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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2 answers
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How to calculate RMS of a sampled analog signal

Consider the below given discrete signal which has been gathered via sampling of an analog current waveform with sampling period $T_s=100\,\mu s$. I would like to evaluate the RMS value of its first ...
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BER result in MATLAB

I build a pam-2 modulation, then I make a pulse shaping with half sine (matched filter). Then I send it through the AWGN channel. At the end I do down sampling and demodulation. But i have problem ...
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Input-output Pair Implications for System Properties [closed]

In the following problem, I know the correct answer for system $A$ is (v) and I know the reason but for the other two systems I don't know which ones are correct and why. Do you have any idea? for ...
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Z transform and convergence domain

Can someone please give me an intuitive explanation of the meaning of the convergence domain in the Z transform? And what is the relation between the convergance and the stability? Thank you!
1 vote
1 answer
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How to correctly get the amplitude and phase of the signal after applying the fast fourier transform to it

I am new at signal processing and was trying to understand the relation of the result of the FFT to the original signal. I generated a signal with a sampling rate of 100 Hz within 1 second ($N=100$), ...
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2 votes
1 answer
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Need help with DTFT problem

Prepping for exam and this is one of the practice problems: I just want some clarification on some of the steps my professor took. This is the answer in the answer sheet Only thing I dont understand ...
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Phase Unwrapping Issue of IQ data sample in Radar Signal Processing

I am doing radar Sensor signal processing. The radar sensor gives iq data corresponding to the range(sweeps) I want to detect micro motion so that phas analysis is used. Sweep is the distance ...
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1 answer
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Fourier transform why can I convert one of the axes into an imaginary number?

Contextualizing This question is inspired by the following video: https://www.youtube.com/watch?v=-qgreAUpPwM&t=60s&ab_channel=3Blue1Brown I own a sign, a drawing of a square with 200 points ...
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2 answers
39 views

Periodicity of a discrete time complex exponential signal?

I'm new to DSP and I'm struggling to solve a basic problem. I think I've solved it but I feel that something's off in my reasoning. The problem involves investigating a signal of the form $e^{jk\pi n}$...
1 vote
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When is perfect analytic filtering (discrete) suboptimal?

Defined as "negative DFT bins zero", when are such filters suboptimal for AM/FM extraction or related filtering? This answer reads, [nulling] also has the worst performance compared to ...
5 votes
2 answers
479 views

Odd artifacts after sinc interpolation

I am trying to upsample a signal using sinc interpolation. I have written a way to do this in python. ...
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Why is Envelope noisy even after filtering and achievement of SNR gain (-6dB SNR to 14dB snr)?

A noisy signal with 500 MHz bandwidth, with negative SNR, when filtered to 6 MHz bandwidth, should attain a theoretical SNR gain of 20 dB. So if the original signal has -6 dB SNR, after filtering we ...
2 votes
1 answer
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Different PI controller implementations and their respective discrete transfer functions

So I need to implement a PI-controller and I found an Implementation of an PID-controller with some background explanation. I adapted the implementation to an PI-controller, implemented it and got the ...
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1 vote
2 answers
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Why use sinc function to downsample an image in fourier domain?

I'm very confused about downsampling in image processing and the use of sinc function to do it. I read this post [1]: 2D Fourier downsampling some time ago that talked about my own doubt, that is to ...
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I just computed an DFT and FFT of a sinc function, but when I visualise them the results are strangely different? what am I missing

The idea here is to improve a Sinc function by manipulating its Fourier transform. As you can see, the tophat has ripples in the bands of interest and I want to eliminate them by smoothing them with a ...
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GNU Radio Volk phase rotation function does not work properly

I am implementing a CFO recovery algorithm in GNU Radio. The CFO is set in the GNU Radio and the correction section in the C++ OOT module is given below, which works fine :) ...
1 vote
1 answer
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Sampling Precision, Jitter, and PID

I am having difficulty understanding the effect of quantization noise and ADC resolution in a digital PID controller. I am also trying to understand the effects of sampling jitter on a PID controller. ...
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1 answer
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Compact books for reviewing signal processing

I am about to start a new engineering job in the fields of signal processing and machine learning. I have a bachelor's degree in electrical engineering, but for the last two years I have been doing a ...
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1 answer
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Understand carrier power, output power and dBC?

