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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Sinusoidal function

I have a problem. I am confused, I have two function like this: $\sin(t)$ $\sin(2\pi t)$ what is the difference between of them and how to calculate period and frequency for second?
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short frame subband coding

I am implementing a subband ADPCM codec, Fs=16 kHz, frame length 3ms, band1=50Hz-2kHz, band2= 2kHz-8kHz. I used the FIR filter for subband coding and %50 overlap. My reconstructed signal does not ...
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29 views

elementary one and multidimensional real examples of continuous/discrete LTI systems

By an LTI system, we mean a time-invariant linear map on continuous/discrete-time signals. What (elementary one and multidimensional) real examples of continuous/discrete LTI systems do you suggest to ...
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27 views

How is wavelet center frequency computed?

PyWavelets (1) takes index of max DFT magnitude, (2) adds 1 to it, (3) divides by domain, which is the range of input values to the wavelet ("support"). ...
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MAP Estimation Problem for Frequency Band Occupancy Calculation

Consider designing a wireless communication system. Your communication link is not iso- lated in the environment, there are other similar devices trying to communicate in the same general frequency ...
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34 views

Noise removal in discrete signal

How do i remove these kinds of noise from the discrete signal in python?
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29 views

Discrete representation of a signal that has unevenly spaced samples in frequency

I'd like to describe a problem that I've been struggling with for a while. I want to apologize in advance due to the long text. I just want to be as clear as possible in my first post. Consider the ...
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88 views

Alternative convolution theorem?

Instead of padding $x_1[n]$ and $x_2[n]$ then taking $$ \text{iDFT}(\text{DFT}(x_1[n])\cdot\text{DFT}(x_2[n])), \tag{1} $$ assuming we know $x_1(t)$ and $x_2(t)$, and their FT's, what if we do $$ \...
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51 views

Fundamental period of $x[kn]$

Let $x[n]$ be a periodic with fundamental period $N$ and $y[n] = x[kn]$ where $k \in \mathbb{N}$ and $k\ge2$. Is $y[n]$ periodic? What's the fundamental period of $y[n]$? Here is my answer: If $N = ...
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44 views

Discrete Fourier Transform (DFT) of a number

I am trying to understand how a DFT for N-samples would be taken for a signal that is only a number, but the number changes for different values of n. For example, a signal that is x[n]=1 where n is ...
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23 views

How do I calculate the correct amplitudes of a discrete Fourier transform (DFT)?

I have a set of samples values in time domain. I know they are uncorrelated and I have to extract the correct amplitudes. However, the values are only ~88% of what they should be. As a test see the ...
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52 views

Optimal Receiver Using Complex Baseband

Given the below signals and a square pulse shape, I want to design the optimal receiver using complex baseband: $s_0 = p(t)sin(300\pi t)$ $s_1 = p(t)sin(301\pi t)$ I know that I will be using a ...
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How to modify zeros and poles in a delta-sigma modulator loop?

In this specific case, I am modeling a delta-sigma analog-to-digital converter with a basic loop in which the output $V$ is fed back with unity gain to be subtracted from the previously sampled input $...
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Determine the Signal Curve from Parameters of a Power Curve by Noisy Measurement

I have a class of signals described by function: $$ f(inc,d,t)=inc\cdot t^d $$ where inc and d have a finite set of values like 1, 2, 3, i.e. $$ inc, d\in \left \{1,2,3 \right \} $$ and $$ 0\leq t<...
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54 views

What is the DFT of $[x_1 -x_2 x_3 -x_4…x_n]$

If DFT of $[x_1 x_2 x_3... x_N]$ is $Y(k)$, what is the DFT of $[x_1 -x_2 x_3 -x_4,....x_N]$ in terms of $Y(k)$? I have tried to formulate it but I cannot get a simplified expression for DFT of ...
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Classic Signal Processing vs Deep Learning / Machine Learning (DNN / ML) Based Signal Processing

Are classic signal processing/statistics based approaches to optimum detection/estimation still relevant/important compared to ML based approaches using DL? There was a time when speech processing was ...
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finding power spectral density from a vector

I have been given a vector: \begin{equation} v= \:\begin{pmatrix}\frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix} \end{equation} my job is to find the power spectral density from this vector \...
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59 views

How to test wavelet transforms?

