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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Does Circular Convolution correspond to Periodically Expanded Linear Convolution?

I have a question whether circular convolution and periodically expanded linear convolution corresponds in following case or why it does not? Think about a signal $x[t]$ and a signal $y[t]$ both of ...
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25 views

2D DFT of a filter kernel

for understanding i want to compute the DFT out of the 3x3 filter kernel using the shifting property: $$\begin{bmatrix}0& 1 & 0\\1 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix} \cdot \...
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What is the QPSK Constellation Diagram used in LTE

I think the question is pretty straightforward. I have to do a class project that requires me to modulate a signal, and one of the steps is Quadrature Phase Shift Keying (QPSK). It is to be done in ...
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43 views

From Orthogonality to DTFT

I have met this question, but cannot prove it using DTFT definition. Given: $g$ is a discrete sequence filter and: $$ g \in l^2(Z)$$ $$\langle g_n, g_{n-2k} \rangle = \delta_{k}$$ Prove: $$|G(e^{j \...
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MIMO multipath delay [duplicate]

How is multi-path delay dealt with in MIMO systems? Most of the theory I have read on MIMO doesn't address multipath delay and assumes the multipath interference is limited to secondary antenna ...
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23 views

Flicker Frequency for taking snapshot of monitor [closed]

When a snapshot of a monitor with refresh rate 60 Hz is taken with a camera with rolling shutter config operating at 30 FPS, what is the expected flicker frequency in the resultant image? I took ...
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2answers
49 views

Window functions and the Fourier transform

I want to clarify the 'correct' way to use windowing and Fourier transforms. My question is somewhat related to this one, but I have a few additional queries. I have some real, non periodic signal ...
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1answer
28 views

How to add a particular noise on a signal?

I have a simple ADC model (an input signal == sampled signal ). The adc should be modelled as with following values: 1.5 V (peak to peak).. meaning --> +1.5 V --> 0 dBFS ... how to do this ? The ...
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Oscillations in a first-order discrete-time linear systems

According to my understanding, continuous first order systems do not exhibit oscillatory behavior because a first order system has only one energy storage element and thus oscillation is not possible. ...
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1answer
40 views

Estimate instantaneous frequency using LMS algorithm - optimization

I hope someone can help me with the following problem: I want to estimate the frequency of a soundfile that is composed of a sinusoid with varying frequency and additive white noise: $x[n] = sin(\...
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25 views

How to express time delayed discrete signals

Hi sorry this question might sound silly but, a signal $$x[n]=[ 6 \: 4\: 0\: 2]$$ what is $$x[n-2]$$ then?
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11 views

average value of modulated signal with Fourier Analysis

I am using an instrument that uses a modulated heating program. The instrument returns an average heat flow signal calculated from the modulated heat flow. I would like to understand how this average ...
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1answer
14 views

How to calculate SNR of dead-band quantizer?

Suppose we have a dead-band quantizer with $\ N = 5 \ quantizing \ levels $ which uses $\ b = 3 \ bits $ for each produced symbol. The quantizer gets as input a uniformly distributed signal $\ X $ ...
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49 views

find the maximum of the DFT of sampled signal

The signal $$x(t)=\cos(10\pi t+\phi)+\cos(20\pi t)$$ is sampled with a sampling frequency $F_s$ as $25 \mathrm{Hz}$ where the phase $\phi$ is unknown. Sampling the continuous time signal $$y[n]=x(nT)$...
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66 views

Basic Understanding of Convolution Operation

I would really appreciate any help in understanding this. If $$y[n] = x[n]*r[n]\tag{1}$$ then what is $y[n-n_0]$ for any system? Is it $$y[n-n_0] = x[n-n_0]*r[n-n_0]\tag{2}$$ or $$y[n-n_0] = x[n-...
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25 views

Discrete-time system: getting the true frequency from normalized frequency

Lеt's say that i have a plot where i can see the spectrum of some discrete signal and let's say that it's x axis is normalized (by normalized i mean $\omega/\pi$ on the $x$ axis). Now, i know that in ...
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1answer
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Discrete Fourier transform - Norms of complex input signals and their transformation

Given a signal $\mathbf{z} \in \mathbb{C}^n$ and its Discrete Fourier transform $\hat{\mathbf{z} }$, does $||\mathbf{z}|| = ||\hat{\mathbf{z} }||$ hold? The question is given to me like this with ...
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36 views

How to generate IQ samples of a signal?

