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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Equivalence of Maximum Likelihood (ML) and Discrete Fourier Transfrom (DFT) Peak Finding for Single Tone Estimation

My understanding is Maximum Likelihood and DFT Peak Finding for a single tone produce the same results assuming the ML is restricted to the same frequencies as the DFT. I was wondering if there was ...
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Algorithms for detecting the difference between two signals

If I have two signals $X$ and $Y$, where $X$ is a clean signal and $Y$ is the same signal with linear white Gaussian noise and an amplitudes of $10^{-4}$. How could one use an algorithm to detect if ...
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Nyquist sampling

I know that if $f_\mathrm{m}$ is the "Nyquist frequency" (max frequency) and $f_\mathrm{s}$ sampling rate then $f_\mathrm{s}>2f_\mathrm{m}$. Am I correct so far? I have a signal $x(t)$ with max ...
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Proof that first difference filter amplifies noise

I'm a bit befuddled by noise's effect on derivative filters. I've always 'known' that straightforward first difference derivative filters of discrete signals amplifies noise, but I'm struggling to ...
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Band Edge Filters

I am interested in using Band Edge Filters to do carrier frequency recovery but this is kind of secondary to my question which is: How do you build an FIR filter which isn't symmetric about the ...
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Difference between autocorrelations

M. H. Hayes calls in his book "Statistical digital signal processing" autocorrelation sequences $r[k]$. For optimal filters the desired autocorrelation has the index d -> $r_d[k]$. However, often ...
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When numerically simulating a system, usually some kind of discretization is necessary, obtained by some kind of z-transform, such as, for instance, the bilinear transform $s\mapsto \frac{2}{\triangle ... 2answers 66 views Correlation between 2 signals of uneven dimensions As a part of my work, I am trying to correlate the audio signal in a video with the pixels of each frame. The steps I follow are: Audio sampling rate and frame rate of the video are known. So, ... 0answers 47 views Why is my resampled signal cutoff when resampling with a windowed FIR filter in MATLAB? I have an exercise to write a function which upsamples or downsamples a signal by a factor of F (integer) using a FIR filter windowed with a Kaiser window function. Exercise I had last week included ... 0answers 33 views Why are patterns repeated in the frequency-power graph of a periodic signal? The original question was posted here. I have a signal, which I'd like to treat as a non-continuous function now, let it be$signal(t)$. It looks like this: Zoomed in a bit: I create a Lomb-Scargle ... 1answer 92 views Active Noise cancellation for non periodic signals I observed that the coded algorithm for active noise cancellation is not able to cancel some of the signals like a human voice. Is there any solution for this? Can we really cancel non-periodic ... 1answer 78 views periodicity of constant discrete time signals are constant discrete time signals periodic? example \begin{equation} e^{i10\pi n} \end{equation} my proffesor says that this signal is aperiodic, in the discrete sense. but it seems wrong, because ... 1answer 42 views Error due to downsampling an image I have two images$I_1$and$I_2$suppose$I_2 = downscale(I_1)$, so for example if$I_1$has resolution 1024x1024$I_2$could be 512x512. How can I measure how much quality I've lost during this ... 0answers 11 views 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.... 1answer 148 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. 2answers 119 views how is this method of proving shift invariance correct I got this answer from here. But i don't know how this method is correct. Until now to prove shift invariance what i did was : step 1: delay output and write it in terms of input. step 2: delay input ... 1answer 117 views Can Temperature data be predicted using adaptive filter using LMS algorithm? I am working on a project which requires me to implement adaptive filter as a predictor. I have just started on adaptive filter and I intend to use least mean square algorithm for weight adjustment. ... 1answer 53 views What's wrong with this Whittaker-Shannon-Kotel’nikov interpolation implementation? I tried to implement Whittaker-Shannon-Kotel’nikov interpolation formula but I get unexpected results: the reconstructed signal lags with respect to the original. I know that I can not expect a ... 2answers 98 views Signals - question due to sampling I don't have an idea how to start it. Help pls :) $$m = z(t) + \frac{\operatorname{Sa}(t-T)}{4}$$ We have some signal$z(t)=\left(\operatorname{Sa}(\frac{t}{T})\right)^2$. How often the m signal ... 3answers 829 views Measure Sine Wave Amplitude from ADC Signal Question I'm trying to do some DSP that I have never done before and a nudge into the right direction would come in handy. The context is replication of this project. The system architecture is the ... 1answer 60 views Sampling - Higher order harmonics I have been studying about the sampling theorem and it seems that even though we sample at a frequency with the nyquist criterion, the harmonics (due to sampling process) remain within the nyquist ... 1answer 409 views Difference between the DTFT and DFT [duplicate] I know this question has been asked before. It is, however, so confusing, that I'd like to give this another try: I have come across the following 2 definitions of the DTFT: So, the first line is the ... 0answers 51 views How to make function in time domain after fft fit with the corresponding function in frequency domain? For example, I want to use fft to transform the simple function exp(-x.^2) defined in time domain. And the corresponding funciton in frequency domain is sqrt(pi).*exp(-k.^2/4). And I use the upper ... 0answers 21 views How does discrete spectral moment relate to continuous spectral moment? It is said in discrete/digital signal processing that$r$th spectral moment of signal$x[n]$is defined as: $$\sum_{n=-\infty}^{\infty}n^r x[n]$$ But how does this relate to usual continuous$r$th ... 0answers 168 views Use 2D FFT to replace 2D Discrete Fourier Transform (MATLAB) I met a problem. I ran a code to implement the 2D discrete Fourier Transform, here is the code: ... 1answer 71 views integral filter Assume we have a time domain signal: s(i), i=1:N. To apply a derivative filter to it, i.e. D*s, where ... 0answers 30 views Adaptive frequency discovery of binary signal First of all, I'm not a signal processing expert. Actually, I'm trying to benefit from some concepts of signal processing theory in my computer science research. My problem is that, I have to find ... 1answer 84 views 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. ... 2answers 251 views Higher order harmonics during sampling I am studying about the sampling theorem in conjunction for ADC. I got little confused while reading about aliased frequencies. I see that as per the Nyquist theorem, the sampling frequency (fs) ... 0answers 38 views Convolution with rectangular function I have a system$h(t)=4e^{-4(t-4)}u(t-4)$and I want to response of the system to$x(t)=rect(2(t+4))$. I have followed those steps:$y(t)=x(t){*}h(t)=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)=4[u(t)-...
I want to retrieve (within a FPGA) the time constant $\tau$ of incoming pulses of the form $$x[n]=Ae^{-n/\tau}u[n]+C$$ In addition to the offset, inputs are subject to noise. To measure the integral ...