One pertinent attribute is normalization, which measures performance in describing signal spectral amplitude and energy, like here. Others are robustness to noise, time vs frequency resolution. ...
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disrupts frequencies detection

Let's say I flew a Drone in the air and someone disrupts frequencies of the Drone, Changing the frequency of the drone to the signal of the jamming frequency can it prevent its falling?
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85 views

Multiplying signals in discrete-time vs continuous-time

Given two discrete-time signals $a[n]$, $b[n]$ and its product $c[n]=a[n] b[n]$. The ideally interpolated, continuous-time version of $c[n]$ is \begin{align} c_1(t)&=\sum_{n=-\infty}^{\infty} a[n] ...
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2answers
54 views

find phase greater than 2*pi in MATLAB

I'm working on extracting the phase information in a given signal in MATLAB. I've the following vector; ...
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1answer
41 views

How to get rid of discontinuities at the start of a signal caused by the filter

I'm processing an audio signal using an overlap add method.Everything at the block boundaries is fine. However I have a discontinuity at the very start of the first block and I'm not sure how to (or ...
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53 views

Discrete Signal Windowing

How do we apply windowing of 50% (4 samples) to a discrete signal with the odd number of values as 1234567? Is it done as: ...
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1answer
26 views

awgn function in MATLAB

I'm using 'awgn(input_signal,snr_db,'measured')' function in MATLAB to add white noise to the input signal. Here is the simplified script. Does zero padding the input signal affect the behavior of ...
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1answer
46 views

FFT results are repeating?

I am trying to detect notes out of a musical sound input. My program can be run here. The problem is the patterns in the frequency response is repeating: I suspect that echoing in the room is causing ...
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38 views

Cosine modulated impulse response

How do we show $y_0(n) = y_1(n)$ when $h_k[n] = h[n] \cos(\frac{2\pi}{L} k n )$
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31 views

expression for the FT of the frequency response of a system

I am trying to find an expression for the Fourier Transform of the frequency response of the cascade system seen here: Here is my approach: $(-1)^n = (-1)^{-n}$ $v[n] = x[n]e^{j\pi n}$ $V(e^{jw}) = X(...
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3answers
70 views

QAM Amplitude Levels

I'm working on a project to stream video between 2fpgas by using QAM. While mapping symbols with different amplitude pulses(PAM) a question popped up in my mind. In real life how does communicating ...
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1answer
51 views

What do different Cepstral or MFCC coefficients represent intuitively?

I understand the explanation for separating slow and rapid changing log spectral components but i need to understand: Why lower coefficients have higher and mostly positive magnitudes? Why Higher ...
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57 views

impulse response of a causal LTI system

This is a difference equation to a causal LTI system: $y[n] = ay[n - 1] + x[n] - a^Nx[n - N]$ Where N is a positive integer. I need to determine the impulse response of the system, so I have the ...
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23 views

Discrete Time Systems with cosine()

I am trying to see if y[n] = [cos(πn)]x[n] is casual, stable, linear and shift-invariant. I came up with the solution that it is not stable since it is not "...
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43 views

Using MATLAB's Spectrogram Function for Analysis

In the documentation - sepctrogram(). Question 1)s = spectrogram(signal) and ...
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1answer
28 views

Apply the Discrete Fourier Transform as a Matrix Multiplication in MATLAB

0 I have a vector x of length N x 1, I need to perform the iDCT operation for it using MATALB. I performed that using the below method: ...
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1answer
46 views

Difference equation system identification

Suppose I have a difference equation modeling a vehicle like this: $$d[k+1]=d[k]+a\cdot u[k]+b,\tag1\label{eq}$$ where $d[k]$ is total distance traveled at time $k$, $u[k]$ is engine input at time $k$ ...
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Estimate signal parameters for known frequency