I am using a HW with LMS7002 RF transceiver chip. This chip takes IQ values as an input. 1. Can anyone point me to a sample IQ value generator? That I can use to test. 2. What will be the IQ values ...
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33 views

Difference equation with variable coefficients in MATLAB

Given the following difference equation $$y[n]-\left(\dfrac{n}{n+1}\right)y[n-1] = n\cdot x[n]$$ How can we use MATLAB to solve it? I know if the coefficients are constant we can simply use ...
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43 views

Fast Fourier Transform for varying period (Order analysis)

I am trying to do a fast Fourier transformation on accelerometer data from a shaft rotating at varying speed in Python. What I have done so far: 1: The original plot was in the time domain, and I ...
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1answer
57 views

Discrete time aperiodic signal: Concept of frequency?

Is concept of frequency to a-periodic signal whether it is continuous or discrete time is valid? I am bit confused, since discrete time sinusoids have frequency $-\pi<\omega<\pi$ or $-\frac{1}{...
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18 views

Phase Difference offset when measuring phase difference between different FFT bins

In application where two sensors are used to calculate the phase difference of the incoming signal, what is the the phase difference offset which should be added when taking phase difference from ...
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1answer
40 views

Hand implementation of Fourier transform have small peaks unseen in Python package

I've implemented the basic version of discrete Fourier Transform and I'm testing it using a pure sinusoid. However, small bumps show up in addition to the large peak. I tried Numpy.fft for this and I ...
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1answer
26 views

Wireless Channel Multiplicative Model

Let's assume a SISO channel in the equivalent baseband, the standard channel model (discrete) is: \begin{align} y(k) = h(k)x(k) + z(k) \tag1 \end{align} Where $y(k)$ is the detected signal, $h(k)$ ...
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Smoothing a discrete function with point wise variances

In Stark's Introduction to numerical methods [1970] it suggests fitting local polynomials to smooth discrete data before the Fourier transform using least squares minimisation. This gives the ...
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1answer
24 views

Linearity and time-shifting of $\mathcal{F}\{0.8^n\cos(0.1πn)u[n]\}$

To preface, this is not a homework related question but purely for self-study purposes. Hi there, I try to calculate $\mathcal{F}\{0.8^n\cos(0.1πn)u[n]\}$ by using the properties of Discrete time ...
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1answer
29 views

Total Harmonic Distortion THD for the rectifier

I have a circuit with rectifier and this cause the non-linearity and consequently harmonic. I show it on the oscilloscope and then collect the signal from the oscilloscope to the computer by using the ...
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24 views

Difference between Cepstrum and Spectral Envelope

I have no background in Signal processing and i don't understand the difference between cepstrum and spectral envelope. IDFT of the log magnitude of the DFT of a signal is cepstrum then what is ...
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2answers
41 views

How to draw a finite-duration sequence

On page $359$ of the 2nd edition of the book "Signals & Systems", by Oppenheim and Willsky, the authors wrote the following words: "Consider a general sequence $x[n]$ that is of finite duration. ...
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How can we do exact simulation for digital systems? [closed]

In digital control system, there are two basic techniques for finding the best digital controller. First, called the discrete equivalent, we find the continuous compensation and then discretize (best ...
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1answer
34 views

convolution expression h(n,k) = h(n-k)

As a new to DSP concepts want to understand the meaning of impulse response and why we do $h(n-k)$ in convolution and $h(n+k)$ in correlation.
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1answer
48 views

Why is DTFT of $e^{jn\omega_0}$ an impulse train?

update : After asking the question, I figured out that DTFT result is an impulse train. Now my question evolved to, how it is derived in this way? Using the DTFT formula seems not to be working, ...
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67 views

FFT Phase interpretation of input signal with non-integer number of cycles in FFT window

It is known that if we take the FFT of a signal at such a frequency which has non-integer number of cycles in the sample window we get different value of phase even if the original signal was at phase ...
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222 views

Phase difference between signals sampled at different frequencies

I want to know that if it is possible to measure the relative phase difference between a signal that has been sampled at two different locations with different sampling frequencies? Also can that ...
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1answer
36 views

Impulse response of a system in z domain

The question 3-23 in the "Discrete-Time Signal Processing - Second Edition" is: and the solution is: I cannot understand the solution. In the second row of the answer when I multiply (-4) with ...
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1answer
63 views

What did I do wrong with this simple filter build?

