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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Discrete convolution tabular method

In the time discrete convolution the order of convolution of 2 signals doesnt matter : $x_{1}(n)\ast x_{2}(n) =x_{2}(n)\ast x_{1}(n) $ When we use the tabular method does it matter which signal we put ...
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Band pass filter = Band stop filter if you switch the cutoff frequencies?

The normalized frequency response of a N points bandpass digital filter is: $\frac{sin(\omega_{c2}(n-M))}{\pi(n-M)}-\frac{sin(\omega_{c1}(n-M))}{\pi(n-M)}$ where $\omega_{c1}$ is the normalized lower ...
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How to perform an analytical computation of the convolution sum for a discrete-time system?

I am trying to follow some notes on "Analytical Computation of the Convolution Sum (Graphical Method)" but am getting stuck on what I am doing, or if what I am doing is correct. There are 5 ...
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undecimated wavelet transformation

I have 20kHz sampled dc current data of 3 second (i.e signal length of 60000). I want to use undecimated wavelet transform to extract statistical features from it. But i don't know how to choose best ...
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1 answer
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Inverse continuous wavelet transform off by constant factor in the y axis

I have implemented the Continuous Wavelet Transform using the pycwt library(https://github.com/regeirk/pycwt/blob/master/pycwt/wavelet.py) and its inverse using Morlet wavelets, however, upon ...
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BPF design as cascaded second order biquads

I am trying to design a bandpass filter in MATLAB with following specs: $$\texttt{f_s = 20000Hz}$$ $$\texttt{3dB freq = [392 464]Hz}$$ $$\texttt{filter order = 8}$$ When I tried to implement the ...
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Invertible system for the eigenfunction $x[n]=e^{j\omega n}$

I was doing some calculations in my LTI systems course and I stumbled in an interesting question I wasn't really sure how to answer so I'd appreciate any direction or solution you can give me: I'm ...
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Convolution of $n(1/3)^n \cos(n\pi)$ and $u(n)$

I am trying to solve the following question in a dsp book on convolution Evaluate the convolution of the sequence $$x(n) = n\cdot(1/3)^n\cdot\cos(\pi n)$$ with the unit step $$h(n)= u(n)$$ I followed ...
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1 answer
45 views

Convolution of $(3/4)^nu(n-2)$ and $2^nu(-n-5)$

I am trying to convolve the two discrete sequences $$\left(\frac34\right)^nu(n-2)$$ and $$2^nu(-n-5)$$ where $u(n)$ is the unit step function. Here is how I approached the problem ,using the ...
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What type of filter is that?

I have a transfer function in z-plane with two poles and two zeros. I plotted the function with matlab ...
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3 answers
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How to align timeseries by decimating while preventing aliasing?

I have two pandas DataFrames, dfb and dfv, where dfb has a higher sampling rate than ...
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1 answer
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Unstable deconvolution in frequency domain (spurious high frequency component?)

I have a black box-like deterministic model $h(t)$, which provided with a real-valued input $x(t)$ returns a real-valued response $y(t)$. The model should produce little to no noise. My goal is to ...
2 votes
0 answers
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Discrete cosine transform as the limit of PCA

On the Wikipedia article about Discrete cosine transform it is said: For strongly correlated Markov processes, the DCT can approach the compaction efficiency of the Karhunen-Loève transform (which is ...
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1 answer
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Why does MP3 use modified DCT?

I read on Wikipedia here that the MP3 standard does use a modified discrete cosine transform. My question is: why does it use a modified transform and not the original DCT (like the JPEG standard)? ...
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Implementing a high pass filter in MATLAB

I am trying to implement a high pass digital filter in MATLAB. High pass filter: ...
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Matlab's FFT wrong?

In my previous question, I tried to implement the DFT. Now I want to compare it to Matlab's FFT My input signal is: x(n) = n-2>=0 Here are the results: As you ...
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1 answer
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Why cant DFT be implemented this way?