Consider real signal of the form: $$ \begin{align*} x(n) = &\sum_{m=1}^{M} \left( c_m \cos(2\pi f_m n) + s_m \sin(2\pi f_m n) \right) =\\ &\sum_{m=1}^{M} a_m \cos(2\pi f_m n + \phi_m) \end{...
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25 views

Quantization types

Suppose i have input sequence {-1.3,1.2,-0.2,-0.5,0.4,0.89,1.3} Which are uniformly quantized through a quantizer having range (-1.5,1.5) with 4 levels My calculted answers for- First method:mid rise ...
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How does image rotation affect the intrinsic camera parameters?

I am considering the problem of how to (manually) change camera model parameter to make it "valid" on a rotated image. This question tackles resizing, but does not consider lens distortion. ...
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Why is the Periodogram Used as an Estimate of PSD?

Why is the periodogram method as given by Schuster (1898) - which is not a consistent estimate of the PSD - still used, as opposed to consistent non-parametric methods for estimating the PSD like ...
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29 views

μ-law compression technique

In μ-law compression formula i have always seen that the value of Xmax and Ymax is always same but can they be different?
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33 views

Quantization processs

In a quantization process what happens when the signal range is more than the quantizer range? Suppose i have a sinusoidal signal which ranges from -5 to +5 but the quantizer which has four levels ...
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45 views

How to reconstruct a time-discrete signal

German: Sie betrachten das zeitkontinuierliche Signal $s(t)$ mit einem digitalen Oszilloskop mit Abtastperiode $T_\mathrm{s}$ und messen das zeitdiskrete Signal $\tilde{s}[n] = s(n\:T_s)$ Nehmen Sie ...
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Estimating Signal-To-Noise ratio from discrete time series

A hidden variable $x(t)$ (in my case, neuronal signal averaged over a brain area) exhibits dynamics on multiple timescales from milliseconds to seconds. An observable $y(t)$ is produced by convolving $...
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1answer
83 views

Fourier Transforms, Convolution, Cross-correlation: what is their physical unit exactly?

Let us assume we are talking about real, deterministic, electrical signals $x(t)$ and $y(t)$ (magnitude in Volts). There are different kind of Fourier Transforms. I made a table to summarize: NB: By ...
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Deriving Fourier Transform of Time-Windowed Discrete Signal

I'm trying to derive the Fourier Transform of a finite-length discrete signal to show the effect of windowing,e.g. spectral leakage and resolution, but I can't seem to arrive at the same answer. Just ...
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1answer
34 views

Effects of delay in a discrete-time controller for a continuous-time plant

I'm trying to understand the effects of sample-to-update delay in digital control of power electronics. I am aware of the issue but not 100% sure how to quantify it. There is an interesting paper by ...
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What is the difference between signal processing and data processing?

I often find the terms 'signal processing' and 'data processing', and sometimes 'information processing' in articles. But what are the differences between these notations. In my opinion, signal ...
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2answers
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How can we measure the quality of the FIR filter?

The process of designing filters includes too many parameters like bandwidth, transition, degree of attenuation in side-bands, phase delay, causality, the magnitude of ripples, and so on. First of all,...
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1answer
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Testing for Linearity and Shift-Invariance

I started school a week and a half ago and we have gotten already a big chunk of material and I wanted to check if what I am currently doing is correct. Here below are the problems to work out that ...
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Noise and harmonic elements w/in a discrete time signal

So I have a discrete-time signal with around 300 samples. It is part of an environmental science application, so is not-strictly periodic although there clearly are periodic components. I have applied ...
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What are the wavelet packet functions and how are they different from the wavelet and scaling functions?

I understand that in the decomposition process, wavelet and scaling functions are used to split the signal to approximation and detail coefficients. Most of the time I saw the wavelet and scaling ...

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