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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Find response of discrete time LTI system given input and impulse response

For this question the guide says to use $Y(e^{j\omega}) = H(e^{j\omega}) X(e^{j\omega})$. I have been able to find the discrete time Fourier transform of the impulse function as $$H(e^{j\omega}) = \...
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Let a LTI system be causal and stable with the transfer function being... show that

if the system is an IIR LTI causal and stable one, and the transfer function is \[H(z)=\sum_{n=0}^{\infty}h[n]z{^{n}}= \frac{G}{1 -\sum_{k=1}^{p}a_kz{^{-k}}}\] show that the cepstrum of this system ...
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What does frequency weighting an acceleration signal mean? And How do I frequency weight the raw acceleration data collected?

Disclaimer: I have very little knowledge in signal processing. I'm trying to calculate a Whole Body Vibration(WBV) measure called Vibration Dose value(VDV). $$VDV = \left(\int_{0}^{T}a(t)^4\,dt\right)^...
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Frequency response of chirp signal changes when extracting burst from repeating chirp waveform

I hope i can make myself clear enough, even though i might not be familiar with the right terms. Using GNU Radio, i created a chirp signal with a sawtooth signal source into a frequency mod block, as ...
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Short Time Fourier Transform has different frequencies than Fourier Transform?

The reason we do the STFT is so that we can analyse for short segments of time how much of the components in the frequencies of the FT are present. However, it may be possible that completely ...
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Periodicity of complex exponential in continuous and discrete time (Eq 1.51, Signals and Systems by Oppenheim & Wilsky)

Hi All: This is very basic but I've always wondered about it and now I see it in print in a textbook so I may as well ask. In Signals and Systems on page 26, it says $$e^{j(\omega_0 + 2\pi)n} = e^{j2\...
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Is there a Python method to calculate moving RMS of a signal? How to calculate the moving RMS using the discrete signal formula? [closed]

I'm trying to calculate a moving RMS of an acceleration signal. One of the answers in the post, shows the formula for calculating moving RMS for discrete signal. The formula they suggest: I have a ...
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83 views

Frequency response of a long signal

I am trying to get the frequency response of a system, so, in theory I would need to do: H = fft(y)./fft(x); I have measured the system with a long stepped sine ...
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92 views

Best temperature compensation equation?

I'm looking for the correct temperature compensation equation to use on our project. We are measuring the output of a detector who's signal is very sensitive to temperature drift. Any external ...
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How to compute dBFS from rms-values if the samples exceed 32bits

For a first approach on audio-sampling I'm currently working with the raspberry pi's pcm pins and MEMS-microphones, using the ALSA library. A problem arises when I want to calculate dBFS from a buffer'...
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Output power of a signal passing through an IIR filter

suppose I have the following discrete time signal $x\left(n\right)=0.7\sin\left(2\pi \times 623\:nT\right)$ where $N=4000$ and $T=\frac{1}{f_s}$, where $f_s=40$ kHz I pass this signal through a simple ...
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59 views

Time scaled version of discrete time signals

I have a confusion regarding time scaling of discrete time signals. Let u[n] be the discrete time unit step signal(or sequence) Now if i plot u[n/3] i know there will be two zeros added between each ...
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Error correcting code? - using RGB space with a lookup table

This problem could be thought about as how to transmit a signal with 3x8bit RGB in a way that is robust to the distortion of antialiasing blends colors. The context: I need to rewrite a short utility ...
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How to reconstruct the signal using overlapping frames in MATLAB

I understand that we can use the buffer function in matlab to split a long signal into overlapping frames. But is there any functions that we can use to put the ...
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Is my interpretation of CAR filter correct?

I am a computer scientist working on a Brain-Computer Interface (BCI) project. So, i am using EEG data from a dataset and classifying them with the use of machine learning algorithms. Initial results ...
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How do i know it is will be periodic

(system is LTI and Casual) 1)If a periodic signal is applied to the input of this system. Does output always have to be periodic ? 2)What conditions are required for this system to be linear? thanks ...
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What is an analysis dictionary or operator in compressive sensing?