I am trying to implement the discrete Fourier transform.Here is my code in MATLAB: ...
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2 answers
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Behaviour of difference equation does not match that of its z-domain transfer function

I have obtained the following z-domain transfer function: $\frac{Y(z)}{U(z)}=\frac{3.3641×10^{-7}×z^{6}+1.5584×10^{-5}×z^{5}+6.7263×10^{-5}×z^{4}+ 5.5016×10^{-5}×z^{3}+8.525×10^{-6}×z^{2}+1.2303×10^{-...
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1 answer
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Discrete Fourier Transform and Incomplete Fourier Series

I'm working on a paper where I'm collecting sound pressure data from a chord's wave and trying to create a frequency spectrum to find the individual frequencies that make up the chord. However, I can'...
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1 answer
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Using the DFT to determine the component of a signal at a given frequency?

I'm struggling understand the mathematics behind how the component of a sampled continuous signal at a given frequency can be determined. Assume my sampling rate is $f_s=100$ for 3 seconds, so $N=300$....
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2 answers
50 views

Discrete-time system: divergent response to exponential input

I’ve been given the following Difference Equation and tasked with finding the response to $x_0[n] = (-p)^n$ - I’ve managed to $h[n]$ but the convolution itself failed.(The given system is IAR). $$y[n] ...
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How to do QAM modulation and plot the constellation diagram for a complex signal (I+jQ)?

I want to plot the constellation diagram of 64-QAM for a complex signal, x = cos(2*pi*n/N) + 1i*sin(2*pi*n/N) where ...
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1 answer
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Why and How the plot between the real and imaginary component of an analytic signal is in the form of an ellipse pattern?

Why and How the plot between the real and imaginary component of an analytic signal is in the form of an ellipse pattern ? How does the ellipse pattern varies with the variation in real and imaginary ...
2 votes
1 answer
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Crossfade for files vs for speakers

I'm fairly new to crossfading albeit having a fairly good understanding of the mathematics and physical units. What I can't wrap my head around is as to whether there is a difference between ...
1 vote
1 answer
184 views

Discrete signal time shift

Suppose we have a discrete signal $x[n]$ and $y[n] = x[2n]$. I want to find $y[n-k]$. Is it $x[2n-k]$ or $x[2n-2k]$? I'm very confused by this operations. Can someone explain what's the logic behind ...
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Understanding the signal to noise ratio (SNR)

In my work, I came across the following expression of signal to noise ratio (SNR) which contains expectation operator. The received sampling vector is $\textbf{y}(n) = \textbf{h}s(n)+\textbf{u}(n)\tag{...
2 votes
2 answers
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Reconstruction of a Ricker Wavelet using inverse discrete fourier transform - signal cut in a half?

I am new here and new to DSP, so maybe my question is really basic. I have the formula for the Ricker wavelet (Mexican Hat) in frequency-domain and I wish to do an inverse Fourier transform to recover ...
-1 votes
2 answers
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Is square of signal more recoverable than signal itself?

Let $x[n]$ be aliased sampling of real-valued $x(t)$ over $t_0 \leq t \leq t_1$. Can $|x(t)|^2$ be recovered more accurately than $x(t)$, over $t_0 \leq t \leq t_1$? If so, how? For $|x[n]|^2$, ...
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Can we control the minimum of a continuous signal $x$ when some Fourier coefficients are constant?

Let us fix a sequence of real numbers $\{a_k\}_{k=-n}^n$ and $\gamma\in \mathbb{R}$. Is there any $2\pi$-periodic continuous signal $x :\mathbb{R}\to \mathbb{R}$ such that the following points ...
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4 answers
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Is it possible to find the FFT of a 1024-point signal by taking 8-input points at a time and calculating the FFT of those 8-points until the end?

Suppose the input signal has 1024 samples, and I want to take a 1024-point FFT. Can I instead take the 8-point FFT of the first 8 input samples then another 8 samples and continue this till the end? ...
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1 answer
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Why is DFT magnitude less than expected?

Code for signal: ...
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117 views

What is the definition of an incrementally linear system?

Even though the concept of an incrementally linear system is mentioned in several textbooks, I haven't found an explicit definition. What exactly do we mean by "incrementally linear"?
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Can we control the maximum norm of a continuous signal whose finitely many Fourier coefficients are fixed?

