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

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63 views

Why is cos(n/6) aperiodic?

This is a very common example in most Signal Processing books I have come across. x(n) = cos($\frac{n}{6}$) is a non-periodic discrete signal because it doesn't satisfy the periodicity condition for ...
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1answer
54 views

Closed form of $\mathcal Z$-transform : decomposition signal $x(n)$

The text of my exercise ask : Determine the closed form of the $\mathcal{Z}$-transform for this $x(n)$ $$ x(n) = \begin{cases} |n-N| & \text{if 0<$n$<2N} \\ 0 & \text{elsewhere} ...
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1answer
33 views

IQ imbalance amplitude

I have to fix the amplitude of measured IQ receiver data. According to my information about the data, I can estimate that one signal needs to be corrected to the other in amplitude. The phase ...
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4answers
140 views

Sampling Theorem: How to know the value between two samples of a Signal

According to Sampling theorem, in order to reconstruct a signal we need to sample it at the rate => twice the highest frequency component of that signal. (provided signal is band limited). Let's say, ...
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1answer
29 views

Initial conditions for the LTI systems described as a difference equations

Why do we need the initial conditions to be zero for the LTI systems described as a difference equations? First question is why do we need it for linearity? I can't think of any example of the non ...
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1answer
68 views

Daubechies wavelet transform

i have N samples obtained by sampling a signal with lot of frequency contents. How will i apply daubechies wavelet transform to obtain the frequency and its location? i need to write a program which ...
3
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1answer
63 views

Downsampling and Then Upsampling

Given this system: I need to show the $\mathcal Z$-transform of $y[n]$ as a function of the $\mathcal Z$-transform of $x[n]$. Now I know that for downsampling alone: $$Y(z) = ...
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1answer
87 views

What is the benefit of FFT when we're already sampling at an acceptable rate?

As I'm learning about DSP I can understand the process of taking a continuous signal into a discrete signal. I understand an oscillator producing different types of signals, including a periodic ...
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7 views

Interpretation of Diagonal detail wavelets

I am a statistics grad student, and I have just begun exploring the topic of wavelet regression (specifically, Haar wavelets for discrete functions). I understand the generalization from a one ...
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0answers
18 views

Fractional Interpolation Polyphase

I explain my problem. I have to implement an oversampled filter bank. The first stage of the general architecture is serial to parallel converter with a decimation factor M < K channels. In my case ...
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1answer
34 views

Finding parameters of exponentially decaying sinusoids (Matrix Pencil Method)

The matrix pencil method is an algorithm which can be used to find the individual exponential decaying sinusoids' parameters (frequency, amplitude, decay factor and initial phase) in a signal ...
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0answers
28 views

polyphase fractional interpolation

i've a tricky question. Suppose to have an adc with 16 output lanes, in which the data are formatted as follow: s16 s0 s17 s1 . . . . . . s31 s15 Each lane ...
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1answer
36 views

Which one is the correct graph for u(2-n)?

U(n) is the unit step function in discrete form. I want to know which one of the following two is the correct waveshape for U(2-n), where k is a constant? I included a picture for your better ...
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3answers
36 views

Does the hold part in sample and hold turns the signal from discrete to continuous?

I am trying to link sample and hold to discrete and continuous time domain. Could someone please confirm: When sampling but not holding for "an extended" period of time, you have discrete samples. ...
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0answers
28 views

Help DFT Filter Bank

I'm implementing maximally decimated FB on matlab and it's happening a strange thing. If i implement parallel filters, the output is near reconstructed, without aliasing in other channels, while if i ...
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0answers
18 views

Optimize an impulse response function to reduce PAPR

I would like to reduce PAPR (Peak to average power ratio) for single carrier system by decreasing magnitude of the side lobes of impulse response function (Nyquist pulse) in time domain at transmitter ...
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1answer
26 views

Frequency range for set of all discrete-time sinusoids

Consider discrete time sinusoids of the form $$x[n] = \cos(\omega n) \ ,$$ where $n$ is an integer. What frequency range of $\omega$ would constitute all the possible sinusoids? I'm thinking that ...
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1answer
33 views

Is this a kind of aliasing error and how to make correction?