I tried to put everything I have learned from people here together to code my first filter from scratch. Unfortunately, it didn't go well and I'm not getting the expected output. The math/code became ...
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1answer
27 views

DFT practice question

This is probably basic but as I am new to the field it confuses me a bit. While looking at some solutions provided to a problem in the final step following happens: $$\begin{aligned} \frac{1}{10}\...
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IID noise assumption at Matched Filter sample time

I read that at the correct sample times of a matched filter output the noise is independent assuming a Nyquist pulse. Can someone provide a proof of this or explain it more? Assuming your matched ...
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1answer
53 views

Impulse and step response

While trying to determine the unit step and impulse response for a discrete LTI system I had several problems: $$ \begin{aligned} (Hx)[n]&=(Hx)[n-1]+\frac{1}{N}(x[n]-x[n-N]) \\x[n]&=(Hx)[n]=0\...
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Calculating average power of a discrete random signal with complex values

I have a Rayleigh channel that transmits discrete values according to the following: $$y(n) = h(n) * s_n + \omega_n$$ Where $y$ is the received message, $s_n$ is the symbol sent (constellation 2-PSM), ...
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Proving for windowing function

Prove that $1+2\cos(\omega)$ is the same as $\frac{\sin(\frac{3\omega}{2})}{\sin(\frac{\omega}{2})}$ Knowing that $$p[n]=\sum_{k=-1}^1 {\delta[n-k]}=\delta[n-1]+\delta[n]+\delta[n+1]$$ Doing the FT ...
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What is the difference between SFO (sampling frequency offset) and SCO (Sampling clock offset)?

What is the difference between SFO (sampling frequency offset) and SCO (Sampling clock offset)? I think they are essentially the same phenomenon?
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Discrete signal - fourier transform coefficient period [closed]

if I have an example signal in the picture, how can i decide its period?
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1answer
37 views

Confused about filter's cutoff frequency in rational sampling rate converter

A interpolator which increase sampling rate by L times is followed by an anti-imaging filter, the filter is said to have a cutoff frequency of Fs/2L. Is Fs here is the frequency before or after ...
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19 views

Applying Wavelet on energy disaggregation as denoising technique to remove uncertainties

I would like to apply Wavelet in MATLAB as a denoising technique on Non-Intrusive load Monitoring data. The data was captured by sensors on each appliance and one sensor on the smart meter (Normally ...
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Deep Learning based NDA Channel Estimation

I was wondering if it is possible to use Deep Learning to estimate the Channel Impulse Response for NDA synchronization? I understand Deep Learning is not normally used for regression problems but I ...
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1answer
41 views

How to Emulate Sample Frequency Offset for OFDM in Matlab?

I am studying the effect of sampling frequency offset on OFDM, and in order to emulate SFO, I have to slightly change the sampling rate of the signal. In order to have a +5ppm offset, I have to change ...
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53 views

FSK carrier frequency estimation

In the MPSK Modulations, Cyclic Spectrum Density method can give a peaks, for example for the QPSK: But in the FSK signal, this peaks do'nt appear. How to solve it?
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89 views

What is the difference between (Sample Timing Offset), (Carrier Frequency offset), and (Sampling Frequency Offset)?

Briefly, can anyone explain to me what is the difference between (Sample Timing Offset), (Carrier Frequency offset), and (Sampling Frequency Offset)? and is Sampling Frequency Offset (SFO) like STO ...
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1answer
35 views

Simulation of IQ imbalance using MATLAB

I already have the value of Image Rejection Ratio (IRR) in dB for IQ imbalanced modulator and I want to simulate this effect using MatLab. How can I obtain $\alpha$ and $\theta$ to calculate the ...

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