# Questions tagged [discrete-signals]

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

318 questions with no upvoted or accepted answers
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### Detection time of a spur using FFT?

Say I have the following parameters, NFFT=2^14 Fs= 50 MHz main signal @ 22 MHz and its alias at 28 MHz at signal power -40 dbfs and a spur @ 2 MHz and its alias at 48 MHz Leave aside the alias's. ...
56 views

### how do I derive the system equation for a simple delay with feedback?

I am a software engineer, and just learning digital signal processing formally, though I've hacked around before a fair amount. I'm implementing a delay audio VST and I'm trying to wrap my head ...
150 views

### Prove that, in DFT ,interpolation in time domain is equal to replication in frequency domain

Given: $x[n]$ is an $N$-point sequence whose DFT is $X[k]$ $$x[n]\xrightarrow{\mathcal{DFT}} X[k]$$ then, Prove that: DFT of the same sequence after insertion of $(M-1)$ zeroes between successive ...
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### ACF of $X_t = a + bt$

I was able to prove the following convergence results. But how can we determine the theoretical autocorrelation function of the deterministic sequence $X_t = a + bt$ and $X_t = c\ \text{cos}(\omega t)$...
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### what is the co-variance of system output cooresponding to a non-iid random variable

Consider the following system.$\DeclareMathOperator{\sign}{sign}$ \begin{aligned} &\dot{e_1}=c_1e_1+c_2e_2+\eta\\ &\dot{e_2}=c_3e_1+c_4e_2-c_5 \sign(e_1)+a \eta \end{aligned} which $\eta$...
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### Discrete vs Continuous Power Spectrum Analysis

Let's suppose we have a time signal of watt units which in the frequency domain transforms into a sinc-like spectrum. The amplitude of that spectrum will likely be also of watt units. In order to find ...
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### Should PSD be smoothed for SNR computation in frequency domain?

When taking the Power Spectral Density of a short duration signal (say 1 second, sampled at 4096 Hz), should it be smoothed to compute SNR? I want to computed the matched filter SNR, perfectly knowing ...
54 views

### How to sketch this multirate system spectrum?

In the following system: The signal x(n) is upsampled by 2 and then filtered. The signal and the filter have the following spectrum: After upsampling the spectrum of X would look the same except ...
39 views

### How to remove sum and difference terms while computing frequency from fft?

I am currently operating in vhf band AND trying to detect frequencies using Fast Fourier transform thresholding method. While detection of multiple frequencies , i received spurs(May not appropriate ...
67 views

### Ways to differentiate three respiratory signals

I have three 1-min respiratory signals I derived from ECG signals. I am wondering if you guys have any suggestion on differentiating those three? The red line represents the experimental signals and ...
93 views

### DFT truncation of signals

How can I calculate 8 point DFT of signals whose length is less then 8 ( say 2,4) then what will I assume other members in formulae "0" or rotation or keep repeating the same two numbers Consider I ...
86 views

### How can I find inverse Z transform using synthetic division method when Region of convergence is bounded rather than right sided or left sided?

Explanation of synthetic division method Above example has region of convergence of type mod(z)>mod(a) I want to solve problems when region of convergence of type mod(e)>mod(z)>mod(d)
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### Detecting changes in signal due to server delay

I'm currently working on an application that can be used to determine when a signal changes due to a server delay. Essentially, I have an API that is used to output data to a UI. However, for reasons ...
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### 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 ...
219 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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### 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 ...
42 views

### Interpreting Auto correlation results

I used xcorr function in Matlab to compute the autocorrelation of my signal. I obtained a graph, which is shown below. How to interpret this? I read that autocorrelation helps in finding the patterns ...
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### How to low pass very few samples

I'm asking myself what is the best way to low pass a signal which only has a few hundred samples? Or is there a proper way at all? It must not be a sound signal but I used Audacity to display the ...
75 views

### Region of convergence for discrete system

I am confused by two questions on the region of convergence (ROC) when applying the $Z$-transform. Consider a discrete-time linear system $$x[n+1] = Ax[n]+Bu[n], \qquad y[n]=Cx[n]+D$$ whose transfer ...
79 views

### About the variance of the coefficient of narrowband noise when using signal-space representation

Assume that n(t) is a white Gaussian noise process with zero-mean and power spectrum density $N_0/2$. By using the signal-space representation, it can be expressed as: n(t) =\sum_{j=1}^N n_j \...
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### How can we do finite-step signal sampling in practical?

The signal has infinite length. We cannot sample it with a whole length. How can we truncate a infinite signal and sample it in finite step? And then how can we analyze it.
116 views

### Active Noise cancellation for non periodic signals

I observed that the coded algorithm for active noise cancellation is not able to cancel some of the signals like a human voice. Is there any solution for this? Can we really cancel non-periodic ...
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### Correct way to calibrate RX into a measuring receiver

While playing with my SDR (Software Defined Radio) Board, I was interested in performing a TX output power table at different center frequencies and TX antenna gains. I have an RF frequency generator....
364 views

### Power Spectral Density of discrete White Gaussian Noise defined with variance and sampling interval

From Creighton and Anderson Chapter 7 on Gravitational Wave data analysis: Please explain where the delta t and the limit came from in this derivation.
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### Distortion in sound after multiplying frequency spectrum by constant

I make a simple sound equalizer that operates in frequency domain and lets user to adjust frequencies in sound by using 4 sliders. The first one responsible for 0 - 5kHz, the fourth one for 15-20kHz. ...
42 views

### Removing outlier data points from frequency-domain signal

Hello signal processing stack exchange, I have a complex frequency-domain signal representing the impulse response of a physical system over some range of frequency space. As an artifact of the ...
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### Interpolation of missing audio signal in a video sequence

Suppose there is a video sequence and there are some frames for which the audio data is missing. I want to interpolate the missing audio data on the basis of the correlation of the audio signal with ...
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### Optimising an input signal for a system to minimise distortion of output signal

I have a discrete time-series signal which I am able to process before passing it through a system which distorts said signal. This system cannot be altered and is non-linear, but a signal can be ...
126 views

### transfer function and 'causal' signal - evaluate transfer function or use z-transform of input?

From my studying difference equations and transfer functions, I understand that when a complex exponential input $x[n]=z_1^n$ is applied to an LTI system with transfer function $H(z)$, determining the ...
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### Can we sample the signal with any period as long as the Nyquist rate is respected

I have a question regarding the sampling rate. Suppose that we transmitted a signal $m(t)$ then at receiver side, we received the continuous signal $x(t)$, which is time varying and sampled with a ...
63 views

### Meaning of a formula about transient frequency bins

I'm trying to understand the following formula in this paper: Sadly, the paper does not define most of the symbols it is using, so my guesses so far are: $T_{tr}$ refers to the sampling interval i....
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### State Space conversion of Sinusoidal model

i would like to learn how to convert sinusoidal model into state space form which has following equation our model consist of sum of periodic components with additive of white noise, given by ...
If you have 2 Lorentzian peaks that partially overlap and you have some frequency resolution df (your points in frequency space are separated by df) and both Lorentzian peaks have FWHM $\Gamma$ is ...