I am doing research on compressive sensing. I am new in this field. I read several papers regarding analysis dictionaries. Here are some papers that I have read so far: https://www.hindawi.com/...
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Unexpected imaginary part in the fft of a zero-padded cosine

I simulated a cosine waveform $ y = \cos(\omega t) $ and I applied the FFT algorithm to it. As expected, I have a frequency peak at $\pm \omega$ only in the real part, and nothing in the imaginary ...
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Oppenheim and Willsky Signals and Systems Solutions

Hi All: This list has been great for me as a beginner but I decided to work my way through Oppenheim and Willsky and Mahab "Signals and Systems" book since I still get sometimes confused by ...
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Adaptive Delta Modulation: Logic for step size control at receiver

I read that in adaptive delta modulation, we have a block for step size control (diagram below) which takes into account the one bit quantizer output in a feedback loop and modulates it, the intent ...
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K-Path sampling overall transfer function

I'm trying to derive the overall Z-transform for the K-path sampling system shown below. I numbered some of the equations that I'll reference. I don't think I understand going from equation 3 to ...
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Where did we get the DC term of the Accumulator from DTFT?

Define $y[n]:=\displaystyle\sum_{m=-\infty}^{n}x[m]$. The DTFT is found as follows: \begin{align*} y[n]&=\sum_{m=-\infty}^{n}x[m]\\ \\ &=\sum_{m=-\infty}^{n-1}x[m]+x[n]\\ \\ &=y[n-1]+x[n]\\...
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Eliminating drift generated from double integration of acceleration signal using Envelope Method

I'm trying to remove the drift generated upon the double integration of a noisy acceleration signal. But this question discusses only removing the drift upon single integration to generate velocity ...
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122 views

Waveform pattern detection in time series

I have some IMU data which I am using to detect activity patterns - walking, running etc. In order to differentiate one activity from another I need to do pattern matching in time series. Different ...
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100 views

how to find the frequency of the downsampled signal?

So, I am trying to solve this question. Consider the signal, $$x=\cos\left(\left(\dfrac{2\pi}{3} \right)n\right)$$ The signal is downsampled by a factor of two. Indicate the frequency of the resulting ...
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This is how my professor is finding the frequency response of an LTI system when given the impulse response. Is this wrong?

My DSP professor uses the freqz() function to find and plot the frequency response and I think it's wrong but I want to make sure before I point it out. Take this ...
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Calculate ACF in C++?

I would like to manually reproduce the method that authors of an article used in their research (DOI: 10.1038/s41598-017-02750-9 (Page 8. top)). It is mentioned as "ACF", so I wrote ...
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88 views

How do I implement a footstep recognition algorithm? One that recognizes the start and end points of each footstep?

I have some time series data captured from a person's footsteps/strides (specifically, a person on rollerblades). It came from an IMU sensor placed on a person's boot. Each data point captures ...
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101 views

Shift operators in graph signal processing (GSP)

A key element of Graph Signal Processing (GSP) is the shift operator, that describes how a signal changes when shifted on the graph. There exists many different proposals of shift operators. Several ...
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176 views

What is the advantage of using a Stepped Frequency waveform over FMCW?

What is the advantage of using a Stepped Frequency Waveform instead of a traditional linear FMCW ?
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Why is the range of frequency for discrete time Fourier transform $-\pi<\omega<\pi$? [duplicate]

In my class we are taught that the range for the frequency is $-\pi<\omega<\pi$ for discrete time Fourier transform, however for continuous time the limit is $-\infty<\omega<\infty$ why is ...
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question with chirped signal

I have some difficulty understanding the following question. I have written a code to plot continuous and discrete version of the chirped signal. ...
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Hypothesis testing with binary pattern

Let's say you have a sequence $\{x_i\}_{i = 1}^N$ of ones and zeros. You know that $P(x_i = 1) = \frac{1}{3}$. You want to test two hypotheses $H_0$: The sequence is $iid$ with $P(x_i = 1) \ \forall \ ...
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1answer
62 views

Different values when calculating signal's energy by hand vs MATLAB

Given the following signal: $$ x(n) = \left\{ \begin{array}{ll} u(0.01n-0.025)2.3704e^{(-0.287682n)}, & n\ge 0 \\ u(-(0.01n+0.025))2.3704e^{(0.287682n)}, & n< 0 \\ \end{array}...
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48 views

How to determine the number of multipath?