I use a Discrete Fourier Transform to have a representation in the frequency domain: Notice that, both the real and the imaginary line are softly reaching zero on the left, from 0.5 Hz to 0 Hz. ...
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24 views

Gaussian signal / image smoothing at sigma 0.5

I am currently reading up on Lowe's paper [1] on SIFT keypoint detection. On the page labeled 97 he mentions We assume that the original image has a blur of at ...
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1answer
13 views

Compression Ratio in ECG compression using Wavelet Decomposition

I have compressed and reconstructed an ECG signal using Wavelet Coefficient. In compressing part, many of Wavelet Coefficient have set to zero. for example, if in original ECG, 5000 wavelet ...
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1answer
43 views

How to calculate the discrete power of a discrete signal?

If I have a time series defined by a series like $$ x = [a_1, a_2, a_3, ..., a_n] $$ for time from $t = 1$ to $t = n$ How can I get to the power of the signal in this form: $$ P_x = [p_1, p_2, p_3, ...
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1answer
40 views

Apply band pass filter (BPF) before calculating the power of a signal (PSD)?

From my understanding PSD tries to give a good estimation on the power each frequency attributes to the overall signal power. If I am only interested in a frequency range $(\omega_0 \leq \omega \leq ...
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0answers
14 views

SISO model? white noise excitation

I'm now trying to do this problem. I have data set including input and output for both 600 gal and 800 gal, and 3 white noise excitations. But i don't understand the model of this problem. 3 White ...
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1answer
35 views

Adjust the power of a digital signal to a given value

I have two signals: $x(n)$ is a white-noise signal with a given variance, $y(n)$ is the sum of white noise plus a sum of sinusoids. $$ x(n) = v_1(n) $$ $$ y(n) = \sum_{i=1}^{q} [ a_i \cos(\omega_i n) ...
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0answers
19 views

what is the relationship between DFS, DTFT and DFT? [duplicate]

The concepts of DFS,DTFT and DFT are pretty confusing. I went through many blogs and books but still the concepts are not clear. However my understanding is that: For an aperiodic discrete time ...
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1answer
23 views

Hessian Matrix. Second partial derivative test

I have a question about the hessian matrix / determinant of the hessian matrix. For the Hessian matrix, one is able to determine the local curvature around a point. And with the Second partial ...
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23 views

Binary Orthogonal Sequences

The set shown below is a biorthogonal signal set. $\{|0000|,|0101|,|0011|,|0110|,|1111|,|1010|,|1100|,|1001| \}$ Any two codewords or signals can be checked for orthogonality using the equation ...
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24 views

Methods for edge detection with non-equidistant samples

This posting describes two methods of edge detection for wave analysis in a water pipe. I am not sure about advantaged and disadvantages. Therefore I want to evaluate the best method for this ...
3
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1answer
52 views

Question related to Disceret signal convolution

I have two finite signals $x[n]$ and $h[n]$, I want to convolve these signals using the method defined in Example 2.2 of Signals and Systems by Oppenheim. I am getting this answer $$ y[-3]=4, ...
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26 views

channel estimation in OFDM systems(MMSE Estimator)

I want to use the mmse estimator to estimate the channel in ofdm systems. I find the formula: h=Rgy*(Ryy)^-1*y[1],while Rgy is RggF'X'. My question is: in the ...
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0answers
13 views

How can I Map demodulated symbols using GRAY code [closed]

Could anyone help me by giving example how to do mapping of bits/ symbols using Gray code. your help will be much appreciated :)
3
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2answers
60 views

Is the book wrong? — How to sketch frequency response obtained from H(z)?

This question is directly related to digital signal processing, so I am asking here. How to sketch frequency response obtained from $H(z)$? I'm adding an example and its solution below. I did not ...
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3answers
51 views

What is the transfer function of this block diagram

I and my friend have different answer for this block diagram Mine: $$y[n] = -\frac23x[n] + x[n-1] -\frac12[n-2]$$ Hence $$H(z) = \frac{1}{-\frac23 + z^{-1} -\frac12z^{-2}}$$ My friend: ...
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1answer
44 views

How can spectrum of DTFT of sampled band-limited analog signal be in $[-\pi,\pi]$

Say the analog signal $x(t)$ and its spectrum $X_a(\Omega)$. After sampling with frequency $F_s$ or sampling period $T$ we get $$x[n] \triangleq x(nT) = x\left(\frac{n}{F_s}\right)$$ and its ...
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1answer
45 views