I have a question regarding the concept of carrier power, output power and power relative to carrier (dBc). Suppose I have a carrier frequency of 4Hz and signal bandwidth = 4 Hz. The signal span is ...
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1 answer
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perform fourier-type integration using DFT misunderstanding

I need to perform the following integral ($i^2 = -1$) (with a fixed value of $m$): $ \int_{\phi=0}^{\phi=2\pi} \psi(\phi) e^{-im \phi} \hspace{0.7mm} d\phi $ for all values of $m$ in $\{-N_{\theta}, -...
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1 answer
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Using cross-correlation of spatially shifted data to gain geometric information

Cross-correlation is usually used to estimate e.g. lags between signals that are detected by different sensors at different times. In my case, the situation is slightly different in that I measure ...
3 votes
3 answers
110 views

Effect of overlapping percentage on STFT output

I know STFT is generally applied to non-stationary signals but I tried to apply it to a stationary signal to get a working knowledge. I created a stationary signal composed of three frequencies as ...
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0 answers
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Feedforward equalizer MMSE vs ZF: I get ZF performs better than MMSE, why is that?

So I am doing some experiments on comparing MMSE and ZF performance. Here is the description of my problem setup: Consider a pulse response $p_{tilde}$ which is equal to: [7.41283693728174e-06 -6....
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1 answer
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Real time processing in matlab

I have to extract a particular frequency range from an audio signal. For that I am using an FIR filter of order 50 and it is written in MATLAB as below: ...
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1 vote
1 answer
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Doubt on Signal Processing Step

I am using a Radar Sensor. So applying Signal Processing on the Radar Sensor Data. PrevSample and PastSample are Radar IQ samples for a present and previous Sweep detecting tiny movement. In the ...
2 votes
1 answer
138 views

How to implement the recursive FIR filtering of a signal with zero boundary condition?

Now I have a signal $f(k)$ with $k=0,1,\ldots, N-1$, and $f(k)=0$ if $k<0$ or $k>N-1$, that is, the signal satisfies the zero boundary condition. Then by convolving this signal with a symmetric ...
1 vote
1 answer
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Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)

Consider the following discrete-time system: \begin{equation} \mathbf{x}(k+1) = \mathbf{A}_d \mathbf{x}(k) + \mathbf{B}_d \mathbf{u}(k) \end{equation} \begin{equation} y(k) = \mathbf{C}_d \mathbf{x}(k)...
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How to calculate Cepstral Peak Prominence (Smoothed) for speech signal - when to take logs

I understand the main steps of finding smoothed cepstral peak prominence, but am confused on some specifics: You first take the log of the Fourier transform of the signal, getting the spectrum. I'm ...
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2 votes
1 answer
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N'-band channelizer (filter bank) via Sliding FFT

I'm trying to figure out how to perform N'-band channelizer for SSCA (strip spectral correlation analyzer) via sliding FFT. I understand that I have to take $N$ points of signal in time domain $x(t)$, ...
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1 answer
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Having Nyquist bin = aliasing?

Here I motivate the question by deriving FFT upsampling for $N \rightarrow 2N$ with even $N$. One might naively try xup = 2*ifft([xf[:N//2], zeros(N), xf[-N//2:]]), ...
1 vote
1 answer
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Time fusion Kalman filter

Suppose I have a set of estimators, $$\{S^1, S^2, S^3, S^4,\ldots,S^n\}$$ that output at each timestep $t$ a measurement representing an estimate of the true signal $y$, however the output of each ...
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Understanding FFT bins interpretability

I am familiar with the continuous Fourier transform yet the more I try to understand FFT, the more I'm confused. If we've got a discrete N sample signal, FFT is a faster way to calculate DFT. If ...
1 vote
1 answer
42 views

FFT Artifacts and their cause beyond frequency resolution

I am trying to work through an issue with an FFT for audio : I have no spectral leakage while playing back audio, but the moment I change or zero out a value in any of the FFT bins, artifacts are ...
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Stability analysis of hybrid discrete-continuous systems

I'm trying to derive the overall state-space system model for a hybrid system, in order to plot its eigenvalues. The system is shown as follows: Which is originally from this paper: Modeling and ...
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0 answers
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How do I convert the Amplitude from Power/Amplitude spectral density?

I recently started working on PSD of seismic signals. PSD signal can be expressed in 2 ways. One in ($PSD=g^2/Hz$) and other in $PSD=((meter/sec.^2)^2/Hz)$ and $ASD = \sqrt(PSD)$. More details have ...
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3 votes
1 answer
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Can we recover $|X(k)|$, given $|x(n)|$?