In a multipath propagation environment if we take the time index of reach channel tap by the integer multiples of sampling periods, assume the RMS delay spread $ \sigma_{tau} $ and maximum excess ...
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78 views

Unit impulse response of a cascade interconnection of three discrete-time systems

I am nearly at the end of finishing a problem in my textbook but I couldn't understand something in the answer; I did everything to the point I found the overall response of the system in terms of $...
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48 views

Calculate impulse response when output contributes in input

I have an exercise in which I need to find the impulse response for this given system: $$y(n)=\frac{1}{2}y(n−1)+x(n−1)+x(n)$$ As per my knowledge, I need to find the homogenous solution. My homogenous ...
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How to simulate a continuous signal passing through a capacitor (simple coupling capacitor)

the differential equation for the current flowing through a serial capacitor (see for example https://www.allaboutcircuits.com/textbook/direct-current/chpt-13/capacitors-and-calculus/) indicates that ...
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552 views

Computing Discrete Convolution in terms of unit step function

Consider : $$ x[n]:=\begin{cases} 1&\text{if $3\leq n\leq 8$}\\ 0&\text{if otherwise} \end{cases} \quad\text{and}\quad h[n]:=\begin{cases} 1&\text{if $4\leq n \leq 15$}\\ 0&\text{if ...
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Confused about shifting convolutions

We know that for two signals $x[n]$ and $h[n]$ such that : $$ y_{1}[n]=(x*h)[n]=\sum_{k=-\infty}^{\infty}x[k]h[n-k]=\sum_{k=-\infty}^{\infty}h[k]x[n-k] $$ We can deduce that :$$y_{2}[n]=x[n+2]*h[n]=y_{...
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Calculate the power of a discrete-time signal

We got this question in our test :- $$S(t) = 5\cos(10πt - π/2) + 6\sin(15πt)\cos(15πt)$$ My Solution :- $$S(t) = 5\cos(10πt - π/2) + 3\sin(30πt)\qquad \textrm{[Using $\sin(2A) = 2\sin(A)\cos(A)$]}$$...
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Unit impulse response $h[n]$ of a discrete time system with multiple characteristic roots 0

I am trying to obtain the unit impulse response of a system in the form: $$y[n+N]+...+a_{N-1}y[n+1]+a_{N}y[n]=b_0x[n+N]+...+b_{N-1}x[n+1]+b_{N}x[n]$$ $$Q[E]y[n]=P[E]x[n]$$ (where E is the unit advance ...
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There appears to be a contradiction with the recurrence solutiom

Consider the equation : $$ y[n]-\frac{1}{2}y[n-1]=x[n] $$ where $x[n]:=\left(\frac{1}{3}\right)^{n}u[n]$. First, I founded the homogenous solution $y_{h}:=A\frac{1}{2^{n}}$ $$ y_{h}[n]=\frac{1}{2^{n}}...
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Is the expansion of this expression correct?

\begin{align*} &(\delta[n]+\delta[n-1])*(\delta[n]+\delta[n-1])\\ \\ =\;&\delta[n]*\delta[n]+2(\delta[n]*\delta[n-1])+\delta[n-1]*\delta[n-1]\\ \\ =\;&(\delta[n]+2(\delta[n]*\delta[n-1])+\...
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Where is the mistake in the convolution?

Let : $$ x[n]=\begin{cases} 1&\text{if $0\leq n\leq 4$}\\ \\ 0&\text{if otherwise} \end{cases} \qquad \text{and} \qquad h[n]=\begin{cases} \alpha^{n}&\text{if $0\leq n\leq 6$}\\ \\ 0&\...
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1answer
32 views

Discrete Convolution of two piecewise sequences having this specific form

Assume I have the following two sequences : $$ x[n]=\begin{cases} \alpha&\text{if $a\leq n\leq b$}\\ \\ \tag{1} 0&\text{if otherwise} \end{cases} \qquad \text{and} \qquad h[n]=\begin{cases} \...
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ADC sampling rate and signal bandwidth for FHSS

If i am correct; for a radio receiver the ADC sample rate will have to be higher than at least twice the BW of the data (disregarding sparse sampling techniques). So for frequency hopping spread ...
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understanding the result of the simulation of In-phase and quadrature part BPSK signal

I am a student and working on a hardware implementation of a transceiver and going to check an algorithm of time recovery that includes symbol synchronization and sampling clock synchronization. The ...
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67 views

Impulse Response of real coefficient, LTI System

I'm trying to obtain the impulse response $h[n]$ of a system whose frequency response is $H(e^{j\omega})=R(\omega)e^{-25j\omega}$. I believed that $h[n]=h[n-25]$, would be the correct answer, however ...
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76 views

Circular wrapping of an asymmetric function (in DFT calculations)

Convoluting a signal (using discrete FT) for a given interval [a, b] with a Gaussian can be done by circular wrapping as shown in Numerical Recipes. I found a shortcut for circular wrapping so that ...

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