Help Solving a Difference Equation

I have an exam in my signals and systems class in a couple of days, and I'm unsure how to go about solving this practice problem. The question is as follows: Consider a discrete time system whose ...
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1answer
41 views

Relation between compressed sensing and incoherence

I am working on CS. I know that as coherence decreases (or incoherence increases) compressed sensing results improve. I know how to calculate the coherence, but I can't find an exact equation between ...
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2answers
67 views

Is the below filter linear phase

$$h(t) = \frac{1}{1 + t^2}$$ and is it IIR or FIR filter. I tried finding the Laplace transform of this filter to get the data flow diagram with 5 taps and T=2s, however, I am unable to solve this. ...
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1answer
55 views

$\int^{\frac12}_{-\frac12}X(f)e^{j2\pi nf}df=\frac{1}{F_s}\int^{\frac {F_s}{2}}_{-{\frac {F_s}{2}}}X(F)e^{j2\pi nF/F_s}dF$ for $f=\frac{F}{F_s}$?

I am using Digital Signal Processing Principles, Algorithms, and Applications 4th edition and by Proakis. Here is what I don't understand say the signal $x_a(t)$ has its Fourier Transform $X_a(F)$ ...
4
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1answer
46 views

Linear Prediction of AR Process

A discrete signal x is generated by the recursive process $$ x_n = x_{n-1} - 0.2 x_{n-2} + w_n $$ where $w_n$ is white noise with zero mean and unit variance. What is the optimum order of a linear ...
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0answers
19 views

Sum of the variances of the real and imaginary parts

I have a noise $\eta[k]$ and I performed IFFT to this discrete function to get $Z[n]$. In other words, $Z[n] = \textrm{IFFT}[\eta[k]][n]$. I have also found the expression for the variance of ...
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1answer
33 views

Which is the total energy of the product of two discrete energy signals

Assume that I have two signals with finite energy. The first, $x_s$ \begin{equation} E_s = \sum_{i=0}^{N} |x_s(i)|^2 \end{equation} and the second, $w$ \begin{equation} E_w = \sum_{i=0}^{N} ...
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4answers
79 views

Is the value of a discrete time signal 0 when the index is a non integer value?

Is it safe to assume that if the index of discrete signal is not an integer, then the value of it is 0? For example is the following true: If we have $x[n] = 1 + (−1)^n$ does $x[3/4]=0$? The TA in ...
1
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1answer
40 views

How to remove or filter the drift problem in measured Strain signal?

I have the strain signal of a lateral beam of a car measured at sampling rate 1,200Hz from data acquiring system. Even after using temperature compensation in strain gage, we are getting drift. So I ...
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1answer
33 views

Calculating similarity between bit strings/signal

I have a project I'm working on where I'm trying to efficiently compare sequences of binary data to determine how similar they are. Basically, a sequence might look like this: 1001010010100011110... ...
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24 views

How to get cofficients in DFT?

In my recent study of signal processing I came to know that we can compress images/signal using DFT/DCT. If we consider the lossy compression of audio or any image then it follows the same steps: ...
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4answers
369 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 thepicture below. But, in terms of signal processing, (a ...
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0answers
21 views

Emulate signal loss of a pixellated detector in Python?

I have a matrix 64x64 where each cell represents the pixel of a pixellated detector. The spacial response of this detector decreases by going further from its center (that is, coordinates "31,31" or ...
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0answers
13 views

'ADC' sort of conversion method to retain information

I have a program that reads 16 bit two's complement format data to plot/analyze graphs. I have a database text file with various decimals which represent real analogue data, ie. let's say they are ...
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2answers
30 views

What is the phase of the Fourier Transform of $h(n)={\frac13,\frac13,\frac13}$ (zero position is at 2nd element)

I am using Digital Signal Processing Principles, Algorithm and Applications, 4th edition written by Proakis and Manolakis. Here is s a part that I don't understand. $h(n)={\frac13,\frac13,\frac13}$. ...
0
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1answer
36 views

Design a FIR filter with a Kaiser window

Here is the exercise I am working on. Use the window design method with the Kaiser window to design a linear phase high pass FIR filter of minimum order that meets the folowing specification: ...