \...
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1answer
59 views

How FIR filters provide a linear phase?

I know that we can design a linear phase FIR filter by choosing filter coefficients symmetric or antisymmetric, what is the intuitive idea behind that?
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1answer
28 views

Discretize process noise in Kalman filter

Reading P. Andrews et al. I see that it is very common to do the following approximation of the process noise covariance matrix: $$Q_{k} = G_{k-1}QG_{k-1}^{T}\Delta t$$ so that the propagation ...
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6 views

For single tone transmission impaired by IES, how Doppler Spread is translated in Channel impulse response computation?

If we are to transmit in single tone transmission in a Single Input Single Output configuration. And the channel is impaired by awgn and inter symbol interference with the following characteristics: ...
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2answers
77 views

Why FIR uses often direct-form instead of transposed-form?

Even though tranposed-form has less computational burden and memory requirements, why FIR uses mostly direct-form?
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1answer
26 views

What do coeffcients mean from Matlab?

I ask for a brief explanation of each coefficient and their sources of related information. Thank you very much in advance. The coefficients comes from this code below: I've got a robust linear ...
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1answer
32 views

Comparison of results with Direct form1 and Direct form2 implementation of IIR filters

The results obtained from Direct form1 and Direct form2 implementations (in C language) of IIR (BiQuad) filters are a little different. In the implementation, i have made the b0 coefficient as 1. So, ...
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1answer
27 views

Determining if the system is linear and time invariant

The Fourier transforms of input $x[n]$ and output $y[n]$ of a discrete-time system are related by the following equation: $$Y(e^{j\omega}) + (e^{-j\omega})Y(e^{j\omega})= X(e^{j\omega}) - X^{'}(e^{j\...
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1answer
82 views

What is the difference of windowing functions for FIR filtering?

What is the difference of window types such as Hann, Rectangular, Hamming in the application. Is there such a thing that the one is better than the other? There will be an oral exam for DSP course ...
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1answer
109 views

Why a pair of complex-conjugate zeros provide a nulling filter? (FIR filter case)

FIR filter having a pair of complex-conjugate zeros that lie on the unit circle, with zeros of the form: $$ z_1 = e^{j\omega_i}\qquad\text{and}\qquad z_2 = e^{-j\omega_i} $$ And transfer function: $$ ...
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18 views

What is the intuitive idea behind FIR filter order and filter parameters? [duplicate]

I know that if we decrease stop-band and pass-band attenuation, and also decreasing the transition band, the filter order will increase as well as filter performance. But what is the intuitive idea ...

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