Given a complex vector $x[n]$, we can find the magnitudes of the spectrum by computing: $X_m[k] = |X[k]| = |FFT[x]|$ This involves performing a complex FFT and computing the absolute value of the ...
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1 answer
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How can I express the flipped output of multiplication in function of original inputs?

I have the vector $y = Dx$ where $D$ is a complex matrix with dimension $N \times N$, and $x$ is a complex vector of dimension $N \times 1$. If the vector $y_2 = [y'_N, y'_{N-1}, y'_{N-2},.... , y'_{...
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1 vote
1 answer
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Basis Pursuit Denoising (BPDN) algorithm for Direction of Arrival Estimation

I am working on Compressive sensing algorithms for DOA estimation. Can i get any references for writing BPDN code in MATLAB.
6 votes
3 answers
140 views

What are the criteria for a change-of-basis transform to be doable in $O(n \log(n))$?

The Fourier basis is a common choice for transformations, but a lot of times, it's not the best for a specific application. For instance, wavelet bases give us better spatial / temporal locality than ...
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Scilab - possible to get transfer function, H[z], with negative powers of z?

I use Scilab. Is is possible using Scilab primatives like poly(), horner(), etc., to generate and display a discrete time transfer function with only negative powers of z? I have tried a number of ...
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1 answer
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What is the best way to decide whether a periodic signal is present in a noisy environment with a limited number of samples?

Suppose I have few samples (e.g. 20) of a decaying sinusoidal function and I am heavily noise-dominated (SNR ~1, noise is Gaussian or Poissonian). Let's think of e.g. \begin{equation} y(t) = A \, \sin(...
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2 votes
1 answer
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A problem on FIR filter design given a difference equation

Given the following difference equation: \begin{equation} y(n)=2x(n-2)+3x(n-5) \end{equation} describing the structure of an FIR filter, design the direct form of one. What is the order of the filter? ...
3 votes
2 answers
193 views

Constructing an input signal whose response is determined by the impulse response

I'm self-studying Signals and Systems by Alan Oppenheim, and I have some trouble understanding the solution to a homework problem. P5.13 tries to find the sufficient and necessary condition on the ...
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2 votes
1 answer
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Problem with the existence of inverse DTFT

I am having trouble on the following exercise and I can't figure out where I am doing something wrong: Given an LTI system described by the following difference equation: $$y(n)=x(n)+2x(n-2)+y(n-1)$$ ...
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How to calculate roll and pitch from an accelerometer in whatever orientation?

I’m trying to use a tri-axial accelerometer as an inclinometer, measuring the so called roll and pitch angles. The underlined principle is that in stationary conditions an accelerometer senses only ...
1 vote
1 answer
106 views

Axes of Discrete Fourier Transform

Problem Given $X[k] = \sum_{n=0}^{N-1} x[n]e^{-j2\pi kn/N}, k = 0, ..., N-1$ What are the units on the x-axis and y-axis? Note that for the x-axis there are two answers. Attempted solution My first ...
1 vote
1 answer
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A problem on $\mathcal{Z}-$transforms and signal stability

I am doing the following problem for my DSP exam and I am doubting my answers while being stuck on the last part: Given a causal LTI system and difference equations $y(n)=x(n)+20y(n-1)-100y(n-2),$ ...
1 vote
1 answer
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If $y(n)-y(n-1)=bx(n)$ is an LTI system, find $b$ such that $\left|H(e^{i\omega})\right|=1$ for $\omega=0$

I am stuck on the following problem and would like your help: Given an LTI system described by the difference equation: $$y(n)-\frac{y(n-1)}{10}=bx(n),$$ find $b$ such that $\left|H(e^{i\omega})\...
0 votes
2 answers
37 views

Easy (?) DTFT calculation

I'm asked to compute the DTFT of the following signal but i'm quite stuck $$ \begin{cases} (-1)^{\frac{n}{2} + 1} & \text{ if } n \text{ is even} \\ 0 & \text{ if } n \text{ is odd} \end{...
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Get shape of a recurring pulse event in my plant video signal

I'm studying plants - specifically how the color of their leaves change throughout a day. I have a camera pointing at a leaf which takes a picture every 47 minutes and calculates the average green ...

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