Let us denote $C_{2\pi}$ by the set of all $2\pi$-periodic continuous signals $x:\mathbb{R}\to \mathbb{R}$. Fix $n\in \mathbb{N}$ and put $$\Lambda_n=\{y\in C_{2\pi}: \mathcal{F}(y)[k]=0 ~\...
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Numerically observe the rotation property of the Fourier transform

I would like to numerically observe the rotation property of the Fourier transform. I believe that it is not possible since the rotation property is for the continuous transform and the DFT introduces ...
1 vote
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39 views

FMCW radar IQ data constellation

I am trying to replicate the basic method of vital signal detection based on FMCW radars I found in classical literature on the subject. The issue I am facing at the moment is that of IQ data DC ...
1 vote
1 answer
35 views

How can I compute the coefficientsof the impuse response given a signal? [closed]

How can I compute the coefficients of the transfer function with the following difference equation: $$y[n]=x[n]+y[n-1]-0.5y[n-2]$$
2 votes
1 answer
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scipy convolve and fftconvolve return different output [closed]

I'm writing an autocorrelation function using and I noticed a difference between fftconvolve and convolve that should use fft if it's faster. This is my function with convolve: ...
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1 answer
54 views

Cross corelation between two complex-valued Time Series Objects

I am exploring the cross correlation function in Julia between two complex-valued Time Series Objects Z1 and Z2 with this simple code: using DSP Compute the cross-...
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1 answer
48 views

Based on the eigen structure, What applications of discrete sine/cosine transformations can be found?

I am a PH.D in mathematics. I am interested in finding some applications of discrete Sine/Cosine transformations (DTTs) that are based on the eigenvectors. I have found some results concerning ...
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How to perform an operation on a signal which depends on 2 variables?

How do we perform DFT when the input signal depends on 2 variables (like in a image the color of the pixel depends on both $x$ and $y$)
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How can I find $x_r(t)$ in this case?

$$x_a(t) = 10 + 4\cos(30\pi t +\frac\pi 3) - \sin(250\pi t + \frac 14) -3\cos(500t + \frac \pi4) $$ $\textbf{Question:}$ This signal is first sampled at a rate of $f_s = 100$ samples per second to ...
1 vote
1 answer
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Distributed Arithmetic FIR Vs basic FIR digital implementation

I make a comparison between the basic FIR filter Vs Distributed Arithmetic FIR First: basic FIR Second: DA FIR Then, I implemented Distributed Arithmetic FIR Filters by 2 methods: 1st: Serial If the ...
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3 votes
3 answers
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Why can two different signals have the same periodogram?

I have just started trying to self-study an intro course on signal processing. I have just been introduced to the periodogram and have a hard time understanding why completely different signals can ...
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0 answers
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Finding delay between two sensors measuring two phenomena

I have two sensor data with noise, a moving object's GPS position and acceleration data. It's known that there is a delay between the data. How do I find this delay? I have no prior knowledge of ...
1 vote
2 answers
123 views

Why Fourier transform can be applied in digital signal processing?

Fourier transform can be used to analyze the frequency domain of a specific period of signal. However, I saw many of these transforms in textbooks are based on entire signal sequences, not processing ...
1 vote
2 answers
114 views

Relationship between energy, power and sampling rate?

Excuse my silly question, but I think the energy increases as the sampling rate increases. In the time domain, the number of samples increases so the energy increases; In the frequency domain, ...
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1 answer
38 views

Can a filter be fit to explain a response?

I'm trying to classify a stimulus-response relationship and would like to fit a filter that best explains the response. I don't really work in DSP so there may be some vocabulary I'm missing, but ...
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1 vote
1 answer
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What are the Kalman filter capabilities for the state estimation in presence of the uncertainties in the system input?

I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system. In the time being I have been using a discrete ...
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1 answer
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Expressing the frequency response in a more 'compact' form

I've just been working through the questions in Discrete-Time Signal Processing (Oppenheim and Schafer) and I came across this (Q33): Consider an LTI system defined by the difference equation $$y[n] =...
2 votes
1 answer
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Signal reconstruction given non-impulse sampling

With sampling modeled as a multiplication with a dirac comb, we can recover the original signal perfectly with a low pass filter given that the sample-rate criterion is satisfied. What about a more ...

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